diff --git a/_pkgdown.yml b/_pkgdown.yml index b3d87ac6..917c4bed 100644 --- a/_pkgdown.yml +++ b/_pkgdown.yml @@ -1,3 +1,4 @@ template: bootstrap: 5 + math-rendering: mathjax url: https://r-spatial.github.io/spdep/ diff --git a/docs/404.html b/docs/404.html index 96522508..000621a6 100644 --- a/docs/404.html +++ b/docs/404.html @@ -10,7 +10,7 @@ - + Skip to contents @@ -20,7 +20,7 @@ spdep - 1.3-13 + 1.4-1 @@ -71,7 +71,7 @@

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-

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/articles/CO69.html b/docs/articles/CO69.html index e943a6dc..71cd653c 100644 --- a/docs/articles/CO69.html +++ b/docs/articles/CO69.html @@ -10,7 +10,7 @@ - + Skip to contents @@ -20,7 +20,7 @@ spdep - 1.3-13 + 1.4-1 @@ -171,16 +171,14 @@

Introductionprint(sapply(as(eire_ge1, "data.frame")[c(13,16,18,19)], function(x) kurtosis(log(x))), digits=4) 
## pagval2_10  cowspacre  pigspacre sheeppacre 
 ##      2.883      2.799      2.212      2.421
-

Using the tabulated value of -23.623.6 -for the percentage of agricultural holdings above 50 in 1950 in -Waterford, the skewness and kurtosis cannot be reproduced, but by -comparison with the irishdata dataset in , it -turns out that the value should rather be -26.626.6, -which yields the tabulated skewness and kurtosis values.

+

Using the tabulated value of \(23.6\) for the percentage of agricultural +holdings above 50 in 1950 in Waterford, the skewness and kurtosis cannot +be reproduced, but by comparison with the +irishdata dataset in , it turns out that the +value should rather be \(26.6\), which +yields the tabulated skewness and kurtosis values.

Before going on, the variables considered are presented in Table -varsvars.

+\[vars\].

@@ -299,13 +297,8 @@

Spatial weights## n nn S0 S1 S2 ## B 25 625 0.8476 0.01871808 0.1229232

Note that the values of S0, S1, and S2 correspond closely with those -given on page 42 of the paper, -0.846886720.84688672, -0.018699860.01869986 -and -0.122673190.12267319. -The discrepancies appear to be due to rounding in the printed table of -weights.

+given on page 42 of the paper, \(0.84688672\), \(0.01869986\) and \(0.12267319\). The discrepancies appear to +be due to rounding in the printed table of weights.

The contiguous neighbours represented in this object ought to match those found using poly2nb. However, we see that the reproduced contiguities have a smaller link count:

@@ -319,8 +312,7 @@

Spatial weights## Average number of links: 4.32

The missing link is between Clare and Kerry, perhaps by the Tarbert–Killimer ferry, but the counties are not contiguous, as Figure -plot_nbplot\_nb -shows:

+\[plot\_nb\] shows:

 xx <- diffnb(nb, lw_unstand$neighbours, legacy=TRUE, verbose=TRUE)
## Neighbour difference for region id: Clare in relation to id: Kerry 
@@ -337,37 +329,34 @@ 
Spatial weightsAn attempt has also been made to reproduce the generalised weights
 for 25 Irish counties reported by Cliff and Ord
 (1969), after Dublin is omitted. Reproducing the inverse distance
-component
-dij−1d_{ij}^{-1}
-of the generalised weights
-dij−1βi(j)d_{ij}^{-1} \beta_{i(j)}
-is eased by the statement in Cliff and Ord (1973,
-55) that the points chosen to represent the counties were their
-“geographic centres,” so not very different from the centroids yielded
-by applying a chosen computational geometry function. The distance
-metric is not given, and may have been in kilometers or miles — both
-were tried, but the results were not sensitive to the difference as it
-applies equally across the weights; miles are used here. Computing the
-proportion of shared distance measure
-βi(j)\beta_{i(j)}
-is harder, because it requires the availability of the full topology of
-the input polygons. Roger S. Bivand, Pebesma, and
-Gómez-Rubio (2008, 244) show how to employ the
-vect2neigh function (written by Markus
-Neteler) in the package when using GRASS GIS vector handling to create a
-full topology from spaghetti vector data and to extract border segment
-lengths; a similar approach also is mentioned there using ArcGIS
-coverages for the same purpose. GRASS was used to create the topology,
-and next the proportion of shared distance measure was calculated.

+component \(d_{ij}^{-1}\) of the
+generalised weights \(d_{ij}^{-1}
+\beta_{i(j)}\) is eased by the statement in Cliff and Ord (1973, 55) that the points chosen
+to represent the counties were their “geographic centres,” so not very
+different from the centroids yielded by applying a chosen computational
+geometry function. The distance metric is not given, and may have been
+in kilometers or miles — both were tried, but the results were not
+sensitive to the difference as it applies equally across the weights;
+miles are used here. Computing the proportion of shared distance measure
+\(\beta_{i(j)}\) is harder, because it
+requires the availability of the full topology of the input polygons.
+Roger S. Bivand, Pebesma, and Gómez-Rubio (2008,
+244) show how to employ the vect2neigh
+function (written by Markus Neteler) in the package when using GRASS GIS
+vector handling to create a full topology from spaghetti vector data and
+to extract border segment lengths; a similar approach also is mentioned
+there using ArcGIS coverages for the same purpose. GRASS was used to
+create the topology, and next the proportion of shared distance measure
+was calculated.

 
 library(terra)
 v_eire_ge1 <-vect(eire_ge1)
 SG <- rasterize(v_eire_ge1, rast(nrows=70, ncols=50, extent=ext(v_eire_ge1)), field="county")
 library(rgrass)
 grass_home <- "/home/rsb/topics/grass/g820/grass82"
-initGRASS(grass_home, home=tempdir(), SG=SG, override=TRUE)
-write_VECT(v_eire_ge1, "eire", flags=c("o", "overwrite"))
-res <- vect2neigh("eire", ID="serlet")

+initGRASS(grass_home, home=tempdir(), SG=SG, override=TRUE)
+write_VECT(v_eire_ge1, "eire", flags=c("o", "overwrite"))
+res <- vect2neigh("eire", ID="serlet")
 res$length <- res$length*1000
 attr(res, "external") <- attr(res, "external")*1000
@@ -514,20 +503,19 @@ 
Measures of spatial autocorrelation
 ##    n  nn S0       S1       S2
 ## W 25 625 25 15.84089 103.6197

The standard representation of the measures is:

-

I=n∑i=1n∑j=1nwij∑i=1n∑j=1nwij(xi−x‾)(xj−x‾)∑i=1n(xi−x‾)2I = \frac{n}{\sum_{i=1}^{n}\sum_{j=1}^{n}w_{ij}} -\frac{\sum_{i=1}^{n}\sum_{j=1}^{n}w_{ij}(x_i-\bar{x})(x_j-\bar{x})}{\sum_{i=1}^{n}(x_i - \bar{x})^2}

-

for Moran’s -II -— in the paper termed the proposed statistic, and for Geary’s -CC:

-

C=(n−1)2∑i=1n∑j=1nwij∑i=1n∑j=1nwij(xi−xj)2∑i=1n(xi−x‾)2C = \frac{(n-1)}{2\sum_{i=1}^{n}\sum_{j=1}^{n}w_{ij}} -\frac{\sum_{i=1}^{n}\sum_{j=1}^{n}w_{ij}(x_i-x_j)^2}{\sum_{i=1}^{n}(x_i - \bar{x})^2}

-

where -xi,i=1,…,nx_i, i=1, \ldots, n -are -nn -observations on the numeric variable of interest, and -wijw_{ij} +

\[I = +\frac{n}{\sum_{i=1}^{n}\sum_{j=1}^{n}w_{ij}} +\frac{\sum_{i=1}^{n}\sum_{j=1}^{n}w_{ij}(x_i-\bar{x})(x_j-\bar{x})}{\sum_{i=1}^{n}(x_i +- \bar{x})^2}\]

+

for Moran’s \(I\) — in the paper +termed the proposed statistic, and for Geary’s \(C\):

+

\[C = +\frac{(n-1)}{2\sum_{i=1}^{n}\sum_{j=1}^{n}w_{ij}} +\frac{\sum_{i=1}^{n}\sum_{j=1}^{n}w_{ij}(x_i-x_j)^2}{\sum_{i=1}^{n}(x_i +- \bar{x})^2}\]

+

where \(x_i, i=1, \ldots, n\) are +\(n\) observations on the numeric +variable of interest, and \(w_{ij}\) are the spatial weights. In order to reproduce the standard deviates given in the paper, it is sufficient to apply moran.test to the variables with three @@ -548,7 +536,7 @@

Measures of spatial autocorrelation Prop_stdR <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=lw_std, randomisation=TRUE)) })

##    user  system elapsed 
-##   0.135   0.000   0.137
+## 0.03 0.00 0.11 
 res <- sapply(c("MoranN", "MoranR", "GearyN", "GearyR", "Prop_unstdN", "Prop_unstdR", "Prop_stdN", "Prop_stdR"), function(x) sapply(get(x), "[[", "statistic"))
 rownames(res) <- vars
@@ -626,17 +614,14 @@ 
Measures of spatial autocorrelation
 ## retailpcap    0.3734  0.1202  0.5267 0.1413  0.3959  0.1515  0.4066 0.1498 
 ## psinglem30_34 0.2828  0.1207  0.6465 0.1385  0.3697  0.1520  0.3583 0.1503

The values are as follows, and match the original with the exception -of those for the initial version of Moran’s -II -in the first two columns. If we write a function implementing equations -3 and 4:

-

I=∑i=1n∑j=i+1nwij(xi−x‾)(xj−x‾)∑i=1n(xi−x‾)2I = \frac{\sum_{i=1}^{n}\sum_{j=i+1}^{n}w_{ij}(x_i-\bar{x})(x_j-\bar{x})}{\sum_{i=1}^{n}(x_i - \bar{x})^2}

-

where crucially the inner summation is over -i+1…ni+1 \ldots n, -not -1…n1 \ldots -n, we can reproduce the values of the -measure shown in the original Table 5:

+of those for the initial version of Moran’s \(I\) in the first two columns. If we write a +function implementing equations 3 and 4:

+

\[I = +\frac{\sum_{i=1}^{n}\sum_{j=i+1}^{n}w_{ij}(x_i-\bar{x})(x_j-\bar{x})}{\sum_{i=1}^{n}(x_i +- \bar{x})^2}\]

+

where crucially the inner summation is over \(i+1 \ldots n\), not \(1 \ldots +n\), we can reproduce the values of the measure shown in the +original Table 5:

 oMoranf <- function(x, nb) {
   z <- scale(x, scale=FALSE)
@@ -703,9 +688,8 @@ 
Simulating measures of s
 nsim <- 4999
 set.seed(1234)

First let us define a function MoranI.boot -just to return the value of Moran’s -II -for variable var and permutation index +just to return the value of Moran’s \(I\) for variable +var and permutation index i, and a function Nsim to generate random samples from the variable of interest assuming Normality. To make it easier to process @@ -733,12 +717,11 @@

Simulating measures of s deviates under Normality and randomisation, and see that in fact the differences are not at all large, as expressed by the median absolute difference between the tables. We can also see that inferences based on -a one-sided -α=0.05\alpha=0.05 -cut-off are the same for the analytical and bootstrap approaches. This -indicates that we can, in general, rely on the analytical standard -deviates, and that bootstrap methods will not help if assumptions -underlying the measures are not met.

+a one-sided \(\alpha=0.05\) cut-off are +the same for the analytical and bootstrap approaches. This indicates +that we can, in general, rely on the analytical standard deviates, and +that bootstrap methods will not help if assumptions underlying the +measures are not met.

 print(formatC(res, format="f", digits=4), quote=FALSE)
##    pagval2_10 ln_pagval2_10   pagval10_50     pagval50p     cowspacre  ln_cowspacre 
@@ -761,17 +744,12 @@ 
Simulating measures of s
 find an equivalent to the analytical or bootstrap-based standard deviate
 for inference (Tiefelsdorf 2002). The
 Saddlepoint approximation requires the eigenvalues of the weights matrix
-and iterative root-finding for global Moran’s
-II,
-while for local Moran’s
-IiI_i,
-analytical forms are known. Even with this computational burden, the
-Saddlepoint approximation for global Moran’s
-II
-runs quite quickly. First we need to fit null linear models (only
-including an intercept) to the variables, then apply
-lm.morantest.sad to the fitted model
-objects:

+and iterative root-finding for global Moran’s \(I\), while for local Moran’s \(I_i\), analytical forms are known. Even
+with this computational burden, the Saddlepoint approximation for global
+Moran’s \(I\) runs quite quickly. First
+we need to fit null linear models (only including an intercept) to the
+variables, then apply lm.morantest.sad to the
+fitted model objects:

 
 lm_objs <- lapply(vars, function(x) lm(formula(paste(x, "~1")), data=eire_ge1))
 system.time({
@@ -780,7 +758,7 @@ 
Simulating measures of s
 Prop_stdSad  <- lapply(lm_objs, function(x) lm.morantest.sad(x, listw=lw_std))
 })

 
##    user  system elapsed 
-##   0.090   0.000   0.091

+##    0.05    0.02    0.08
 res <- sapply(c("MoranSad", "Prop_unstdSad", "Prop_stdSad"), function(x) sapply(get(x), "[[", "statistic"))
 rownames(res) <- vars
@@ -788,19 +766,11 @@

Simulating measures of s larger than those reached using the Saddlepoint approximation when measured by median absolute deviation, the differences do not lead to different inferences at this chosen cut-off. This reflects the fact that -the shape of the distribution is very sensitive to small -nn, -but for moderate -nn -and global Moran’s -II, -the effects are seen only further out in the tails. The consequences for -local Moran’s -IiI_i -are much stronger, because the clique of neighbours of each observation -is typically very small. It is perhaps of interest that the differences -are much smaller for the case of general weights than for unstandardised -binary weights.

+the shape of the distribution is very sensitive to small \(n\), but for moderate \(n\) and global Moran’s \(I\), the effects are seen only further out +in the tails. The consequences for local Moran’s \(I_i\) are much stronger, because the clique +of neighbours of each observation is typically very small. It is perhaps +of interest that the differences are much smaller for the case of +general weights than for unstandardised binary weights.

 print(formatC(res, format="f", digits=4), quote=FALSE)
##               MoranSad Prop_unstdSad Prop_stdSad
@@ -829,13 +799,11 @@ 
Simulating measures of s
 all((res >= alpha_0.05) == (ores[,c(1,3,5)] >= alpha_0.05))

## [1] TRUE

In addition we could choose to use the exact distribution of Moran’s -II, -as described by Tiefelsdorf (2000); its -implementation is covered in R. S. Bivand, -Müller, and Reder (2009). The global case also needs the -eigenvalues of the weights matrix, and the solution of a numerical -integration function, but for these cases, the timings are quite -acceptable.

+\(I\), as described by Tiefelsdorf (2000); its implementation is +covered in R. S. Bivand, Müller, and Reder +(2009). The global case also needs the eigenvalues of the weights +matrix, and the solution of a numerical integration function, but for +these cases, the timings are quite acceptable.

 system.time({ 
 MoranEx <- lapply(lm_objs, function(x) lm.morantest.exact(x, listw=nb_B))
@@ -843,7 +811,7 @@ 
Simulating measures of s
 Prop_stdEx  <- lapply(lm_objs, function(x) lm.morantest.exact(x, listw=lw_std))
 })
##    user  system elapsed 
-##   0.105   0.000   0.104
+## 0.05 0.01 0.15 
 res <- sapply(c("MoranEx", "Prop_unstdEx", "Prop_stdEx"), function(x) sapply(get(x), "[[", "statistic"))
 rownames(res) <- vars
@@ -881,11 +849,9 @@

Simulating measures of s the challenge in Cliff and Ord (1969, 31), to try to give the statistic a bounded fixed range. Their APLE measure is intended to approximate the spatial dependence parameter of a -simultaneous autoregressive model better than Moran’s -II, -and re-scales the measure by a function of the eigenvalues of the -spatial weights matrix. APLE requires the use of row standardised -weights.

+simultaneous autoregressive model better than Moran’s \(I\), and re-scales the measure by a +function of the eigenvalues of the spatial weights matrix. APLE requires +the use of row standardised weights.

 vars_scaled <- lapply(vars, function(x) scale(eire_ge1[[x]], scale=FALSE))
 nb_W <- nb2listw(lw_unstand$neighbours, style="W")
@@ -909,39 +875,18 @@ 
Simulating measures of s
 to general does make a difference.

 
 print(formatC(res, format="f", digits=4), quote=FALSE)

-
##               APLE W APLE Gstd
-## pagval2_10    0.7702 0.6628   
-## ln_pagval2_10 0.7615 0.6655   
-## pagval10_50   0.3954 0.3446   
-## pagval50p     0.7519 0.7313   
-## cowspacre     0.8329 0.7408   
-## ln_cowspacre  0.8148 0.7487   
-## ocattlepacre  0.1468 0.4092   
-## pigspacre     0.6227 0.6205   
-## ln_pigspacre  0.5582 0.5887   
-## sheeppacre    0.1594 0.2841   
-## ln_sheeppacre 0.2046 0.4550   
-## townvillp     0.3442 0.2644   
-## carspcap      0.7140 0.6166   
-## radiopcap     0.0083 0.1376   
-## retailpcap    0.6376 0.5307   
-## psinglem30_34 0.4094 0.4889
-

Odds and ends -…\ldots +

Odds and ends \(\ldots\)

The differences found in the case of a few variables in inference using the original binary weights, and the general weights proposed by Cliff and Ord (1969) are necessarily -related to the the weights thenselves. Figures -plot_wtsplot\_wts -and -plot_mapplot\_map -show the values of the weights in sparse matrix form, and the sums of -weights by county where these sums are not identical by design. In the -case of binary weights, the matrix entries are equal, but the sums -up-weight counties with many neighbours.

+related to the the weights thenselves. Figures \[plot\_wts\] and \[plot\_map\] show the values of the weights +in sparse matrix form, and the sums of weights by county where these +sums are not identical by design. In the case of binary weights, the +matrix entries are equal, but the sums up-weight counties with many +neighbours.

General weights up-weight counties that are close to each other, have more neighbours, and share larger boundary proportions (an asymmetric relationship). There is a further impact of using boundary proportions, @@ -950,12 +895,11 @@

Odds and ends even if there are few of them. Standardised general weights up-weight further up-weight counties with few neighbours, chiefly those on the edges of the study area.

-

With a small data set, here with -n=25n=25, -it is very possible that edge and other configuration effects are -relatively strong, and may impact inference in different ways. The issue -of egde effects has not really been satisfactorily resolved, and should -be kept in mind in analyses of data sets of this size and shape.

+

With a small data set, here with \(n=25\), it is very possible that edge and +other configuration effects are relatively strong, and may impact +inference in different ways. The issue of egde effects has not really +been satisfactorily resolved, and should be kept in mind in analyses of +data sets of this size and shape.

References @@ -963,9 +907,8 @@

References
Bivand, R. S., W. Müller, and M. Reder. 2009. “Power Calculations -for Global and Local Moran’s -II.” -Computational Statistics and Data Analysis 53: 2859–72. +for Global and Local Moran’s \(I\).” Computational +Statistics and Data Analysis 53: 2859–72.
Bivand, Roger S., Edzer J. Pebesma, and Virgilio Gómez-Rubio. 2008. @@ -1002,16 +945,13 @@

References Tiefelsdorf, M. 2000. Modelling Spatial Processes: The Identification and Analysis of Spatial Relationships in Regression -Residuals by Means of Moran’s -II. -Berlin: Springer. +Residuals by Means of Moran’s \(I\). Berlin: Springer.

———. 2002. “The Saddlepoint Approximation of Moran’s -I and Local Moran’s -Ii{I}_i -Reference Distributions and Their Numerical Evaluation.” -Geographical Analysis 34: 187–206. +I and Local Moran’s \({I}_i\) Reference Distributions and Their +Numerical Evaluation.” Geographical Analysis 34: +187–206.

@@ -1027,7 +967,7 @@

References -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/articles/CO69_files/figure-html/unnamed-chunk-15-1.png b/docs/articles/CO69_files/figure-html/unnamed-chunk-15-1.png index 89094276..299ed25e 100644 Binary files a/docs/articles/CO69_files/figure-html/unnamed-chunk-15-1.png and b/docs/articles/CO69_files/figure-html/unnamed-chunk-15-1.png differ diff --git a/docs/articles/index.html b/docs/articles/index.html index 138ca6ad..d6e5f35a 100644 --- a/docs/articles/index.html +++ b/docs/articles/index.html @@ -1,5 +1,5 @@ -Articles • spdep +Articles • spdep Skip to contents @@ -7,7 +7,7 @@ spdep - 1.3-13 + 1.4-1 @@ -44,11 +44,11 @@

All vignettes

“The Problem of Spatial Autocorrelation:” forty years on
-
-
Creating Neighbours using sf objects
Creating Neighbours
+
Creating Neighbours using sf objects
+
Introduction to the North Carolina SIDS data set (re-revised)
No-neighbour observation and subgraph handling
@@ -62,7 +62,7 @@

All vignettes

-

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/articles/nb.html b/docs/articles/nb.html index 368f1454..fbd0c1cd 100644 --- a/docs/articles/nb.html +++ b/docs/articles/nb.html @@ -10,7 +10,7 @@ - + Skip to contents @@ -20,7 +20,7 @@ spdep - 1.3-13 + 1.4-1 @@ -104,9 +104,12 @@

Introduction
 library(spdep)
## Loading required package: spData
+
## To access larger datasets in this package, install the spDataLarge
+## package with: `install.packages('spDataLarge',
+## repos='https://nowosad.github.io/drat/', type='source')`
## Loading required package: sf
-
## Linking to GEOS 3.13.1, GDAL 3.11.0, PROJ 9.6.2; sf_use_s2() is TRUE
-
+
## Linking to GEOS 3.13.0, GDAL 3.10.1, PROJ 9.5.1; sf_use_s2() is TRUE

+
 if (packageVersion("spData") >= "2.3.2") {
     NY8a <- sf::st_read(system.file("shapes/NY8_utm18.gpkg", package="spData"))
 } else {
@@ -115,13 +118,14 @@ 
IntroductionNY8a$Cases <- NY8a$TRACTCAS
 }

 
## Reading layer `NY8_utm18' from data source 
-##   `/home/rsb/lib/r_libs/spData/shapes/NY8_utm18.gpkg' using driver `GPKG'
+##   `C:\Users\rzomor2\AppData\Local\R\win-library\4.4\spData\shapes\NY8_utm18.gpkg' 
+##   using driver `GPKG'
 ## Simple feature collection with 281 features and 17 fields
 ## Geometry type: POLYGON
 ## Dimension:     XY
 ## Bounding box:  xmin: 358241.9 ymin: 4649755 xmax: 480393.1 ymax: 4808545
 ## Projected CRS: WGS 84 / UTM zone 18N

-
+
 NY8 <- as(NY8a, "Spatial")
 NY_nb <- read.gal(system.file("weights/NY_nb.gal", package="spData"), region.id=as.character(as.integer(row.names(NY8))-1L))

 
For the sake of simplicity in showing how to create neighbour
@@ -129,7 +133,7 @@ 
Introduction
+
 Syracuse <- NY8[!is.na(NY8$AREANAME) & NY8$AREANAME == "Syracuse city",]
 Sy0_nb <- subset(NY_nb, !is.na(NY8$AREANAME) & NY8$AREANAME == "Syracuse city")
 summary(Sy0_nb)

@@ -157,12 +161,12 @@ 
Creating Contiguity Neighbours
class(Syracuse)

 
## [1] "SpatialPolygonsDataFrame"
 ## attr(,"package")
 ## [1] "sp"

-
+
 Sy1_nb <- poly2nb(Syracuse)
 isTRUE(all.equal(Sy0_nb, Sy1_nb, check.attributes=FALSE))

 
## [1] TRUE

@@ -181,11 +185,11 @@ 
Creating Contiguity Neighbours
+
 Sy2_nb <- poly2nb(Syracuse, queen=FALSE)
 isTRUE(all.equal(Sy0_nb, Sy2_nb, check.attributes=FALSE))

 
## [1] FALSE

-
+
 oopar <- par(mfrow=c(1,2), mar=c(3,3,1,1)+0.1)
 plot(Syracuse, border="grey60")
 plot(Sy0_nb, coordinates(Syracuse), add=TRUE, pch=19, cex=0.6)
@@ -216,13 +220,13 @@ 
Creating Contiguity Neighbours
+
 library(rgrass)
 v <- terra::vect(sf::st_as_sf(Syracuse))
 SG <- terra::rast(terra::ext(v), crs=terra::crs(v))
-pr <- initGRASS("/home/rsb/topics/grass/g840/grass84", tempdir(), SG=SG, override=TRUE)
-write_VECT(v, "SY0", flags=c("o", "overwrite"))
-contig <- vect2neigh("SY0")
+pr <- initGRASS("/home/rsb/topics/grass/g840/grass84", tempdir(), SG=SG, override=TRUE)
+write_VECT(v, "SY0", flags=c("o", "overwrite"))
+contig <- vect2neigh("SY0")
 Sy3_nb <- sn2listw(contig, style="B")$neighbours
 isTRUE(all.equal(Sy3_nb, Sy2_nb, check.attributes=FALSE))
 ## [1] TRUE

@@ -247,9 +251,7 @@ 
Creating Graph-Based Neighbourskk-nearest
-neighbours.

+measures, distance thresholds, and \(k\)-nearest neighbours.

 
The most direct graph representation of neighbours is to make a
 Delaunay triangulation of the points, shown in the first panel in the
 figure. The neighbour relationships are defined by the triangulation,
@@ -264,23 +266,17 @@ 
Creating Graph-Based Neighbours(Avis and Horton
 1985). Functions for graph-based neighbours were kindly
 contributed by Nicholas Lewin-Koh.

-
+
 coords <- coordinates(Syracuse)
 IDs <- row.names(as(Syracuse, "data.frame"))
 #FIXME library(tripack)
 Sy4_nb <- tri2nb(coords, row.names=IDs)
 if (require(dbscan, quietly=TRUE)) {
   Sy5_nb <- graph2nb(soi.graph(Sy4_nb, coords), row.names=IDs)
-} else Sy5_nb <- NULL

-
## 
-## Attaching package: 'dbscan'

-
## The following object is masked from 'package:stats':
-## 
-##     as.dendrogram

-
-Sy6_nb <- graph2nb(gabrielneigh(coords), row.names=IDs)
+} else Sy5_nb <- NULL
+Sy6_nb <- graph2nb(gabrielneigh(coords), row.names=IDs)
 Sy7_nb <- graph2nb(relativeneigh(coords), row.names=IDs)

-
+
 oopar <- par(mfrow=c(2,2), mar=c(1,1,1,1)+0.1)
 plot(Syracuse, border="grey60")
 plot(Sy4_nb, coords, add=TRUE, pch=".")
@@ -301,73 +297,65 @@ 
Creating Graph-Based Neighbours
 
Delaunay triangulation neighbours and SOI neighbours are symmetric by
-design – if
-ii
-is a neighbour of
-jj,
-then
-jj
-is a neighbour of
-ii.
-The Gabriel graph is also a subgraph of the Delaunay triangulation,
-retaining a different set of neighbours (Matula
-and Sokal 1980). It does not, however, guarantee symmetry; the
-same applies to Relative graph neighbours (Toussaint 1980). The graph2nb()
-function takes a sym argument to insert links to restore
-symmetry, but the graphs then no longer exactly fulfil their neighbour
-criteria. All the graph-based neighbour schemes always ensure that all
-the points will have at least one neighbour. Subgraphs of the full
-triangulation may also have more than one graph after trimming. The
-functions is.symmetric.nb() can be used to check for
-symmetry, with argument force=TRUE if the symmetry
-attribute is to be overridden, and n.comp.nb() reports the
-number of graph components and~the components to which points belong
-(after enforcing symmetry, because the algorithm assumes that the graph
-is not directed). When there are more than one graph component, the
-matrix representation of the spatial weights can become block-diagonal
-if observations are appropriately sorted.

-
+design – if \(i\) is a neighbour of
+\(j\), then \(j\) is a neighbour of \(i\). The Gabriel graph is also a subgraph
+of the Delaunay triangulation, retaining a different set of neighbours
+(Matula and Sokal 1980). It does not,
+however, guarantee symmetry; the same applies to Relative graph
+neighbours (Toussaint 1980). The
+graph2nb() function takes a sym argument to
+insert links to restore symmetry, but the graphs then no longer exactly
+fulfil their neighbour criteria. All the graph-based neighbour schemes
+always ensure that all the points will have at least one neighbour.
+Subgraphs of the full triangulation may also have more than one graph
+after trimming. The functions is.symmetric.nb() can be used
+to check for symmetry, with argument force=TRUE if the
+symmetry attribute is to be overridden, and n.comp.nb()
+reports the number of graph components and~the components to which
+points belong (after enforcing symmetry, because the algorithm assumes
+that the graph is not directed). When there are more than one graph
+component, the matrix representation of the spatial weights can become
+block-diagonal if observations are appropriately sorted.

+
 nb_l <- list(Triangulation=Sy4_nb, Gabriel=Sy6_nb,
   Relative=Sy7_nb)
 if (!is.null(Sy5_nb)) nb_l <- c(nb_l, list(SOI=Sy5_nb))
 sapply(nb_l, function(x) is.symmetric.nb(x, verbose=FALSE, force=TRUE))

-
## Triangulation       Gabriel      Relative           SOI 
-##          TRUE         FALSE         FALSE          TRUE

-
+
## Triangulation       Gabriel      Relative 
+##          TRUE         FALSE         FALSE

+
 sapply(nb_l, function(x) n.comp.nb(x)$nc)

-
## Triangulation       Gabriel      Relative           SOI 
-##             1             1             1             1

+
## Triangulation       Gabriel      Relative 
+##             1             1             1

 

 

 
Distance-Based Neighbours
 

-
An alternative method is to choose the
-kk
-nearest points as neighbours – this adapts across the study area, taking
-account of differences in the densities of areal entities. Naturally, in
-the overwhelming majority of cases, it leads to asymmetric neighbours,
-but will ensure that all areas have
-kk
-neighbours. The knearneigh() function returns an
-intermediate form converted to an nb object by
-knn2nb(); knearneigh() can also take a
-longlat= argument to handle geographical coordinates.

-
+
An alternative method is to choose the \(k\) nearest points as neighbours – this
+adapts across the study area, taking account of differences in the
+densities of areal entities. Naturally, in the overwhelming majority of
+cases, it leads to asymmetric neighbours, but will ensure that all areas
+have \(k\) neighbours. The
+knearneigh() function returns an intermediate form
+converted to an nb object by knn2nb();
+knearneigh() can also take a longlat= argument
+to handle geographical coordinates.

+
 Sy8_nb <- knn2nb(knearneigh(coords, k=1), row.names=IDs)

 
## Warning in knn2nb(knearneigh(coords, k = 1), row.names = IDs): neighbour object
 ## has 15 sub-graphs

-
+
 Sy9_nb <- knn2nb(knearneigh(coords, k=2), row.names=IDs)
 Sy10_nb <- knn2nb(knearneigh(coords, k=4), row.names=IDs)
 nb_l <- list(k1=Sy8_nb, k2=Sy9_nb, k4=Sy10_nb)
 sapply(nb_l, function(x) is.symmetric.nb(x, verbose=FALSE, force=TRUE))

 
##    k1    k2    k4 
 ## FALSE FALSE FALSE

-
+
 sapply(nb_l, function(x) n.comp.nb(x)$nc)

 
## k1 k2 k4 
 ## 15  1  1

-
+
 oopar <- par(mfrow=c(1,3), mar=c(1,1,1,1)+0.1)
 plot(Syracuse, border="grey60")
 plot(Sy8_nb, coords, add=TRUE, pch=".")
@@ -379,57 +367,45 @@ 
Distance-Based Neighboursplot(Sy10_nb, coords, add=TRUE, pch=".")
 text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels="c)", cex=0.8)
 par(oopar)

-
a:
-k=1k=1
-neighbours; b:
-k=2k=2
-neighbours; c:
-k=4k=4
-neighbours

-
The figure shows the neighbour relationships for
-k=1,2,4k= 1, 2, 4,
-with many components for
-k=1k=1.
-If need be,
-kk-nearest
-neighbour objects can be made symmetrical using the
-make.sym.nb() function. The
-k=1k=1
-object is also useful in finding the minimum distance at which all areas
-have a distance-based neighbour. Using the nbdists()
-function, we can calculate a list of vectors of distances corresponding
-to the neighbour object, here for first nearest neighbours. The greatest
-value will be the minimum distance needed to make sure that all the
-areas are linked to at least one neighbour. The
-dnearneigh() function is used to find neighbours with an
-interpoint distance, with arguments d1 and d2
-setting the lower and upper distance bounds; it can also take a
-longlat argument to handle geographical coordinates.

-
+
a: \(k=1\) neighbours; b: \(k=2\) neighbours; c: \(k=4\) neighbours

+
The figure shows the neighbour relationships for \(k= 1, 2, 4\), with many components for
+\(k=1\). If need be, \(k\)-nearest neighbour objects can be made
+symmetrical using the make.sym.nb() function. The \(k=1\) object is also useful in finding the
+minimum distance at which all areas have a distance-based neighbour.
+Using the nbdists() function, we can calculate a list of
+vectors of distances corresponding to the neighbour object, here for
+first nearest neighbours. The greatest value will be the minimum
+distance needed to make sure that all the areas are linked to at least
+one neighbour. The dnearneigh() function is used to find
+neighbours with an interpoint distance, with arguments d1
+and d2 setting the lower and upper distance bounds; it can
+also take a longlat argument to handle geographical
+coordinates.

+
 dsts <- unlist(nbdists(Sy8_nb, coords))
 summary(dsts)

 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 ##   395.7   587.3   700.1   760.4   906.1  1544.6

-
+
 max_1nn <- max(dsts)
 max_1nn

 
## [1] 1544.615

-
+
 Sy11_nb <- dnearneigh(coords, d1=0, d2=0.75*max_1nn, row.names=IDs)

 
## Warning in dnearneigh(coords, d1 = 0, d2 = 0.75 * max_1nn, row.names = IDs):
 ## neighbour object has 4 sub-graphs

-
+
 Sy12_nb <- dnearneigh(coords, d1=0, d2=1*max_1nn, row.names=IDs)
 Sy13_nb <- dnearneigh(coords, d1=0, d2=1.5*max_1nn, row.names=IDs)
 nb_l <- list(d1=Sy11_nb, d2=Sy12_nb, d3=Sy13_nb)
 sapply(nb_l, function(x) is.symmetric.nb(x, verbose=FALSE, force=TRUE))

 
##   d1   d2   d3 
 ## TRUE TRUE TRUE

-
+
 sapply(nb_l, function(x) n.comp.nb(x)$nc)

 
## d1 d2 d3 
 ##  4  1  1

-
+
 oopar <- par(mfrow=c(1,3), mar=c(1,1,1,1)+0.1)
 plot(Syracuse, border="grey60")
 plot(Sy11_nb, coords, add=TRUE, pch=".")
@@ -444,17 +420,14 @@ 
Distance-Based Neighboursa: Neighbours within 1,158m; b: neighbours within 1,545m; c:
 neighbours within 2,317m

 
The figure shows how the numbers of distance-based neighbours
-increase with moderate increases in distance. Moving from
-0.750.75
-times the minimum all-included distance, to the all-included distance,
-and
-1.51.5
-times the minimum all-included distance, the numbers of links grow
-rapidly. This is a major problem when some of the first nearest
-neighbour distances in a study area are much larger than others, since
-to avoid no-neighbour areal entities, the distance criterion will need
-to be set such that many areas have many neighbours.

-
+increase with moderate increases in distance. Moving from \(0.75\) times the minimum all-included
+distance, to the all-included distance, and \(1.5\) times the minimum all-included
+distance, the numbers of links grow rapidly. This is a major problem
+when some of the first nearest neighbour distances in a study area are
+much larger than others, since to avoid no-neighbour areal entities, the
+distance criterion will need to be set such that many areas have many
+neighbours.

+
 dS <- c(0.75, 1, 1.5)*max_1nn
 res <- sapply(nb_l, function(x) table(card(x)))
 mx <- max(card(Sy13_nb))
@@ -477,7 +450,7 @@ 
Distance-Based Neighbours
-
+
 
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
@@ -503,21 +476,17 @@ 
Higher-Order Neighboursii
-a neighbour of
-ii
-itself (O’Sullivan and Unwin 2003). The
+traversed, but not permitting cycles, which could risk making \(i\) a neighbour of \(i\) itself (O’Sullivan and Unwin 2003). The
 nblag() function takes an existing neighbour list and
 returns a list of lists, from first to maxlag= order
 neighbours.

-
+
 Sy0_nb_lags <- nblag(Sy0_nb, maxlag=9)

 
## Warning in nblag(Sy0_nb, maxlag = 9): lag 6 neighbour object has 7 sub-graphs

 
## Warning in nblag(Sy0_nb, maxlag = 9): lag 7 neighbour object has 22 sub-graphs

 
## Warning in nblag(Sy0_nb, maxlag = 9): lag 8 neighbour object has 52 sub-graphs

 
## Warning in nblag(Sy0_nb, maxlag = 9): lag 9 neighbour object has 63 sub-graphs

-
+
 names(Sy0_nb_lags) <- c("first", "second", "third", "fourth", "fifth", "sixth", "seventh", "eighth", "ninth")
 res <- sapply(Sy0_nb_lags, function(x) table(card(x)))
 mx <- max(unlist(sapply(Sy0_nb_lags, function(x) card(x))))
@@ -555,14 +524,14 @@ 
Grid Neighbours
-
+
 cell2nb(7, 7, type="rook", torus=TRUE)

 
## Neighbour list object:
 ## Number of regions: 49 
 ## Number of nonzero links: 196 
 ## Percentage nonzero weights: 8.163265 
 ## Average number of links: 4

-
+
 cell2nb(7, 7, type="rook", torus=FALSE)

 
## Neighbour list object:
 ## Number of regions: 49 
@@ -574,19 +543,12 @@ 
Grid Neighboursnn,
-here
-n=3n=3,103,
-that the use of a sparse, list based representation shows its strength.
-Handling a
-281×281281 \times 281
-matrix for the eight-county census tracts is feasible, easy for a
-63×6363 \times 63
-matrix for Syracuse census tracts, but demanding for a
-3,103×3103 \times 3,103
-matrix.

-
+scale. It is also in these settings, with moderately large \(n\), here \(n=3\),103, that the use of a sparse, list
+based representation shows its strength. Handling a \(281 \times 281\) matrix for the
+eight-county census tracts is feasible, easy for a \(63 \times 63\) matrix for Syracuse census
+tracts, but demanding for a 3,\(103 \times
+3\),103 matrix.

+
 data(meuse.grid)
 coordinates(meuse.grid) <- c("x", "y")
 gridded(meuse.grid) <- TRUE
@@ -598,7 +560,7 @@ 
Grid Neighbours## Number of nonzero links: 12022 
 ## Percentage nonzero weights: 0.1248571 
 ## Average number of links: 3.874315

-
+
 table(card(mg_nb))

 
## 
 ##    1    2    3    4 
@@ -645,7 +607,7 @@ 
References
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     
diff --git a/docs/articles/nb_files/figure-html/unnamed-chunk-15-1.png b/docs/articles/nb_files/figure-html/unnamed-chunk-15-1.png
index 41e9bd04..198f986b 100644
Binary files a/docs/articles/nb_files/figure-html/unnamed-chunk-15-1.png and b/docs/articles/nb_files/figure-html/unnamed-chunk-15-1.png differ
diff --git a/docs/articles/nb_sf.html b/docs/articles/nb_sf.html
index 718d126e..8c342663 100644
--- a/docs/articles/nb_sf.html
+++ b/docs/articles/nb_sf.html
@@ -10,7 +10,7 @@
 
 
 
-
+
 
 
     Skip to contents
@@ -20,7 +20,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -204,9 +204,9 @@ 
Comparison of sp and sf approaches}
 if (dothis) sf_extSoftVersion()

 
##           GEOS           GDAL         proj.4 GDAL_with_GEOS     USE_PROJ_H 
-##       "3.13.1"       "3.11.0"        "9.6.2"         "true"         "true" 
+##       "3.13.0"       "3.10.1"        "9.5.1"         "true"         "true" 
 ##           PROJ 
-##        "9.6.2"

+##        "9.5.1"

 
Let us read the GPKG file with valid geometries in to ‘sf’ and ‘sp’
 objects:

 
@@ -233,7 +233,7 @@ 
Contiguity neighbours for pol
 eps <- sqrt(.Machine$double.eps)
 system.time(for(i in 1:reps) NY8_sf_1_nb <- poly2nb(NY8_sf, queen=TRUE, snap=eps))/reps

 
##    user  system elapsed 
-##  0.1957  0.0078  0.2045

+##   0.047   0.008   0.120

 
Using spatial indices to check intersection of polygons is much
 faster than the legacy method in poly2nb. From spdep
 1.1-7, use is made of GEOS through sf to find candidate
@@ -278,7 +278,8 @@ 
Contiguity neighbours from
     NY8_sf_old <- sf::st_read(system.file("shapes/NY8_utm18.shp", package="spData"))
 }

 
## Reading layer `NY8_utm18' from data source 
-##   `/home/rsb/lib/r_libs/spData/shapes/NY8_utm18.gpkg' using driver `GPKG'
+##   `C:\Users\rzomor2\AppData\Local\R\win-library\4.4\spData\shapes\NY8_utm18.gpkg' 
+##   using driver `GPKG'
 ## Simple feature collection with 281 features and 17 fields
 ## Geometry type: POLYGON
 ## Dimension:     XY
@@ -387,16 +388,8 @@ 
Graph-based neighboursNY84_nb <- tri2nb(NY8_ct_sf)
 if (require(dbscan, quietly=TRUE)) {
   NY85_nb <- graph2nb(soi.graph(NY84_nb, NY8_ct_sf))
-} else NY85_nb <- NULL

-
## 
-## Attaching package: 'dbscan'

-
## The following object is masked from 'package:stats':
-## 
-##     as.dendrogram

-
## Warning in graph2nb(soi.graph(NY84_nb, NY8_ct_sf)): neighbour object has 2
-## sub-graphs

-
-NY86_nb <- graph2nb(gabrielneigh(NY8_ct_sf))
+} else NY85_nb <- NULL
+NY86_nb <- graph2nb(gabrielneigh(NY8_ct_sf))
 NY87_nb <- graph2nb(relativeneigh(NY8_ct_sf))

 

 

@@ -404,46 +397,46 @@ 
K-nearest neighboursdbscan::kNN() in 2D or 3D
+set used is planar, in which case dbscan::kNN() in 2D or 3D
 building a kd-tree is used:

-
+
 system.time(for (i in 1:reps) suppressWarnings(NY88_nb_sf <- knn2nb(knearneigh(NY8_ct_sf, k=1))))/reps

 
##    user  system elapsed 
-##  0.0277  0.0012  0.0289

+##   0.029   0.000   0.050

 
Legacy code may be used omitting the kd-tree:

-
+
 system.time(for (i in 1:reps) suppressWarnings(NY89_nb_sf <- knn2nb(knearneigh(NY8_ct_sf, k=1, use_kd_tree=FALSE))))/reps

 
##    user  system elapsed 
-##  0.0280  0.0010  0.0291

+##   0.017   0.002   0.044

 

 

 
Distance neighbours
 

 
Distance neighbours need a threshold - nbdists shows the
 maximum distance to first nearest neighbour:

-
+
 dsts <- unlist(nbdists(NY88_nb_sf, NY8_ct_sf))
 summary(dsts)

 
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
 ##    82.85   912.85  1801.11  3441.04  4461.26 17033.11

-
+
 max_1nn <- max(dsts)

 
dnearneigh can also handle Great Circle distances, but
 this is not demonstrated here, as the data set used is planar:

-
+
 system.time(for (i in 1:reps) suppressWarnings(NY810_nb <- dnearneigh(NY8_ct_sf, d1=0, d2=0.75*max_1nn)))/reps

 
##    user  system elapsed 
-##  0.0683  0.0003  0.0690

-
By default, the function uses dbscan::frNN() to build a
+##   0.008   0.000   0.033

+
By default, the function uses dbscan::frNN() to build a
 kd-tree in 2D or 3D which is then used to find distance neighbours. For
 small n, the argument use_kd_tree=FALSE may speed up
 computation a little by reverting to legacy code not building a kd-tree
 first, but in general the differences are so small that the user will
 not notice:

-
+
 system.time(for (i in 1:reps) suppressWarnings(NY811_nb <- dnearneigh(NY8_ct_sf, d1=0, d2=0.75*max_1nn, use_kd_tree=FALSE)))/reps

 
##    user  system elapsed 
-##  0.0522  0.0007  0.0531

+##   0.017   0.006   0.033

 

 

 

@@ -454,7 +447,7 @@ 
Spherical point-based neighbourssf 1.0-0 to use s2 by default has
 opened up new opportunities where spatial indexing on the sphere may
 help.

-
+
 pts_ll <- st_transform(NY8_ct_sf, "OGC:CRS84")
 st_is_longlat(pts_ll)

 
## [1] TRUE

@@ -465,45 +458,45 @@ 
K-nearest neighbourssf_use_s2() is TRUE, knearneigh()
 will use spatially indexed points and
 s2::s2_closest_edges() (see https://github.com/r-spatial/s2/issues/125#issuecomment-860107442)

-
+
 (old_use_s2 <- sf_use_s2())

 
## [1] TRUE

 
and performs well with also with larger data sets:

-
+
 sf_use_s2(TRUE)
 system.time(for (i in 1:reps) pts_ll1_nb <- knn2nb(knearneigh(pts_ll, k=6)))/reps

 
##    user  system elapsed 
-##  0.0428  0.0001  0.0431

+##   0.023   0.000   0.051

 
For this smaller data set, the legacy approach without spatial
 indexing is adequate, but slows down as the number of observations
 increases:

-
+
 sf_use_s2(FALSE)

 
## Spherical geometry (s2) switched off

-
+
 system.time(for (i in 1:reps) pts_ll2_nb <- knn2nb(knearneigh(pts_ll, k=6)))/reps

 
##    user  system elapsed 
-##  0.0301  0.0000  0.0301

+##   0.020   0.001   0.046

 
The WGS84 ellipsoid Great Circle distances differ a very little from
 the s2 spherical distances, yielding output that here
 diverges for two tract centroids:

-
+
 all.equal(pts_ll1_nb, pts_ll2_nb, check.attributes=FALSE)

 
## [1] "Component 52: Mean relative difference: 1.466667"  
 ## [2] "Component 124: Mean relative difference: 0.0251046"

-
+
 pts_ll1_nb[[52]]

 
## [1] 15 38 48 49 50 53

-
+
 pts_ll2_nb[[52]]

 
## [1] 37 38 48 49 50 53

-
+
 pts_ll1_nb[[124]]

 
## [1] 117 122 123 125 133 134

-
+
 pts_ll2_nb[[124]]

 
## [1] 116 117 123 125 133 134

-
+
 sf_use_s2(old_use_s2)

 
## Spherical geometry (s2) switched on

 

@@ -519,11 +512,11 @@ 
Distance neighbours.

-
+
 
## Warning in knn2nb(knearneigh(pts_ll, k = 1)): neighbour object has 62
 ## sub-graphs

-
+
 args(dnearneigh)

 
## function (x, d1, d2, row.names = NULL, longlat = NULL, bounds = c("GE", 
 ##     "LE"), use_kd_tree = TRUE, symtest = FALSE, use_s2 = packageVersion("s2") > 
@@ -532,57 +525,57 @@ 
Distance neighbourss2::s2_dwithin_matrix() is run:

-
+
 if (packageVersion("s2") > "1.0.7") {
   system.time(for (i in 1:(reps/5)) suppressWarnings(pts_ll3_nb <- dnearneigh(pts_ll, d1=0,
       d2=0.75*max_1nn_ll)))/(reps/5)
 }

 
##    user  system elapsed 
-##  0.0820  0.0000  0.0825

+##   0.015   0.000   0.065

 
Alternatively, spherical distances can be used with
 dwithin=FALSE and s2::s2_closest_edges();
 although running in similar time, s2::s2_closest_edges()
 depends on the additional k= argument, which, if mis-set,
 may miss valid neighbours:

-
+
 system.time(for (i in 1:(reps/5)) suppressWarnings(pts_ll5_nb <- dnearneigh(pts_ll, d1=0, d2=0.75*max_1nn_ll, dwithin=FALSE)))/(reps/5)

 
##    user  system elapsed 
-##  0.0700  0.0005  0.0710

-
+##   0.010   0.000   0.025

+
 if (packageVersion("s2") > "1.0.7") all.equal(pts_ll3_nb, pts_ll5_nb, check.attributes=FALSE)

 
## [1] TRUE

 
Using s2::s2_closest_edges() respects
 d1 > 0 without requiring a second pass in R, so is
 faster than s2::s2_dwithin_matrix():

-
+
 if (packageVersion("s2") > "1.0.7") {
   system.time(for (i in 1:(reps/5)) suppressWarnings(pts_ll3a_nb <- dnearneigh(pts_ll, d1=5,
       d2=0.75*max_1nn_ll, dwithin=FALSE)))/(reps/5)
 }

 
##    user  system elapsed 
-##  0.0610  0.0000  0.0615

+##   0.035   0.000   0.030

 
Using s2::s2_dwithin_matrix() requires a second pass,
 one for the lower bound, another for the upper bound, and a set
 difference operation to find neighbours in the distance band:

-
+
 if (packageVersion("s2") > "1.0.7") {
     system.time(for (i in 1:(reps/5)) suppressWarnings(pts_ll5a_nb <- dnearneigh(pts_ll, d1=5,
         d2=0.75*max_1nn_ll)))/(reps/5)
 }

 
##    user  system elapsed 
-##  0.1075  0.0000  0.1080

-
+##   0.055   0.000   0.085

+
 if (packageVersion("s2") > "1.0.7") all.equal(pts_ll3a_nb, pts_ll5a_nb, check.attributes=FALSE)

 
## [1] TRUE

 
Setting use_s2=FALSE falls back to the legacy version,
 which uses symmetry to reduce time:

-
+
 system.time(for (i in 1:reps) suppressWarnings(pts_ll6_nb <- dnearneigh(pts_ll, d1=0, d2=0.75*max_1nn_ll, use_s2=FALSE)))/reps

 
##    user  system elapsed 
-##  0.0400  0.0000  0.0402

+##   0.014   0.000   0.022

 
Minor differences may occur between the legacy ellipsoid and
 s2 spherical approaches:

-
+
 all.equal(pts_ll5_nb, pts_ll6_nb, check.attributes=FALSE)

 
##  [1] "Component 20: Numeric: lengths (6, 5) differ"     
 ##  [2] "Component 28: Numeric: lengths (7, 6) differ"     
@@ -606,11 +599,11 @@ 
Distance neighbours## [20] "Component 235: Numeric: lengths (40, 39) differ"  
 ## [21] "Component 237: Numeric: lengths (14, 15) differ"  
 ## [22] "Component 245: Numeric: lengths (16, 15) differ"

-
+
 system.time(for (i in 1:reps) suppressWarnings(pts_ll6a_nb <- dnearneigh(pts_ll, d1=5, d2=0.75*max_1nn_ll, use_s2=FALSE)))/reps

 
##    user  system elapsed 
-##  0.0319  0.0000  0.0319

-
+##   0.007   0.001   0.019

+
 if (packageVersion("s2") > "1.0.7") all.equal(pts_ll5a_nb, pts_ll6a_nb, check.attributes=FALSE)

 
##  [1] "Component 20: Numeric: lengths (6, 5) differ"       
 ##  [2] "Component 28: Numeric: lengths (7, 6) differ"       
@@ -649,7 +642,7 @@ 
Contiguity neighbours for spherical polygon supports2 spatial indexing
 functionality is accessed in finding candidate neighbours in
 intersecting geometries.

-
+
 NY8_sf_ll <- st_transform(NY8_sf, "OGC:CRS84")
 st_is_longlat(NY8_sf_ll)

 
## [1] TRUE

@@ -657,12 +650,12 @@ 
Contiguity neighbours for spherical polygon supports2_intersects_matrix(),
 but the results are the same, and because spatial indexing is used, this
 scales well for larger data sets:

-
+
 sf_use_s2(TRUE)
 system.time(for (i in 1:reps) NY8_sf_1_nb_ll <- poly2nb(NY8_sf_ll, queen=TRUE, snap=eps))/reps

 
##    user  system elapsed 
-##  0.1759  0.0029  0.1794

-
+##   0.085   0.011   0.179

+
 all.equal(NY8_sf_1_nb, NY8_sf_1_nb_ll, check.attributes=FALSE)

 
## [1] TRUE

 

@@ -679,7 +672,7 @@ 
Contiguity neighbours for spherical polygon support
 
 

-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     
diff --git a/docs/articles/sids.html b/docs/articles/sids.html
index 27add15a..6d37f560 100644
--- a/docs/articles/sids.html
+++ b/docs/articles/sids.html
@@ -10,7 +10,7 @@
 
 
 
-
+
 
 
     Skip to contents
@@ -20,7 +20,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -95,8 +95,8 @@ 
IntroductionGetting the data into R
 

 
We will be using the spdep and
-spreg packages, here version: spdep, version 1.3-13,
-2025-06-10, the sf package and the
+spreg packages, here version: spdep, version 1.4-1,
+2025-06-12, the sf package and the
 tmap package. The data from the sources referred to
 above is documented in the help page for the nc.sids data
 set in spData. The actual data, included in a shapefile
@@ -149,7 +149,7 @@ 
Getting the data into R##  Max.   :2241   Max.   :0.2410   Max.   :3.640   Max.   :2241  
 ##      NAME               FIPS               FIPSNO         CRESS_ID     
 ##  Length:100         Length:100         Min.   :37001   Min.   :  1.00  
-##  Class :character   Class :character   1st Qu.:37050   1st Qu.: 25.75  
+##  Class :character   Class :character   1st Qu.:37051   1st Qu.: 25.75  
 ##  Mode  :character   Mode  :character   Median :37100   Median : 50.50  
 ##                                        Mean   :37100   Mean   : 50.50  
 ##                                        3rd Qu.:37150   3rd Qu.: 75.25  
@@ -367,7 +367,7 @@ 
Getting the data into RspData (formerly in
 spdep), and add the neighbour relationships used in
 Cressie and Chan (1989) to the background
-map as a graph shown in Figure :

+map as a graph shown in Figure \(\ref{plot-CC89.nb}\):

 
 gal_file <- system.file("weights/ncCR85.gal", package="spData")[1]
 ncCR85 <- read.gal(gal_file, region.id=nc$FIPSNO)
@@ -446,12 +446,11 @@ 
Probability mappingα\alpha,
-occur for spatial units with either unusually high or low rates. For
-this reason, the high and low counties are plotted separately below.
-Note that cut returns a factor labeled with
-cut intervals.

+a chosen \(\alpha\), occur for spatial
+units with either unusually high or low rates. For this reason, the high
+and low counties are plotted separately below. Note that
+cut returns a factor labeled with cut
+intervals.

 
 ch <- choynowski(nc$SID74, nc$BIR74)
 nc$ch_pmap_low <- ifelse(ch$type, ch$pmap, NA)
@@ -463,17 +462,16 @@ 
Probability mappingis_tmap <- FALSE
 if (require(tmap, quietly=TRUE)) is_tmap <- TRUE
 is_tmap

-
## [1] TRUE

+
## [1] FALSE

 
 library(tmap)
 tmap4 <- packageVersion("tmap") >= "3.99"
 if (tmap4) {
-  tm_shape(nc) + tm_polygons(fill=c("low", "high"), fill.scale = tm_scale(values="brewer.set1"), fill.legend = tm_legend("p-values", frame=FALSE, item.r = 0), fill.free=FALSE, lwd=0.01) + tm_layout(panel.labels=c("low", "high"))
+  tm_shape(nc) + tm_polygons(fill=c("low", "high"), fill.scale = tm_scale(values="brewer.set1"), fill.legend = tm_legend("p-values", frame=FALSE, item.r = 0), fill.free=FALSE, lwd=0.01) + tm_layout(panel.labels=c("low", "high"))
 } else {
-tm_shape(nc) + tm_fill(c("low", "high"), palette="Set1", title="p-values") +
-  tm_facets(free.scales=FALSE) + tm_layout(panel.labels=c("low", "high"))
+tm_shape(nc) + tm_fill(c("low", "high"), palette="Set1", title="p-values") +
+  tm_facets(free.scales=FALSE) + tm_layout(panel.labels=c("low", "high"))
 }

-

 
For more complicated thematic maps, it may be helpful to use
 ColorBrewer (https://colorbrewer2.org) colour palettes. Here we use
 palettes accessed through tmap, available in R in the
@@ -495,22 +493,19 @@ 
Probability mapping
 brks <- c(0,0.001,0.01,0.025,0.05,0.95,0.975,0.99,0.999,1)
 if (tmap4) {
-  tm_shape(nc) + tm_polygons(fill="pmap", fill.scale = tm_scale(values="brewer.rd_bu", midpoint=0.5, breaks=brks), fill.legend = tm_legend(frame=FALSE, item.r = 0, position = tm_pos_out("right", "center")), lwd=0.01) + tm_layout(component.autoscale=FALSE)
+  tm_shape(nc) + tm_polygons(fill="pmap", fill.scale = tm_scale(values="brewer.rd_bu", midpoint=0.5, breaks=brks), fill.legend = tm_legend(frame=FALSE, item.r = 0, position = tm_pos_out("right", "center")), lwd=0.01) + tm_layout(component.autoscale=FALSE)
 } else {
-tm_shape(nc) + tm_fill("pmap", breaks=brks, midpoint=0.5, palette="RdBu") + tm_layout(legend.outside=TRUE)
+tm_shape(nc) + tm_fill("pmap", breaks=brks, midpoint=0.5, palette="RdBu") + tm_layout(legend.outside=TRUE)
 }

-

 
Marilia Carvalho (personal communication) and Virgilio Gómez Rubio
 (Gómez-Rubio, Ferrándiz-Ferragud, and
 López-Quílez 2005) have pointed to the unusual shape of the
 distribution of the Poisson probability values (histogram below),
-repeating the doubts about probability mapping voiced by Cressie (1991, 392): “an extreme value
-…\ldots
-may be more due to its lack of fit to the Poisson model than to its
-deviation from the constant rate assumption”. There are many more high
-values than one would have expected, suggesting perhaps overdispersion,
-that is that the ratio of the variance and mean is larger than
-unity.

+repeating the doubts about probability mapping voiced by Cressie (1991, 392): “an extreme value \(\ldots\) may be more due to its lack of fit
+to the Poisson model than to its deviation from the constant rate
+assumption”. There are many more high values than one would have
+expected, suggesting perhaps overdispersion, that is that the ratio of
+the variance and mean is larger than unity.

 
 hist(nc$pmap, main="")

 

@@ -526,11 +521,10 @@ 
Probability mapping
 brks <- c(-4, -3, -2, -1.5, -1, -0.5, 0.5, 1, 1.5, 2, 3, 4)
 if (tmap4) {
-  tm_shape(nc) + tm_polygons(fill="stdres", fill.scale = tm_scale(values="brewer.rd_bu", midpoint=0.5, breaks=brks), fill.legend = tm_legend(frame=FALSE, item.r = 0, position = tm_pos_out("right", "center")), lwd=0.01) + tm_layout(component.autoscale=FALSE)
+  tm_shape(nc) + tm_polygons(fill="stdres", fill.scale = tm_scale(values="brewer.rd_bu", midpoint=0.5, breaks=brks), fill.legend = tm_legend(frame=FALSE, item.r = 0, position = tm_pos_out("right", "center")), lwd=0.01) + tm_layout(component.autoscale=FALSE)
 } else {
-  tm_shape(nc) + tm_fill("stdres", breaks=brks, midpoint=0, palette="RdBu") + tm_layout(legend.outside=TRUE)
+  tm_shape(nc) + tm_fill("stdres", breaks=brks, midpoint=0, palette="RdBu") + tm_layout(legend.outside=TRUE)
 }

-

 
The dispersion is equal to 2.2786188, much greater than unity; we
 calculate the corrected probability map values by taking the
 standardised residuals of the model, taking the size of the dispersion
@@ -569,23 +563,21 @@ 
Probability mappingbrks <- c(0, 0.25, 0.5, 0.75, 1, 2, 3, 4, 5)
 nc_miss <- st_centroid(st_geometry(nc[card(ncCC89) == 0,]), of_largest_polygon)
 if (tmap4) {
-  tm_shape(nc) + tm_polygons(fill="stdres", fill.scale = tm_scale(values="brewer.rd_bu", midpoint=0.5, breaks=brks), fill.legend = tm_legend(frame=FALSE, item.r = 0, position = tm_pos_out("right", "center")), lwd=0.01) + tm_layout(component.autoscale=FALSE) + tm_shape(nc_miss) + tm_symbols(shape=8, size=0.5)
+  tm_shape(nc) + tm_polygons(fill="stdres", fill.scale = tm_scale(values="brewer.rd_bu", midpoint=0.5, breaks=brks), fill.legend = tm_legend(frame=FALSE, item.r = 0, position = tm_pos_out("right", "center")), lwd=0.01) + tm_layout(component.autoscale=FALSE) + tm_shape(nc_miss) + tm_symbols(shape=8, size=0.5)
 } else {
-tm_shape(nc) + tm_fill("EB_loc", breaks=brks, midpoint=1, palette="RdBu") + tm_layout(legend.outside=TRUE) + tm_shape(nc_miss) + tm_symbols(shape=8, size=0.5)
+tm_shape(nc) + tm_fill("EB_loc", breaks=brks, midpoint=1, palette="RdBu") + tm_layout(legend.outside=TRUE) + tm_shape(nc_miss) + tm_symbols(shape=8, size=0.5)
 }

-

-
The results are shown in Figure . Like other relevant functions in
-spdep,EBlocal() takes a
+
The results are shown in Figure \(\ref{EBlocal}\). Like other relevant
+functions in spdep,EBlocal() takes a
 zero.policy argument to allow missing values to be passed
 through. In this case, no local estimate is available for the two
 counties with no neighbours, marked by stars.

 
In addition to Empirical Bayes smoothing globally, used both for
 disease mapping and the Assuncão and Reis correction to
-Moran’s
-II
-for rates data (to shrink towards the global rate when the population at
-risk is small, here as a Monte Carlo test), lists of local neighbours
-can be used to shrink towards a local rate.

+Moran’s \(I\) for rates data (to shrink
+towards the global rate when the population at risk is small, here as a
+Monte Carlo test), lists of local neighbours can be used to shrink
+towards a local rate.

 
 set.seed(1)
 EBImoran.mc(nc$SID74, nc$BIR74, nb2listw(ncCC89, style="B", zero.policy=TRUE), nsim=999, zero.policy=TRUE)

@@ -605,8 +597,7 @@ 
Exploration and modelling of the
 

 
One of the first steps taken by Cressie and
 Read (1985) is to try to bring out spatial trends by dividing
-North Carolina up into
-4×44\times4
+North Carolina up into \(4\times4\)
 rough rectangles. Just to see how this works, let us map these rough
 rectangles before proceeding further.

 
@@ -614,11 +605,10 @@ 
Exploration and modelling of the
 nboth <- length(table(unclass(nc$both)))

 
 if (tmap4) {
-  tm_shape(nc) + tm_polygons(fill="both", fill.scale=tm_scale(values="brewer.set1"), fill.legend = tm_legend("rough\nrectangles", frame=FALSE, item.r = 0, position = tm_pos_out("right", "center")), lwd=0.01) + tm_layout(component.autoscale=FALSE)
+  tm_shape(nc) + tm_polygons(fill="both", fill.scale=tm_scale(values="brewer.set1"), fill.legend = tm_legend("rough\nrectangles", frame=FALSE, item.r = 0, position = tm_pos_out("right", "center")), lwd=0.01) + tm_layout(component.autoscale=FALSE)
 } else {
-tm_shape(nc) + tm_fill("both", palette="Set1", title="rough\nrectangles") + tm_layout(legend.outside=TRUE)
+tm_shape(nc) + tm_fill("both", palette="Set1", title="rough\nrectangles") + tm_layout(legend.outside=TRUE)
 }

-

 
Cressie constructs a transformed SIDS rates variable, 1974–78, for
 his analyses (with co-workers). We can replicate his stem-and-leaf
 figure on p. 396 in the book, taken from Cressie
@@ -703,14 +693,13 @@ 
Median polish smoothingnc$mp_resid <- nc$ft.SID74 - nc$pred

 
 if (tmap4) {
-  out1 <- tm_shape(nc) + tm_polygons(fill=c("ft.SID74", "pred"), fill.scale=tm_scale(values="brewer.yl_or_br"), fill.legend=tm_legend(position=tm_pos_out("right", "center"), frame=FALSE, item.r = 0), fill.free=FALSE, lwd=0.01) + tm_layout(panel.labels=c("Observed", "Median polish prediction"))
-  out2 <- tm_shape(nc) + tm_polygons(fill="mp_resid", fill.scale=tm_scale(values="brewer.rd_yl_gn", midpoint=0), fill.legend=tm_legend(position=tm_pos_out("right", "center"), frame=FALSE, item.r = 0), lwd=0.01)
+  out1 <- tm_shape(nc) + tm_polygons(fill=c("ft.SID74", "pred"), fill.scale=tm_scale(values="brewer.yl_or_br"), fill.legend=tm_legend(position=tm_pos_out("right", "center"), frame=FALSE, item.r = 0), fill.free=FALSE, lwd=0.01) + tm_layout(panel.labels=c("Observed", "Median polish prediction"))
+  out2 <- tm_shape(nc) + tm_polygons(fill="mp_resid", fill.scale=tm_scale(values="brewer.rd_yl_gn", midpoint=0), fill.legend=tm_legend(position=tm_pos_out("right", "center"), frame=FALSE, item.r = 0), lwd=0.01)
 } else {
-out1 <- tm_shape(nc) + tm_fill(c("ft.SID74", "pred")) + tm_facets(free.scales=FALSE) + tm_layout(panel.labels=c("Observed", "Median polish prediction"))
-out2 <- tm_shape(nc) + tm_fill("mp_resid", midpoint=0) + tm_layout(legend.outside=TRUE)
+out1 <- tm_shape(nc) + tm_fill(c("ft.SID74", "pred")) + tm_facets(free.scales=FALSE) + tm_layout(panel.labels=c("Observed", "Median polish prediction"))
+out2 <- tm_shape(nc) + tm_fill("mp_resid", midpoint=0) + tm_layout(legend.outside=TRUE)
 }
-tmap_arrange(out1, out2, ncol=1)

-

+tmap_arrange(out1, out2, ncol=1)

 
The figure shows the median polish smoothing results as three maps,
 the observed Freeman-Tukey transformed SIDS rates, the fitted smoothed
 values, and the residuals. In addition, a plot for the median polish
@@ -790,7 +779,7 @@ 
References
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     
diff --git a/docs/articles/sids_files/figure-html/poishist-1.png b/docs/articles/sids_files/figure-html/poishist-1.png
index 6e2eade2..572ef3b1 100644
Binary files a/docs/articles/sids_files/figure-html/poishist-1.png and b/docs/articles/sids_files/figure-html/poishist-1.png differ
diff --git a/docs/articles/subgraphs.html b/docs/articles/subgraphs.html
index 6cda8ea3..82a21326 100644
--- a/docs/articles/subgraphs.html
+++ b/docs/articles/subgraphs.html
@@ -10,7 +10,7 @@
 
 
 
-
+
 
 
     Skip to contents
@@ -20,7 +20,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -79,13 +79,11 @@ 
Introduction[1,N][1, N],
-where
-NN
-is the observation count. Functions taking neighbour objects as
-arguments use the zero.policy argument to guide how to
-handle no-neighbour observations.

+invalid index on \([1, N]\), where
+\(N\) is the observation count.
+Functions taking neighbour objects as arguments use the
+zero.policy argument to guide how to handle no-neighbour
+observations.

 
spdep has also had n.comp.nb to find the
 number of disjoint connected subgraphs in an nb object,
 contributed by Nicholas Lewin-Koh in 2001 and using depth-first search
@@ -125,31 +123,30 @@ 
No-neighbour observations
 library(spdep)

 
## Loading required package: spData

+
## To access larger datasets in this package, install the spDataLarge
+## package with: `install.packages('spDataLarge',
+## repos='https://nowosad.github.io/drat/', type='source')`

 
## Loading required package: sf

-
## Linking to GEOS 3.13.1, GDAL 3.11.0, PROJ 9.6.2; sf_use_s2() is TRUE

-
+
## Linking to GEOS 3.13.0, GDAL 3.10.1, PROJ 9.5.1; sf_use_s2() is TRUE

+
 args(moran.test)

 
## function (x, listw, randomisation = TRUE, zero.policy = attr(listw, 
 ##     "zero.policy"), alternative = "greater", rank = FALSE, na.action = na.fail, 
 ##     spChk = NULL, adjust.n = TRUE, drop.EI2 = FALSE) 
 ## NULL

-
If observation
-ii
-has no neighbours, its weights sum
-∑j=1Nwij=0\sum_{j=1}^N w_{ij} = 0,
-as
-wij=0,∀jw_{ij} = 0, \forall j
-(see discussion in Bivand and Portnov
+
If observation \(i\) has no
+neighbours, its weights sum \(\sum_{j=1}^N
+w_{ij} = 0\), as \(w_{ij} = 0, \forall
+j\) (see discussion in Bivand and Portnov
 (2004)). Its eigenvalue will also be zero, with consequences for
 analytical inference:

-
+
 eigen(0)$values

 
## [1] 0

 
The adjust.n argument to measures of spatial
 autocorrelation is by default TRUE, and subtracts the count of singleton
-nodes from
-NN
-in an attempt to acknowledge the reduction in information available.

+nodes from \(N\) in an attempt to
+acknowledge the reduction in information available.

 
This discussion will address problems arising when analysing
 areal/lattice data, and neighbours are defined as polygon features with
 contiguous boundaries. One way in which no-neighbour observations may
@@ -158,7 +155,7 @@ 
No-neighbour observations
-
+
 GDAL37 <- numeric_version(unname(sf::sf_extSoftVersion()["GDAL"]), strict=FALSE)
 (GDAL37 <- ifelse(is.na(GDAL37), FALSE, GDAL37 >= "3.7.0"))

 
## [1] TRUE

@@ -168,7 +165,7 @@ 
No-neighbour observationshttps://electionresults.parliament.uk/countries/1, (https://www.nationalarchives.gov.uk/doc/open-government-licence/version/3/).
 Here, the subset for Wales is useful as we will see:

-
+
 file <- "etc/shapes/GB_2024_Wales_50m.gpkg.zip"
 zipfile <- system.file(file, package="spdep")
 if (GDAL37) {
@@ -180,14 +177,14 @@ 
No-neighbour observations    w50m <- st_read(target)
 }

 
## Reading layer `GB_2024_Wales_50m' from data source 
-##   `/tmp/Rtmp5vVziX/temp_libpath224d25059ed81/spdep/etc/shapes/GB_2024_Wales_50m.gpkg.zip' 
+##   `C:\Users\rzomor2\AppData\Local\Temp\RtmpErQTm3\temp_libpath1a5cde63ff3\spdep\etc\shapes\GB_2024_Wales_50m.gpkg.zip' 
 ##   using driver `GPKG'
 ## Simple feature collection with 32 features and 19 fields
 ## Geometry type: MULTIPOLYGON
 ## Dimension:     XY
 ## Bounding box:  xmin: 146597.1 ymin: 164536.5 xmax: 355287 ymax: 395993.5
 ## Projected CRS: OSGB36 / British National Grid

-
+
 (nb_W_50m <- poly2nb(w50m, row.names=as.character(w50m$Constituency)))

 
## Warning in poly2nb(w50m, row.names = as.character(w50m$Constituency)): some observations have no neighbours;
 ## if this seems unexpected, try increasing the snap argument.

@@ -203,7 +200,7 @@ 
No-neighbour observations## 2 disjoint connected subgraphs

 
The two subgraphs are the singleton Ynys Môn and all the other 31
 constituencies:

-
+
 table(table(attr(nb_W_50m, "ncomp")$comp.id))

 
## 
 ##  1 31 
@@ -213,7 +210,7 @@ 
No-neighbour observationscard, filling the polygon. The right map shows the location
 of the island, known in English as Anglesey, north-west of the Welsh
 mainland, and with no neighbour links:

-
+
 ynys_mon <- w50m$Constituency == "Ynys Môn"
 pts <- st_point_on_surface(st_geometry(w50m))
 opar <- par(mfrow=c(1, 2))
@@ -223,13 +220,13 @@ 
No-neighbour observationsplot(st_geometry(w50m), border="grey75")
 plot(nb_W_50m, pts, add=TRUE)

 

-
+
 par(opar)

 
From the maps, we can see that the island is close to two
 constituencies across the Afon Menai (Menai Strait in English), the
 three simplified polygons being less than 280m apart, measured between
 polygon boundaries:

-
+
 dym <- c(st_distance(w50m[ynys_mon,], w50m))
 sort(dym)[1:12]

 
## Units: [m]
@@ -237,14 +234,14 @@ 
No-neighbour observations##  [7]  58146.4320  65550.2491  67696.3323  93741.9873 113007.3659 137858.1826

 
Using a snap distance of 280m, we can join the island to
 its two obvious proximate neighbours:

-
+
 (nb_W_50m_snap <- poly2nb(w50m, row.names=as.character(w50m$Constituency), snap=280))

 
## Neighbour list object:
 ## Number of regions: 32 
 ## Number of nonzero links: 140 
 ## Percentage nonzero weights: 13.67188 
 ## Average number of links: 4.375

-
+
 plot(st_geometry(w50m), border="grey75")
 plot(nb_W_50m_snap, pts, add=TRUE)

 

@@ -252,7 +249,7 @@ 
No-neighbour observationssqrt(.Machine$double.eps) 1.4901161^{-8} in all cases)
 helps. The symmetric links added are to:

-
+
 attr(nb_W_50m_snap, "region.id")[nb_W_50m_snap[[which(ynys_mon)]]]

 
## [1] "Bangor Aberconwy"   "Dwyfor Meirionnydd"

 
This is not always going to be the case, but here the strait is
@@ -266,12 +263,12 @@ 
No-neighbour observationsWe can also use the distances to pick out those neighbour candidates
 that meet our criterion of 280m, taking care not to lose the ordering
 needed to identify the correct observations:

-
+
 (meet_criterion <- sum(dym <= units::set_units(280, "m")))

 
## [1] 3

 
These candidates are the island itself, and the two neighbours across
 the Menai Strait:

-
+
 (cands <- attr(nb_W_50m, "region.id")[order(dym)[1:meet_criterion]])

 
## [1] "Ynys Môn"           "Bangor Aberconwy"   "Dwyfor Meirionnydd"

 
The addlinks1 function can be used to add both the links
@@ -279,33 +276,31 @@ 
No-neighbour observations
-
+
 (nb_W_50m_add <- addlinks1(nb_W_50m, from = cands[1], to = cands[2:meet_criterion]))

 
## Neighbour list object:
 ## Number of regions: 32 
 ## Number of nonzero links: 140 
 ## Percentage nonzero weights: 13.67188 
 ## Average number of links: 4.375

-
+
 all.equal(nb_W_50m_add, nb_W_50m_snap, check.attributes=FALSE)

 
## [1] TRUE

 
Since these constituency observations have areal support, it is not
-surprising that changing support to points and using
-kk-nearest
-neighbours does not work adequately, because the distance measurements
-are between the points representing the polygons rather than as above
-between the areal unit boundaries:

-
+surprising that changing support to points and using \(k\)-nearest neighbours does not work
+adequately, because the distance measurements are between the points
+representing the polygons rather than as above between the areal unit
+boundaries:

+
 k2 <- knn2nb(knearneigh(pts, k=2), row.names=as.character(w50m$Constituency), sym=TRUE)

 
## Warning in knn2nb(knearneigh(pts, k = 2), row.names =
 ## as.character(w50m$Constituency), : neighbour object has 2 sub-graphs

-
+
 attr(k2, "region.id")[k2[[which(ynys_mon)]]]

 
## [1] "Bangor Aberconwy" "Clwyd North"

 
Here, Clwyd North, east of Bangor Aberconwy, is given as a neighbour
 of Ynys Môn but Dwyfor Meirionnydd, west of Bangor Aberconwy, is not. In
-addition, there are two subgraphs, which still remain up to
-k=6k=6.

+addition, there are two subgraphs, which still remain up to \(k=6\).

 

 

 
Subgraphs
@@ -314,7 +309,7 @@ 
Subgraphs
+
 (k6 <- knn2nb(knearneigh(pts, k=6), row.names=as.character(w50m$Constituency), sym=TRUE))

 
## Warning in knn2nb(knearneigh(pts, k = 6), row.names =
 ## as.character(w50m$Constituency), : neighbour object has 2 sub-graphs

@@ -324,13 +319,13 @@ 
Subgraphs## Percentage nonzero weights: 23.24219 
 ## Average number of links: 7.4375 
 ## 2 disjoint connected subgraphs

-
+
 plot(st_geometry(w50m), border="grey75")
 plot(k6, pts, add=TRUE)

 

 We can show the block structure by displaying the binary spatial weights
 matrix:

-
+
 o <- order(attr(k6, "ncomp")$comp.id)
 image(t(nb2mat(k6, style="B")[o, rev(o)]), axes=FALSE, asp=1)

 

@@ -340,13 +335,13 @@ 
Subgraphsigraph::components to compute the graph components,
+uses igraph::components to compute the graph components,
 also using depth-first search. The original implementation is as fast,
 but for directed (asymmetric) graphs converts first to symmetry, while
-igraph::components can handle directed graphs without such
+igraph::components can handle directed graphs without such
 conversion (see https://github.com/r-spatial/spdep/issues/160 for
 details).

-
+
 (k6a <- knn2nb(knearneigh(pts, k=6), row.names=as.character(w50m$Constituency)))

 
## Warning in knn2nb(knearneigh(pts, k = 6), row.names =
 ## as.character(w50m$Constituency)): neighbour object has 2 sub-graphs

@@ -360,7 +355,7 @@ 
Subgraphs
+
 file <- "etc/shapes/GB_2024_southcoast_50m.gpkg.zip"
 zipfile <- system.file(file, package="spdep")
 if (GDAL37) {
@@ -372,14 +367,14 @@ 
Subgraphssc50m <- st_read(target)
 }

 
## Reading layer `GB_2024_southcoast_50m' from data source 
-##   `/tmp/Rtmp5vVziX/temp_libpath224d25059ed81/spdep/etc/shapes/GB_2024_southcoast_50m.gpkg.zip' 
+##   `C:\Users\rzomor2\AppData\Local\Temp\RtmpErQTm3\temp_libpath1a5cde63ff3\spdep\etc\shapes\GB_2024_southcoast_50m.gpkg.zip' 
 ##   using driver `GPKG'
 ## Simple feature collection with 119 features and 19 fields
 ## Geometry type: MULTIPOLYGON
 ## Dimension:     XY
 ## Bounding box:  xmin: 82643.12 ymin: 5342.9 xmax: 640301.6 ymax: 187226.2
 ## Projected CRS: OSGB36 / British National Grid

-
+
 (nb_sc_50m <- poly2nb(sc50m, row.names=as.character(sc50m$Constituency)))

 
## Warning in poly2nb(sc50m, row.names = as.character(sc50m$Constituency)): neighbour object has 2 sub-graphs;
 ## if this sub-graph count seems unexpected, try increasing the snap argument.

@@ -391,17 +386,17 @@ 
Subgraphs## 2 disjoint connected subgraphs

 
The second subgraph only has two members, who are each others’ only
 neighbours, known as a cyclical component.

-
+
 nc <- attr(nb_sc_50m, "ncomp")$comp.id
 table(nc)

 
## nc
 ##   1   2 
 ## 117   2

 
Both constituencies are on the Isle of Wight:

-
+
 (sub2 <- attr(nb_sc_50m, "region.id")[nc == 2L])

 
## [1] "Isle of Wight East" "Isle of Wight West"

-
+
 pts <- st_point_on_surface(st_geometry(sc50m))
 plot(st_geometry(sc50m), border="grey75")
 plot(st_geometry(sc50m)[nc == 2L], border="orange", lwd=2, add=TRUE)
@@ -412,31 +407,31 @@ 
SubgraphsBivand, Hauke, and Kossowski
 (2013). With row-standardised weights, the eigenvalues of this
 component are:

-
+
 1/range(eigen(cbind(c(0, 1), c(1, 0)))$values)

 
## [1] -1  1

-
+
 1/range(eigen(nb2mat(subset(nb_sc_50m, nc == 2L), style="W"))$values)

 
## [1] -1  1

 
This “takes over” the lower domain boundary, which for the whole data
 set is now the same:

-
+
 1/range(eigen(nb2mat(nb_sc_50m, style="W"))$values)

 
## [1] -1  1

 
compared to the lower domain boundary for the remainder of the study
 area:

-
+
 1/range(eigen(nb2mat(subset(nb_sc_50m, nc == 1L), style="W"))$values)

 
## [1] -1.094637  1.000000

 
This subgraph may be added to the remainder as shown above:

-
+
 iowe <- match(sub2[1], attr(nb_sc_50m, "region.id"))
 diowe <- c(st_distance(sc50m[iowe,], sc50m))
 sort(diowe)[1:12]

 
## Units: [m]
 ##  [1]     0.000     0.000  1886.833  3509.366  6693.575  6943.672  7678.999
 ##  [8]  8576.454 10579.530 12163.332 16875.920 17161.786

-
+
 ioww <- match(sub2[2], attr(nb_sc_50m, "region.id"))
 dioww <- c(st_distance(sc50m[ioww,], sc50m))
 sort(dioww)[1:12]

@@ -446,17 +441,17 @@ 
Subgraphs
+
 (meet_criterion <- sum(diowe <= units::set_units(5000, "m")))

 
## [1] 4

 
Obviously the contiguous neighbour is among them with zero distance,
 and needs to be dropped, although addlinks1 would drop the
 duplicate:

-
+
 (cands <- attr(nb_sc_50m, "region.id")[order(diowe)[1:meet_criterion]])

 
## [1] "Isle of Wight East" "Isle of Wight West" "Portsmouth South"  
 ## [4] "Gosport"

-
+
 (nb_sc_50m_iowe <- addlinks1(nb_sc_50m, from = cands[1], to = cands[3:meet_criterion]))

 
## Neighbour list object:
 ## Number of regions: 119 
@@ -466,25 +461,25 @@ 
Subgraphs
+
 (meet_criterion <- sum(dioww <= units::set_units(5000, "m")))

 
## [1] 4

 
It, does, but we need to beware of the sorting order of the zero
 self-distance and contiguous neighbour distance, where from
 is now in the second position:

-
+
 (cands <- attr(nb_sc_50m, "region.id")[order(dioww)[1:meet_criterion]])

 
## [1] "Isle of Wight East" "Isle of Wight West" "New Forest West"   
 ## [4] "New Forest East"

 
This then yields links to the north-west:

-
+
 (nb_sc_50m_iow <- addlinks1(nb_sc_50m_iowe, from = cands[2], to = cands[3:meet_criterion]))

 
## Neighbour list object:
 ## Number of regions: 119 
 ## Number of nonzero links: 538 
 ## Percentage nonzero weights: 3.799167 
 ## Average number of links: 4.521008

-
+
 pts <- st_point_on_surface(st_geometry(sc50m))
 plot(st_geometry(sc50m), border="grey75")
 plot(st_geometry(sc50m)[nc == 2L], border="orange", lwd=2, add=TRUE)
@@ -501,13 +496,13 @@ 
Per-session control of functi
 argument to many methods and functions was NULL. If the
 value was NULL, zero.policy would be set from
 get.ZeroPolicyOption:

-
+
 
## [1] FALSE

 
On loading spdep, the internal option is set to
 FALSE, so functions and methods using
 zero.policy need to choose how to handle islands:

-
+
 try(nb2listw(nb_W_50m))

 
## Error in nb2listw(nb_W_50m) : 
 ##   Empty neighbour sets found (zero.policy: FALSE)

@@ -516,12 +511,12 @@ 
Per-session control of functi
 the user wishes to override the default,
 set.ZeroPolicyOption may be used to set a different
 per-session default:

-
 
+
 
## [1] TRUE

-
+
 (lw <- nb2listw(nb_W_50m))

 
## Characteristics of weights list object:
 ## Neighbour list object:
@@ -537,10 +532,10 @@ 
Per-session control of functi
 ## Weights constants summary:
 ##    n  nn S0       S1      S2
 ## W 31 961 31 15.36355 129.051

-
+
 attr(lw, "zero.policy")

 
## [1] TRUE

-
+
 
When a listw object is created with
 zero.policy set to TRUE, this choice is added
@@ -553,13 +548,13 @@ 
Per-session control of functi
 
Other internal options have been introduced to suppress no-neighbour
 and subgraph warnings when creating nb objects. The default
 values are as follows:

-
+
 
## [1] TRUE

-
+
 
## [1] TRUE

-
+
 
## [1] 100000

 
get.NoNeighbourOption controls the issuing of warnings
@@ -580,7 +575,7 @@ 
Per-session control of functi
 creation of training and test data sets. Here the Welsh constituency
 boundaries will be used to show the behaviour of the internal
 options:

-
+
 set.NoNeighbourOption(FALSE)
 (nb_W_50mz <- poly2nb(w50m, row.names=as.character(w50m$Constituency)))

 
## Warning in poly2nb(w50m, row.names = as.character(w50m$Constituency)): neighbour object has 2 sub-graphs;
@@ -594,7 +589,7 @@ 
Per-session control of functi
 ## Ynys Môn
 ## 2 disjoint connected subgraphs

 
Turning both off removes the warnings:

-
+
 set.SubgraphOption(FALSE)
 (nb_W_50my <- poly2nb(w50m, row.names=as.character(w50m$Constituency)))

 
## Neighbour list object:
@@ -606,12 +601,12 @@ 
Per-session control of functi
 ## Ynys Môn

 
When get.SubgraphOption is FALSE, the attribute
 containing the output of n.comp.nb is not added:

-
+
 str(attr(nb_W_50my, "ncomp"))

 
##  NULL

 
The reduction of the ceiling to below node count 32 plus edge count
 136 also supresses the calculation of graph components:

-
+
 set.SubgraphOption(TRUE)
 set.SubgraphCeiling(100L)
 (nb_W_50mx <- poly2nb(w50m, row.names=as.character(w50m$Constituency)))

@@ -622,11 +617,11 @@ 
Per-session control of functi
 ## Average number of links: 4.25 
 ## 1 region with no links:
 ## Ynys Môn

-
+
 str(attr(nb_W_50mx, "ncomp"))

 
##  NULL

 
Restoring the remaining default values:

-
@@ -643,7 +638,7 @@ 
Unintentional disconnected graphs
-
+
 file <- "etc/shapes/tokyo.gpkg.zip"
 zipfile <- system.file(file, package="spdep")
 if (GDAL37) {
@@ -655,7 +650,7 @@ 
Unintentional disconnected graphs    tokyo <- st_read(target)
 }

 
## Reading layer `tokyo' from data source 
-##   `/tmp/Rtmp5vVziX/temp_libpath224d25059ed81/spdep/etc/shapes/tokyo.gpkg.zip' 
+##   `C:\Users\rzomor2\AppData\Local\Temp\RtmpErQTm3\temp_libpath1a5cde63ff3\spdep\etc\shapes\tokyo.gpkg.zip' 
 ##   using driver `GPKG'
 ## Simple feature collection with 262 features and 3 fields
 ## Geometry type: MULTIPOLYGON
@@ -663,15 +658,15 @@ 
Unintentional disconnected graphs## Bounding box:  xmin: 266206.6 ymin: -90932.11 xmax: 411400.3 ymax: 37142.75
 ## Projected CRS: Tokyo / Japan Plane Rectangular CS VI

 
After correcting invalid polygons:

-
+
 
## [1] TRUE

-
+
 tokyo <- st_make_valid(tokyo)

 
applying poly2nb with the legacy default snap value
 produced numerous singleton observations as well as many
 multiple-observation subgraphs:

-
+
 (nb_t0 <- poly2nb(tokyo, snap=sqrt(.Machine$double.eps)))

 
## Warning in poly2nb(tokyo, snap = sqrt(.Machine$double.eps)): some observations have no neighbours;
 ## if this seems unexpected, try increasing the snap argument.

@@ -688,38 +683,38 @@ 
Unintentional disconnected graphsThe legacy default snap value when the coordinates are
 measured in metres was 15 nanometres, which effectively assumed that the
 coordinates making up polygon boundaries were identical:

-
+
 units::set_units(units::set_units(attr(nb_t0, "snap"), "m"), "nm")

 
## 14.90116 [nm]

 
Stepping out a little to 2mm, the lack of contact ceased to be a
 problem.

-
+
 (nb_t1 <- poly2nb(tokyo, snap=0.002))

 
## Neighbour list object:
 ## Number of regions: 262 
 ## Number of nonzero links: 1390 
 ## Percentage nonzero weights: 2.02494 
 ## Average number of links: 5.305344

-
+
 units::set_units(units::set_units(attr(nb_t1, "snap"), "m"), "mm")

 
## 2 [mm]

 
On that basis, the default was changed from spdep 1.3-6
 to 10mm for projected polygons, and the snap value used was returned as
 an attribute of the neighbour object:

-
+
 (nb_t2 <- poly2nb(tokyo))

 
## Neighbour list object:
 ## Number of regions: 262 
 ## Number of nonzero links: 1390 
 ## Percentage nonzero weights: 2.02494 
 ## Average number of links: 5.305344

-
+
 units::set_units(units::set_units(attr(nb_t2, "snap"), "m"), "mm")

 
## 10 [mm]

 
Where the polygons are represented by geographical (spherical)
 coordinates, the new default from spdep 1.3-6 is set to a
 value mimicking 10mm:

-
+
 (nb_t3 <- poly2nb(st_transform(tokyo, "OGC:CRS84")))

 
## Neighbour list object:
 ## Number of regions: 262 
@@ -728,12 +723,12 @@ 
Unintentional disconnected graphs## Average number of links: 5.099237

 
The default snap value used in poly2nb when
 the polygons are expressed in decimal degrees is:

-
+
 attr(nb_t3, "snap")

 
## [1] 9e-08

 
This was set based on the apparent “size” of 10mm in decimal
 degrees:

-
+
 (180 * 0.01) / (pi * 6378137)

 
## [1] 8.983153e-08

 

@@ -780,7 +775,7 @@ 
References
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     
diff --git a/docs/articles/subgraphs_files/figure-html/unnamed-chunk-10-1.png b/docs/articles/subgraphs_files/figure-html/unnamed-chunk-10-1.png
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diff --git a/docs/articles/subgraphs_files/figure-html/unnamed-chunk-7-1.png b/docs/articles/subgraphs_files/figure-html/unnamed-chunk-7-1.png
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diff --git a/docs/authors.html b/docs/authors.html
index a4ed4fad..f23fca8c 100644
--- a/docs/authors.html
+++ b/docs/authors.html
@@ -1,5 +1,5 @@
 
-Authors and Citation • spdep
+Authors and Citation • spdep
     Skip to contents
 
 
@@ -7,7 +7,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -250,7 +250,7 @@ 
Citation

 

 
 

-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/deps/MathJax-3.2.2/tex-chtml.min.js b/docs/deps/MathJax-3.2.2/tex-chtml.min.js
new file mode 100644
index 00000000..043aa25b
--- /dev/null
+++ b/docs/deps/MathJax-3.2.2/tex-chtml.min.js
@@ -0,0 +1,3 @@
+!function(){"use strict";var __webpack_modules__={351:function(t,e,r){var n,o,a=this&&this.__extends||(n=function(t,e){return(n=Object.setPrototypeOf||{__proto__:[]}instanceof Array&&function(t,e){t.__proto__=e}||function(t,e){for(var r in e)Object.prototype.hasOwnProperty.call(e,r)&&(t[r]=e[r])})(t,e)},function(t,e){if("function"!=typeof e&&null!==e)throw new TypeError("Class extends value "+String(e)+" is not a constructor or null");function r(){this.constructor=t}n(t,e),t.prototype=null===e?Object.create(e):(r.prototype=e.prototype,new r)}),s=this&&this.__assign||function(){return(s=Object.assign||function(t){for(var e,r=1,n=arguments.length;r=t.length?void 0:t)&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")},p=(Object.defineProperty(e,"__esModule",{value:!0}),e.AssistiveMmlHandler=e.AssistiveMmlMathDocumentMixin=e.AssistiveMmlMathItemMixin=e.LimitedMmlVisitor=void 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0,r(6469)),l=r(505),c=r(5884);e.DirectionVH=((r={})[1]="v",r[2]="h",r),e.CommonMoMixin=function(t){return o(e,n=t),e.prototype.computeBBox=function(t,e){void 0===e&&(e=!1),this.protoBBox(t),this.node.attributes.get("symmetric")&&2!==this.stretch.dir&&(e=this.getCenterOffset(t),t.h+=e,t.d-=e),this.node.getProperty("mathaccent")&&(0===this.stretch.dir||0<=this.size)&&(t.w=0)},e.prototype.protoBBox=function(t){var e=0!==this.stretch.dir;e&&null===this.size&&this.getStretchedVariant([0]),e&&this.size<0||(n.prototype.computeBBox.call(this,t),this.copySkewIC(t))},e.prototype.getAccentOffset=function(){var t=a.BBox.empty();return this.protoBBox(t),-t.w/2},e.prototype.getCenterOffset=function(t){return(t=void 0===t?null:t)||(t=a.BBox.empty(),n.prototype.computeBBox.call(this,t)),(t.h+t.d)/2+this.font.params.axis_height-t.h},e.prototype.getVariant=function(){this.node.attributes.get("largeop")?this.variant=this.node.attributes.get("displaystyle")?"-largeop":"-smallop":this.node.attributes.getExplicit("mathvariant")||!1!==this.node.getProperty("pseudoscript")?n.prototype.getVariant.call(this):this.variant="-tex-variant"},e.prototype.canStretch=function(t){if(0!==this.stretch.dir)return this.stretch.dir===t;if(!this.node.attributes.get("stretchy"))return!1;var e=this.getText();if(1!==Array.from(e).length)return!1;e=this.font.getDelimiter(e.codePointAt(0));return this.stretch=e&&e.dir===t?e:c.NOSTRETCH,0!==this.stretch.dir},e.prototype.getStretchedVariant=function(t,e){var r,n;if(void 0===e&&(e=!1),0!==this.stretch.dir){var o=this.getWH(t),i=this.getSize("minsize",0),a=this.getSize("maxsize",1/0),s=this.node.getProperty("mathaccent"),o=Math.max(i,Math.min(a,o)),a=this.font.params.delimiterfactor/1e3,l=this.font.params.delimitershortfall,c=i||e?o:s?Math.min(o/a,o+l):Math.max(o*a,o-l),u=this.stretch,p=u.c||this.getText().codePointAt(0),h=0;if(u.sizes)try{for(var d=y(u.sizes),f=d.next();!f.done;f=d.next()){if(f.value>=c)return s&&h&&h--,this.variant=this.font.getSizeVariant(p,h),this.size=h,void(u.schar&&u.schar[h]&&(this.stretch=m(m({},this.stretch),{c:u.schar[h]})));h++}}catch(t){r={error:t}}finally{try{f&&!f.done&&(n=d.return)&&n.call(d)}finally{if(r)throw r.error}}u.stretch?(this.size=-1,this.invalidateBBox(),this.getStretchBBox(t,this.checkExtendedHeight(o,u),u)):(this.variant=this.font.getSizeVariant(p,h-1),this.size=h-1)}},e.prototype.getSize=function(t,e){var r=this.node.attributes;return e=r.isSet(t)?this.length2em(r.get(t),1,1):e},e.prototype.getWH=function(t){if(0===t.length)return 0;if(1===t.length)return t[0];var t=s(t,2),e=t[0],t=t[1],r=this.font.params.axis_height;return this.node.attributes.get("symmetric")?2*Math.max(e-r,t+r):e+t},e.prototype.getStretchBBox=function(t,e,r){r.hasOwnProperty("min")&&r.min>e&&(e=r.min);var n=s(r.HDW,3),o=n[0],i=n[1],n=n[2];1===this.stretch.dir?(o=(t=s(this.getBaseline(t,e,r),2))[0],i=t[1]):n=e,this.bbox.h=o,this.bbox.d=i,this.bbox.w=n},e.prototype.getBaseline=function(t,e,r){var n=2===t.length&&t[0]+t[1]===e,o=this.node.attributes.get("symmetric"),t=s(n?t:[e,0],2),e=t[0],t=t[1],i=s([e+t,0],2),a=i[0],i=i[1];return i=o?(o=this.font.params.axis_height,(a=n?2*Math.max(e-o,t+o):a)/2-o):n?t:(o=(e=s(r.HDW||[.75,.25],2))[0],(n=e[1])*(a/(o+n))),[a-i,i]},e.prototype.checkExtendedHeight=function(t,e){var r;return e.fullExt&&(r=(e=s(e.fullExt,2))[0],t=(e=e[1])+Math.ceil(Math.max(0,t-e)/r)*r),t},e.prototype.remapChars=function(t){var e=this.node.getProperty("primes");return e?(0,l.unicodeChars)(e):(1===t.length&&(e=this.node.coreParent().parent,e=this.isAccent&&!e.isKind("mrow")?"accent":"mo",(e=this.font.getRemappedChar(e,t[0]))&&(t=this.unicodeChars(e,this.variant))),t)},e;function e(){for(var t=[],e=0;e=t.length?void 0:t)&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")},u=(Object.defineProperty(e,"__esModule",{value:!0}),e.CommonInferredMrowMixin=e.CommonMrowMixin=void 0,r(6469));e.CommonMrowMixin=function(t){return o(e,s=t),Object.defineProperty(e.prototype,"fixesPWidth",{get:function(){return!1},enumerable:!1,configurable:!0}),e.prototype.stretchChildren=function(){var t,e,r,n,o,i,a=[];try{for(var s=x(this.childNodes),l=s.next();!l.done;l=s.next())(S=l.value).canStretch(1)&&a.push(S)}catch(e){t={error:e}}finally{try{l&&!l.done&&(e=s.return)&&e.call(s)}finally{if(t)throw t.error}}var c=a.length,u=this.childNodes.length;if(c&&1p&&(p=g),(b*=v)>h&&(h=b))}}catch(t){r={error:t}}finally{try{m&&!m.done&&(n=f.return)&&n.call(f)}finally{if(r)throw r.error}}try{for(var S,O=x(a),M=O.next();!M.done;M=O.next())(S=M.value).coreMO().getStretchedVariant([p,h])}catch(t){o={error:t}}finally{try{M&&!M.done&&(i=O.return)&&i.call(O)}finally{if(o)throw o.error}}}},e;function e(){for(var e,t,r=[],n=0;nthis.surdH?(t.h+t.d-(this.surdH-2*e-r/2))/2:e+r/4]},e.prototype.getRootDimens=function(t,e){return[0,0,0,0]},e;function e(){for(var t=[],e=0;e=t.length?void 0:t)&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")},s=(Object.defineProperty(e,"__esModule",{value:!0}),e.CommonMtableMixin=void 0,r(6469)),l=r(505),u=r(7875);e.CommonMtableMixin=function(t){return i(e,o=t),Object.defineProperty(e.prototype,"tableRows",{get:function(){return this.childNodes},enumerable:!1,configurable:!0}),e.prototype.findContainer=function(){for(var t=this,e=t.parent;e&&(e.node.notParent||e.node.isKind("mrow"));)e=(t=e).parent;this.container=e,this.containerI=t.node.childPosition()},e.prototype.getPercentageWidth=function(){var t;this.hasLabels?this.bbox.pwidth=s.BBox.fullWidth:(t=this.node.attributes.get("width"),(0,l.isPercent)(t)&&(this.bbox.pwidth=t))},e.prototype.stretchRows=function(){for(var t=this.node.attributes.get("equalrows"),e=t?this.getEqualRowHeight():0,r=t?this.getTableData():{H:[0],D:[0]},n=r.H,o=r.D,i=this.tableRows,a=0;ao[r]&&(o[r]=c),u>i[r]&&(i[r]=u),sa[e]&&(a[e]=l),s},e.prototype.extendHD=function(t,e,r,n){n=(n-(e[t]+r[t]))/2;n<1e-5||(e[t]+=n,r[t]+=n)},e.prototype.recordPWidthCell=function(t,e){t.childNodes[0]&&t.childNodes[0].getBBox().pwidth&&this.pwidthCells.push([t,e])},e.prototype.computeBBox=function(t,e){void 0===e&&(e=!1);var e=this.getTableData(),r=e.H,e=e.D,r=(n=this.node.attributes.get("equalrows")?(n=this.getEqualRowHeight(),(0,u.sum)([].concat(this.rLines,this.rSpace))+n*this.numRows):(0,u.sum)(r.concat(e,this.rLines,this.rSpace)),n+=2*(this.fLine+this.fSpace[1]),this.getComputedWidths()),e=(0,u.sum)(r.concat(this.cLines,this.cSpace))+2*(this.fLine+this.fSpace[0]),r=this.node.attributes.get("width"),n=("auto"!==r&&(e=Math.max(this.length2em(r,0)+2*this.fLine,e)),p(this.getBBoxHD(n),2)),o=n[0],n=n[1],o=(t.h=o,t.d=n,t.w=e,p(this.getBBoxLR(),2)),n=o[0],e=o[1];t.L=n,t.R=e,(0,l.isPercent)(r)||this.setColumnPWidths()},e.prototype.setChildPWidths=function(t,e,r){var n=this.node.attributes.get("width");if(!(0,l.isPercent)(n))return!1;this.hasLabels||(this.bbox.pwidth="",this.container.bbox.pwidth="");var o=this.bbox,i=o.w,a=o.L,o=o.R,s=this.node.attributes.get("data-width-includes-label"),n=Math.max(i,this.length2em(n,Math.max(e,a+i+o)))-(s?a+o:0),e=this.node.attributes.get("equalcolumns")?Array(this.numCols).fill(this.percent(1/Math.max(1,this.numCols))):this.getColumnAttributes("columnwidth",0),s=(this.cWidths=this.getColumnWidthsFixed(e,n),this.getComputedWidths());return this.pWidth=(0,u.sum)(s.concat(this.cLines,this.cSpace))+2*(this.fLine+this.fSpace[0]),this.isTop&&(this.bbox.w=this.pWidth),this.setColumnPWidths(),this.pWidth!==i&&this.parent.invalidateBBox(),this.pWidth!==i},e.prototype.setColumnPWidths=function(){var t,e,r=this.cWidths;try{for(var n=_(this.pwidthCells),o=n.next();!o.done;o=n.next()){var i=p(o.value,2),a=i[0],s=i[1];a.setChildPWidths(!1,r[s])&&(a.invalidateBBox(),a.getBBox())}}catch(e){t={error:e}}finally{try{o&&!o.done&&(e=n.return)&&e.call(n)}finally{if(t)throw t.error}}},e.prototype.getBBoxHD=function(t){var e,r=p(this.getAlignmentRow(),2),n=r[0],r=r[1];if(null===r)return{top:[0,t],center:[e=t/2,e],bottom:[t,0],baseline:[e,e],axis:[e+(o=this.font.params.axis_height),e-o]}[n]||[e,e];var o=this.getVerticalPosition(r,n);return[o,t-o]},e.prototype.getBBoxLR=function(){var t,e,r,n;return this.hasLabels?(t=(n=this.node.attributes).get("side"),e=(r=p(this.getPadAlignShift(t),2))[0],r=r[1],(n=this.hasLabels&&!!n.get("data-width-includes-label"))&&this.frame&&this.fSpace[0]&&(e-=this.fSpace[0]),"center"!==r||n?"left"===t?[e,0]:[0,e]:[e,e]):[0,0]},e.prototype.getPadAlignShift=function(t){var e=this.getTableData().L+this.length2em(this.node.attributes.get("minlabelspacing")),r=p(null==this.styles?["",""]:[this.styles.get("padding-left"),this.styles.get("padding-right")],2),n=r[0],r=r[1],n=((n||r)&&(e=Math.max(e,this.length2em(n||"0"),this.length2em(r||"0"))),p(this.getAlignShift(),2)),r=n[0],n=n[1];return[e,r,n=r===t?"left"===t?Math.max(e,n)-e:Math.min(-e,n)+e:n]},e.prototype.getAlignShift=function(){return this.isTop?o.prototype.getAlignShift.call(this):[this.container.getChildAlign(this.containerI),0]},e.prototype.getWidth=function(){return this.pWidth||this.getBBox().w},e.prototype.getEqualRowHeight=function(){var t=this.getTableData(),e=t.H,r=t.D,t=Array.from(e.keys()).map(function(t){return e[t]+r[t]});return Math.max.apply(Math,t)},e.prototype.getComputedWidths=function(){var e=this,r=this.getTableData().W,t=Array.from(r.keys()).map(function(t){return("number"==typeof e.cWidths[t]?e.cWidths:r)[t]});return t=this.node.attributes.get("equalcolumns")?Array(t.length).fill((0,u.max)(t)):t},e.prototype.getColumnWidths=function(){var t=this.node.attributes.get("width");if(this.node.attributes.get("equalcolumns"))return this.getEqualColumns(t);var e=this.getColumnAttributes("columnwidth",0);return"auto"===t?this.getColumnWidthsAuto(e):(0,l.isPercent)(t)?this.getColumnWidthsPercent(e):this.getColumnWidthsFixed(e,this.length2em(t))},e.prototype.getEqualColumns=function(t){var e,r=Math.max(1,this.numCols);return t="auto"===t?(e=this.getTableData().W,(0,u.max)(e)):(0,l.isPercent)(t)?this.percent(1/r):(e=(0,u.sum)([].concat(this.cLines,this.cSpace))+2*this.fSpace[0],Math.max(0,this.length2em(t)-e)/r),Array(this.numCols).fill(t)},e.prototype.getColumnWidthsAuto=function(t){var e=this;return t.map(function(t){return"auto"===t||"fit"===t?null:(0,l.isPercent)(t)?t:e.length2em(t)})},e.prototype.getColumnWidthsPercent=function(r){var n=this,o=0<=r.indexOf("fit"),i=(o?this.getTableData():{W:null}).W;return Array.from(r.keys()).map(function(t){var e=r[t];return"fit"===e?null:"auto"===e?o?i[t]:null:(0,l.isPercent)(e)?e:n.length2em(e)})},e.prototype.getColumnWidthsFixed=function(r,t){var n=this,e=Array.from(r.keys()),o=e.filter(function(t){return"fit"===r[t]}),i=e.filter(function(t){return"auto"===r[t]}),i=o.length||i.length,a=(i?this.getTableData():{W:null}).W,s=t-(0,u.sum)([].concat(this.cLines,this.cSpace))-2*this.fSpace[0],l=s,c=(e.forEach(function(t){var e=r[t];l-="fit"===e||"auto"===e?a[t]:n.length2em(e,s)}),i&&0this.numRows?null:t-1]},e.prototype.getColumnAttributes=function(t,e){var r=this.numCols-(e=void 0===e?1:e),n=this.getAttributeArray(t);if(0===n.length)return null;for(;n.lengthr&&n.splice(r),n},e.prototype.getRowAttributes=function(t,e){var r=this.numRows-(e=void 0===e?1:e),n=this.getAttributeArray(t);if(0===n.length)return null;for(;n.lengthr&&n.splice(r),n},e.prototype.getAttributeArray=function(t){var e=this.node.attributes.get(t);return e?(0,l.split)(e):[this.node.attributes.getDefault(t)]},e.prototype.addEm=function(t,e){var r=this;return void 0===e&&(e=1),t?t.map(function(t){return r.em(t/e)}):null},e.prototype.convertLengths=function(t){var e=this;return t?t.map(function(t){return e.length2em(t)}):null},e;function e(){for(var t=[],e=0;e=t.length?void 0:t)&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")};Object.defineProperty(e,"__esModule",{value:!0}),e.CommonMlabeledtrMixin=e.CommonMtrMixin=void 0,e.CommonMtrMixin=function(t){return o(e,r=t),Object.defineProperty(e.prototype,"fixesPWidth",{get:function(){return!1},enumerable:!1,configurable:!0}),Object.defineProperty(e.prototype,"numCells",{get:function(){return this.childNodes.length},enumerable:!1,configurable:!0}),Object.defineProperty(e.prototype,"labeled",{get:function(){return!1},enumerable:!1,configurable:!0}),Object.defineProperty(e.prototype,"tableCells",{get:function(){return this.childNodes},enumerable:!1,configurable:!0}),e.prototype.getChild=function(t){return this.childNodes[t]},e.prototype.getChildBBoxes=function(){return this.childNodes.map(function(t){return t.getBBox()})},e.prototype.stretchChildren=function(t){void 0===t&&(t=null);var e,r,n,o,i=[],a=this.labeled?this.childNodes.slice(1):this.childNodes;try{for(var s=M(a),l=s.next();!l.done;l=s.next())(_=l.value.childNodes[0]).canStretch(1)&&i.push(_)}catch(t){u={error:t}}finally{try{l&&!l.done&&(c=s.return)&&c.call(s)}finally{if(u)throw u.error}}var c=i.length,u=this.childNodes.length;if(c&&1=t.length?void 0:t)&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")},a=(Object.defineProperty(e,"__esModule",{value:!0}),e.CommonScriptbaseMixin=void 0,r(9007));e.CommonScriptbaseMixin=function(t){var o;return i(e,o=t),Object.defineProperty(e.prototype,"baseChild",{get:function(){return this.childNodes[this.node.base]},enumerable:!1,configurable:!0}),Object.defineProperty(e.prototype,"scriptChild",{get:function(){return this.childNodes[1]},enumerable:!1,configurable:!0}),e.prototype.getBaseCore=function(){for(var t=this.getSemanticBase()||this.childNodes[0];t&&(1===t.childNodes.length&&(t.node.isKind("mrow")||t.node.isKind("TeXAtom")&&t.node.texClass!==a.TEXCLASS.VCENTER||t.node.isKind("mstyle")||t.node.isKind("mpadded")||t.node.isKind("mphantom")||t.node.isKind("semantics"))||t.node.isKind("munderover")&&t.isMathAccent);)this.setBaseAccentsFor(t),t=t.childNodes[0];return t||(this.baseHasAccentOver=this.baseHasAccentUnder=!1),t||this.childNodes[0]},e.prototype.setBaseAccentsFor=function(t){t.node.isKind("munderover")&&(null===this.baseHasAccentOver&&(this.baseHasAccentOver=!!t.node.attributes.get("accent")),null===this.baseHasAccentUnder&&(this.baseHasAccentUnder=!!t.node.attributes.get("accentunder")))},e.prototype.getSemanticBase=function(){var t=this.node.attributes.getExplicit("data-semantic-fencepointer");return this.getBaseFence(this.baseChild,t)},e.prototype.getBaseFence=function(t,e){var r,n;if(!t||!t.node.attributes||!e)return null;if(t.node.attributes.getExplicit("data-semantic-id")===e)return t;try{for(var o=O(t.childNodes),i=o.next();!i.done;i=o.next()){var a=i.value,s=this.getBaseFence(a,e);if(s)return s}}catch(t){r={error:t}}finally{try{i&&!i.done&&(n=o.return)&&n.call(o)}finally{if(r)throw r.error}}return null},e.prototype.getBaseScale=function(){for(var t=this.baseCore,e=1;t&&t!==this;)e*=t.getOuterBBox().rscale,t=t.parent;return e},e.prototype.getBaseIc=function(){return this.baseCore.getOuterBBox().ic*this.baseScale},e.prototype.getAdjustedIc=function(){var t=this.baseCore.getOuterBBox();return(t.ic?1.05*t.ic+.05:0)*this.baseScale},e.prototype.isCharBase=function(){var t=this.baseCore;return(t.node.isKind("mo")&&null===t.size||t.node.isKind("mi")||t.node.isKind("mn"))&&1===t.bbox.rscale&&1===Array.from(t.getText()).length},e.prototype.checkLineAccents=function(){this.node.isKind("munderover")&&(this.node.isKind("mover")?this.isLineAbove=this.isLineAccent(this.scriptChild):this.node.isKind("munder")?this.isLineBelow=this.isLineAccent(this.scriptChild):(this.isLineAbove=this.isLineAccent(this.overChild),this.isLineBelow=this.isLineAccent(this.underChild)))},e.prototype.isLineAccent=function(t){t=t.coreMO().node;return t.isToken&&"―"===t.getText()},e.prototype.getBaseWidth=function(){var t=this.baseChild.getOuterBBox();return t.w*t.rscale-(this.baseRemoveIc?this.baseIc:0)+this.font.params.extra_ic},e.prototype.computeBBox=function(t,e){void 0===e&&(e=!1);var r=this.getBaseWidth(),n=y(this.getOffset(),2),o=n[0],n=n[1];t.append(this.baseChild.getOuterBBox()),t.combine(this.scriptChild.getOuterBBox(),r+o,n),t.w+=this.font.params.scriptspace,t.clean(),this.setChildPWidths(e)},e.prototype.getOffset=function(){return[0,0]},e.prototype.baseCharZero=function(t){var e=!!this.baseCore.node.attributes.get("largeop"),r=this.baseScale;return this.baseIsChar&&!e&&1===r?0:t},e.prototype.getV=function(){var t=this.baseCore.getOuterBBox(),e=this.scriptChild.getOuterBBox(),r=this.font.params,n=this.length2em(this.node.attributes.get("subscriptshift"),r.sub1);return Math.max(this.baseCharZero(t.d*this.baseScale+r.sub_drop*e.rscale),n,e.h*e.rscale-.8*r.x_height)},e.prototype.getU=function(){var t=this.baseCore.getOuterBBox(),e=this.scriptChild.getOuterBBox(),r=this.font.params,n=this.node.attributes.getList("displaystyle","superscriptshift"),o=this.node.getProperty("texprimestyle")?r.sup3:n.displaystyle?r.sup1:r.sup2,n=this.length2em(n.superscriptshift,o);return Math.max(this.baseCharZero(t.h*this.baseScale-r.sup_drop*e.rscale),n,e.d*e.rscale+.25*r.x_height)},e.prototype.hasMovableLimits=function(){var t=this.node.attributes.get("displaystyle"),e=this.baseChild.coreMO().node;return!t&&!!e.attributes.get("movablelimits")},e.prototype.getOverKU=function(t,e){var r=this.node.attributes.get("accent"),n=this.font.params,e=e.d*e.rscale,o=n.rule_thickness*n.separation_factor,i=this.baseHasAccentOver?o:0,o=this.isLineAbove?3*n.rule_thickness:o,r=(r?o:Math.max(n.big_op_spacing1,n.big_op_spacing3-Math.max(0,e)))-i;return[r,t.h*t.rscale+r+e]},e.prototype.getUnderKV=function(t,e){var r=this.node.attributes.get("accentunder"),n=this.font.params,e=e.h*e.rscale,o=n.rule_thickness*n.separation_factor,i=this.baseHasAccentUnder?o:0,o=this.isLineBelow?3*n.rule_thickness:o,r=(r?o:Math.max(n.big_op_spacing2,n.big_op_spacing4-e))-i;return[r,-(t.d*t.rscale+r+e)]},e.prototype.getDeltaW=function(e,t){void 0===t&&(t=[0,0,0]);var r,n,o,i,a=this.node.attributes.get("align"),s=e.map(function(t){return t.w*t.rscale}),l=(s[0]-=this.baseRemoveIc&&!this.baseCore.node.attributes.get("largeop")?this.baseIc:0,Math.max.apply(Math,g([],y(s),!1))),c=[],u=0;try{for(var p=O(s.keys()),h=p.next();!h.done;h=p.next()){var d=h.value;c[d]=("center"===a?(l-s[d])/2:"right"===a?l-s[d]:0)+t[d],c[d]=t.length?void 0:t)&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")},u=this&&this.__read||function(t,e){var r="function"==typeof Symbol&&t[Symbol.iterator];if(!r)return t;var n,o,i=r.call(t),a=[];try{for(;(void 0===e||0=t.length?void 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MathJax is a JavaScript library that allows page"," authors to include mathematics within their web pages."," As a reader, you don't need to do anything to make that happen.
","
Browsers: MathJax works with all modern browsers including"," Edge, Firefox, Chrome, Safari, Opera, and most mobile browsers.
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Copy to Clipboard: These options copy the formula's source markup,"," as MathML or in its original format, to the clipboard"," (in browsers that support that).
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Accessibility: MathJax can work with screen"," readers to make mathematics accessible to the visually impaired."," Turn on the explorer to enable generation of speech strings"," and the ability to investigate expressions interactively.
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Language: This menu lets you select the language used by MathJax"," for its menus and warning messages. (Not yet implemented in version 3.)
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","
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","
Preferences: MathJax uses your browser's localStorage database"," to save the preferences set via this menu locally in your browser.  These"," are not used to track you, and are not transferred or used remotely by"," MathJax in any way.
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r.copyOriginal()}),this.submenu("Annotation","Annotation")]),this.rule(),this.submenu("Settings","Math Settings",[this.submenu("Renderer","Math Renderer",this.radioGroup("renderer",[["CHTML"],["SVG"]])),this.rule(),this.submenu("ZoomTrigger","Zoom Trigger",[this.command("ZoomNow","Zoom Once Now",function(){return r.zoom(null,"",r.menu.mathItem)}),this.rule(),this.radioGroup("zoom",[["Click"],["DoubleClick","Double-Click"],["NoZoom","No Zoom"]]),this.rule(),this.label("TriggerRequires","Trigger Requires:"),this.checkbox(v?"Option":"Alt",v?"Option":"Alt","alt"),this.checkbox("Command","Command","cmd",{hidden:!v}),this.checkbox("Control","Control","ctrl",{hiddne:v}),this.checkbox("Shift","Shift","shift")]),this.submenu("ZoomFactor","Zoom Factor",this.radioGroup("zscale",[["150%"],["175%"],["200%"],["250%"],["300%"],["400%"]])),this.rule(),this.command("Scale","Scale All Math...",function(){return r.scaleAllMath()}),this.rule(),this.checkbox("texHints","Add TeX hints to MathML","texHints"),this.checkbox("semantics","Add original as annotation","semantics"),this.rule(),this.command("Reset","Reset to defaults",function(){return r.resetDefaults()})]),this.submenu("Accessibility","Accessibility",[this.checkbox("Activate","Activate","explorer"),this.submenu("Speech","Speech",[this.checkbox("Speech","Speech Output","speech"),this.checkbox("Subtitles","Speech Subtitles","subtitles"),this.checkbox("Braille","Braille Output","braille"),this.checkbox("View Braille","Braille Subtitles","viewBraille"),this.rule(),this.submenu("A11yLanguage","Language"),this.rule(),this.submenu("Mathspeak","Mathspeak Rules",this.radioGroup("speechRules",[["mathspeak-default","Verbose"],["mathspeak-brief","Brief"],["mathspeak-sbrief","Superbrief"]])),this.submenu("Clearspeak","Clearspeak Rules",this.radioGroup("speechRules",[["clearspeak-default","Auto"]])),this.submenu("ChromeVox","ChromeVox Rules",this.radioGroup("speechRules",[["chromevox-default","Standard"],["chromevox-alternative","Alternative"]]))]),this.submenu("Highlight","Highlight",[this.submenu("Background","Background",this.radioGroup("backgroundColor",[["Blue"],["Red"],["Green"],["Yellow"],["Cyan"],["Magenta"],["White"],["Black"]])),{type:"slider",variable:"backgroundOpacity",content:" "},this.submenu("Foreground","Foreground",this.radioGroup("foregroundColor",[["Black"],["White"],["Magenta"],["Cyan"],["Yellow"],["Green"],["Red"],["Blue"]])),{type:"slider",variable:"foregroundOpacity",content:" "},this.rule(),this.radioGroup("highlight",[["None"],["Hover"],["Flame"]]),this.rule(),this.checkbox("TreeColoring","Tree Coloring","treeColoring")]),this.submenu("Magnification","Magnification",[this.radioGroup("magnification",[["None"],["Keyboard"],["Mouse"]]),this.rule(),this.radioGroup("magnify",[["200%"],["300%"],["400%"],["500%"]])]),this.submenu("Semantic Info","Semantic Info",[this.checkbox("Type","Type","infoType"),this.checkbox("Role","Role","infoRole"),this.checkbox("Prefix","Prefix","infoPrefix")],!0),this.rule(),this.checkbox("Collapsible","Collapsible Math","collapsible"),this.checkbox("AutoCollapse","Auto Collapse","autocollapse",{disabled:!0}),this.rule(),this.checkbox("InTabOrder","Include in Tab Order","inTabOrder"),this.checkbox("AssistiveMml","Include Hidden MathML","assistiveMml")]),this.submenu("Language","Language"),this.rule(),this.command("About","About MathJax",function(){return r.about.post()}),this.command("Help","MathJax Help",function(){return r.help.post()})]}),this.menu);this.about.attachMenu(t),this.help.attachMenu(t),this.originalText.attachMenu(t),this.annotationText.attachMenu(t),this.mathmlCode.attachMenu(t),this.zoomBox.attachMenu(t),this.checkLoadableItems(),this.enableExplorerItems(this.settings.explorer),t.showAnnotation=this.annotationText,t.copyAnnotation=this.copyAnnotation.bind(this),t.annotationTypes=this.options.annotationTypes,y.CssStyles.addInfoStyles(this.document.document),y.CssStyles.addMenuStyles(this.document.document)},_.prototype.checkLoadableItems=function(){var t,e;if(b&&b._&&b.loader&&b.startup)!this.settings.collapsible||b._.a11y&&b._.a11y.complexity||this.loadA11y("complexity"),!this.settings.explorer||b._.a11y&&b._.a11y.explorer||this.loadA11y("explorer"),!this.settings.assistiveMml||b._.a11y&&b._.a11y["assistive-mml"]||this.loadA11y("assistive-mml");else{var r=this.menu;try{for(var n=u(Object.keys(this.jax)),o=n.next();!o.done;o=n.next()){var i=o.value;this.jax[i]||r.findID("Settings","Renderer",i).disable()}}catch(e){t={error:e}}finally{try{o&&!o.done&&(e=n.return)&&e.call(n)}finally{if(t)throw t.error}}r.findID("Accessibility","Activate").disable(),r.findID("Accessibility","AutoCollapse").disable(),r.findID("Accessibility","Collapsible").disable()}},_.prototype.enableExplorerItems=function(t){var e,r,n=this.menu.findID("Accessibility","Activate").menu;try{for(var o=u(n.items.slice(1)),i=o.next();!i.done;i=o.next()){var a=i.value;if(a instanceof m.Rule)break;t?a.enable():a.disable()}}catch(t){e={error:t}}finally{try{i&&!i.done&&(r=o.return)&&r.call(o)}finally{if(e)throw e.error}}},_.prototype.mergeUserSettings=function(){try{var t=localStorage.getItem(_.MENU_STORAGE);if(!t)return;Object.assign(this.settings,JSON.parse(t)),this.setA11y(this.settings)}catch(t){console.log("MathJax localStorage error: "+t.message)}},_.prototype.saveUserSettings=function(){var e,t,r={};try{for(var n=u(Object.keys(this.settings)),o=n.next();!o.done;o=n.next()){var i=o.value;this.settings[i]!==this.defaultSettings[i]&&(r[i]=this.settings[i])}}catch(t){e={error:t}}finally{try{o&&!o.done&&(t=n.return)&&t.call(n)}finally{if(e)throw e.error}}try{Object.keys(r).length?localStorage.setItem(_.MENU_STORAGE,JSON.stringify(r)):localStorage.removeItem(_.MENU_STORAGE)}catch(t){console.log("MathJax localStorage error: "+t.message)}},_.prototype.setA11y=function(t){b._.a11y&&b._.a11y.explorer&&b._.a11y.explorer_ts.setA11yOptions(this.document,t)},_.prototype.getA11y=function(t){if(b._.a11y&&b._.a11y.explorer)return(void 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t.constructors&&(t.useOutput(r,!0),t.output=t.getOutputJax(),n.jax[e]=t.output,n.setOutputJax(e))}))},_.prototype.setOutputJax=function(t){this.jax[t].setAdaptor(this.document.adaptor),this.document.outputJax=this.jax[t],this.rerender()},_.prototype.setTabOrder=function(t){this.menu.store.inTaborder(t)},_.prototype.setAssistiveMml=function(t){!(this.document.options.enableAssistiveMml=t)||b._.a11y&&b._.a11y["assistive-mml"]?this.rerender():this.loadA11y("assistive-mml")},_.prototype.setExplorer=function(t){this.enableExplorerItems(t),!(this.document.options.enableExplorer=t)||b._.a11y&&b._.a11y.explorer?this.rerender(this.settings.collapsible?c.STATE.RERENDER:c.STATE.COMPILED):this.loadA11y("explorer")},_.prototype.setCollapsible=function(t){!(this.document.options.enableComplexity=t)||b._.a11y&&b._.a11y.complexity?this.rerender(c.STATE.COMPILED):this.loadA11y("complexity")},_.prototype.scaleAllMath=function(){var t=(100*parseFloat(this.settings.scale)).toFixed(1).replace(/.0$/,""),t=prompt("Scale all mathematics (compared to surrounding text) by",t+"%");t&&(t.match(/^\s*\d+(\.\d*)?\s*%?\s*$/)?(t=parseFloat(t)/100)?this.menu.pool.lookup("scale").setValue(String(t)):alert("The scale should not be zero"):alert("The scale should be a percentage (e.g., 120%)"))},_.prototype.resetDefaults=function(){_.loading++;var e,t,r=this.menu.pool,n=this.defaultSettings;try{for(var o=u(Object.keys(this.settings)),i=o.next();!i.done;i=o.next()){var a,s=i.value,l=r.lookup(s);l?(l.setValue(n[s]),(a=l.items[0])&&a.executeCallbacks_()):this.settings[s]=n[s]}}catch(t){e={error:t}}finally{try{i&&!i.done&&(t=o.return)&&t.call(o)}finally{if(e)throw e.error}}_.loading--,this.rerender(c.STATE.COMPILED)},_.prototype.checkComponent=function(t){t=_.loadingPromises.get(t);t&&i.mathjax.retryAfter(t)},_.prototype.loadComponent=function(t,e){var r;_.loadingPromises.has(t)||(r=b.loader)&&(_.loading++,r=r.load(t).then(function(){_.loading--,_.loadingPromises.delete(t),e(),0===_.loading&&_._loadingPromise&&(_._loadingPromise=null,_._loadingOK())}).catch(function(t){_._loadingPromise?(_._loadingPromise=null,_._loadingFailed(t)):console.log(t)}),_.loadingPromises.set(t,r))},_.prototype.loadA11y=function(r){var n=this,o=!c.STATE.ENRICHED;this.loadComponent("a11y/"+r,function(){var t=b.startup,e=(i.mathjax.handlers.unregister(t.handler),t.handler=t.getHandler(),i.mathjax.handlers.register(t.handler),n.document);n.document=t.document=t.getDocument(),(n.document.menu=n).document.outputJax.reset(),n.transferMathList(e),n.document.processed=e.processed,_._loadingPromise||(n.document.outputJax.reset(),n.rerender("complexity"===r||o?c.STATE.COMPILED:c.STATE.TYPESET))})},_.prototype.transferMathList=function(t){var e,r,n=this.document.options.MathItem;try{for(var o=u(t.math),i=o.next();!i.done;i=o.next()){var a=i.value,s=new n;Object.assign(s,a),this.document.math.push(s)}}catch(t){e={error:t}}finally{try{i&&!i.done&&(r=o.return)&&r.call(o)}finally{if(e)throw e.error}}},_.prototype.formatSource=function(t){return t.trim().replace(/&/g,"&").replace(//g,">")},_.prototype.toMML=function(t){return this.MmlVisitor.visitTree(t.root,t,{texHints:this.settings.texHints,semantics:this.settings.semantics&&"MathML"!==t.inputJax.name})},_.prototype.zoom=function(t,e,r){t&&!this.isZoomEvent(t,e)||(this.menu.mathItem=r,t&&this.menu.post(t),this.zoomBox.post())},_.prototype.isZoomEvent=function(t,e){return this.settings.zoom===e&&(!this.settings.alt||t.altKey)&&(!this.settings.ctrl||t.ctrlKey)&&(!this.settings.cmd||t.metaKey)&&(!this.settings.shift||t.shiftKey)},_.prototype.rerender=function(t){void 0===t&&(t=c.STATE.TYPESET),this.rerenderStart=Math.min(t,this.rerenderStart),_.loading||(this.rerenderStart<=c.STATE.COMPILED&&this.document.reset({inputJax:[]}),this.document.rerender(this.rerenderStart),this.rerenderStart=c.STATE.LAST)},_.prototype.copyMathML=function(){this.copyToClipboard(this.toMML(this.menu.mathItem))},_.prototype.copyOriginal=function(){this.copyToClipboard(this.menu.mathItem.math.trim())},_.prototype.copyAnnotation=function(){this.copyToClipboard(this.menu.annotation.trim())},_.prototype.copyToClipboard=function(t){var e=document.createElement("textarea");e.value=t,e.setAttribute("readonly",""),e.style.cssText="height: 1px; width: 1px; padding: 1px; position: absolute; left: -10px",document.body.appendChild(e),e.select();try{document.execCommand("copy")}catch(t){alert("Can't copy to clipboard: "+t.message)}document.body.removeChild(e)},_.prototype.addMenu=function(e){var r=this,t=e.typesetRoot;t.addEventListener("contextmenu",function(){return 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t,e=0;t=this.contentNodes[e];e++)n=n.concat(t.querySelectorAll(r));return r(this)&&n.unshift(this),n}xml(o,i){function t(t,e){const r=e.map(function(t){return t.xml(o,i)}),n=o.createElementNS("",t);for(let t,e=0;t=r[e];e++)n.appendChild(t);return n}const e=o.createElementNS("",this.type);return i||this.xmlAttributes(e),e.textContent=this.textContent,0");return n.serializeXml(this.xml(e,t))}allAttributes(){const t=[];return t.push(["role",this.role]),"unknown"!==this.font&&t.push(["font",this.font]),Object.keys(this.annotation).length&&t.push(["annotation",this.xmlAnnotation()]),this.embellished&&t.push(["embellished",this.embellished]),this.fencePointer&&t.push(["fencepointer",this.fencePointer]),t.push(["id",this.id.toString()]),t}xmlAnnotation(){const e=[];for(const r in this.annotation)this.annotation[r].forEach(function(t){e.push(r+":"+t)});return e.join(";")}toJson(){const r={};r.type=this.type;var n=this.allAttributes();for(let t,e=0;t=n[e];e++)r[t[0]]=t[1].toString();return this.textContent&&(r.$t=this.textContent),this.childNodes.length&&(r.children=this.childNodes.map(function(t){return t.toJson()})),this.contentNodes.length&&(r.content=this.contentNodes.map(function(t){return t.toJson()})),r}updateContent(t,e){var e=e?t.replace(/^[ \f\n\r\t\v\u200b]*/,"").replace(/[ \f\n\r\t\v\u200b]*$/,""):t.trim();this.textContent!==(t=t&&!e?t:e)&&(e=(0,o.lookupMeaning)(t),this.textContent=t,this.role=e.role,this.type=e.type,this.font=e.font)}addMathmlNodes(r){for(let t,e=0;t=r[e];e++)-1===this.mathml.indexOf(t)&&this.mathml.push(t)}appendChild(t){this.childNodes.push(t),this.addMathmlNodes(t.mathml),t.parent=this}replaceChild(e,r){var t,n=this.childNodes.indexOf(e);-1!==n&&(e.parent=null,(r.parent=this).childNodes[n]=r,n=e.mathml.filter(function(t){return-1===r.mathml.indexOf(t)}),t=r.mathml.filter(function(t){return-1===e.mathml.indexOf(t)}),this.removeMathmlNodes(n),this.addMathmlNodes(t))}appendContentNode(t){t&&(this.contentNodes.push(t),this.addMathmlNodes(t.mathml),t.parent=this)}removeContentNode(t){t&&-1!==(t=this.contentNodes.indexOf(t))&&this.contentNodes.slice(t,1)}equals(n){if(!n)return!1;if(this.type!==n.type||this.role!==n.role||this.textContent!==n.textContent||this.childNodes.length!==n.childNodes.length||this.contentNodes.length!==n.contentNodes.length)return!1;for(let t,e,r=0;t=this.childNodes[r],e=n.childNodes[r];r++)if(!t.equals(e))return!1;for(let t,e,r=0;t=this.contentNodes[r],e=n.contentNodes[r];r++)if(!t.equals(e))return!1;return!0}displayTree(){console.info(this.displayTree_(0))}addAnnotation(t,e){e&&this.addAnnotation_(t,e)}getAnnotation(t){return this.annotation[t]||[]}hasAnnotation(t,e){const r=this.annotation[t];return!!r&&-1!==r.indexOf(e)}parseAnnotation(t){const r=t.split(";");for(let t=0,e=r.length;ti(t,"infixop")))return!1}return!0},n.isPrefixFunctionBoundary=function(t){return c(t)&&!s(t,"division")||i(t,"appl")||l(t)},n.isBigOpBoundary=function(t){return c(t)||l(t)},n.isIntegralDxBoundary=function(t,e){return!!e&&i(e,"identifier")&&r.lookupSecondary("d",t.textContent)},n.isIntegralDxBoundarySingle=function(t){var e;return!!i(t,"identifier")&&((e=t.textContent[0])&&t.textContent[1]&&r.lookupSecondary("d",e))},n.isGeneralFunctionBoundary=l,n.isEmbellished=function(t){return t.embellished||(r.isEmbellishedType(t.type)?t.type:null)},n.isOperator=c,n.isRelation=u,n.isPunctuation=p,n.isFence=h,n.isElligibleEmbellishedFence=function(t){return!(!t||!h(t))&&(!t.embellished||function t(e){return!e.embellished||!(i(e,"tensor")&&(!i(e.childNodes[1],"empty")||!i(e.childNodes[2],"empty"))&&(!i(e.childNodes[3],"empty")||!i(e.childNodes[4],"empty")))&&(!s(e,"close")||!i(e,"tensor"))&&(!s(e,"open")||!i(e,"subscript")&&!i(e,"superscript"))&&t(e.childNodes[0])}(t))},n.isTableOrMultiline=d,n.tableIsMatrixOrVector=function(t){return!!t&&f(t)&&d(t.childNodes[0])},n.isFencedElement=f,n.tableIsCases=function(t,e){return 0=r)){const o=n.childNodes[0].role;"unknown"!==o&&t.childNodes.every(function(t){t=t.childNodes[0];return!t||t.role===o&&(c.isType(t,"relation")||c.isType(t,"relseq"))})&&(t.role=o)}}static classifyTable(t){var e=y.computeColumns_(t);y.classifyByColumns_(t,e,"equality")||y.classifyByColumns_(t,e,"inequality",["equality"])||y.classifyByColumns_(t,e,"arrow")||y.detectCaleyTable(t)}static detectCaleyTable(t){if(!t.mathmlTree)return!1;const e=t.mathmlTree,r=e.getAttribute("columnlines"),n=e.getAttribute("rowlines");return!(!r||!n||!y.cayleySpacing(r)||!y.cayleySpacing(n)||(t.role="cayley",0))}static cayleySpacing(t){const e=t.split(" ");return("solid"===e[0]||"dashed"===e[0])&&e.slice(1).every(t=>"none"===t)}static proof(t,e,r){e=y.separateSemantics(e);return y.getInstance().proof(t,e,r)}static findSemantics(t,e,r){r=null==r?null:r,t=y.getSemantics(t);return!(!t||!t[e]||null!=r&&t[e]!==r)}static getSemantics(t){t=t.getAttribute("semantics");return t?y.separateSemantics(t):null}static removePrefix(t){const[,...e]=t.split("_");return e.join("_")}static separateSemantics(t){const r={};return t.split(";").forEach(function(t){var[t,e]=t.split(":");r[y.removePrefix(t)]=e}),r}static matchSpaces_(r,n){for(let t,e=0;t=n[e];e++){const n=r[e].mathmlTree,i=r[e+1].mathmlTree;var o;n&&i&&((o=n.nextSibling)&&o!==i&&(o=y.getSpacer_(o))&&(t.mathml.push(o),t.mathmlTree=o,t.role="space"))}}static getSpacer_(t){if("MSPACE"===m.tagName(t))return t;for(;u.hasEmptyTag(t)&&1===t.childNodes.length;)if(t=t.childNodes[0],"MSPACE"===m.tagName(t))return t;return null}static fenceToPunct_(t){var e=y.FENCE_TO_PUNCT_[t.role];if(e){for(;t.embellished;)t.embellished="punctuation",c.isRole(t,"subsup")||c.isRole(t,"underover")||(t.role=e),t=t.childNodes[0];t.type="punctuation",t.role=e}}static classifyFunction_(e,r){if("appl"===e.type||"bigop"===e.type||"integral"===e.type)return"";if(r[0]&&r[0].textContent===s.functionApplication()){y.getInstance().funcAppls[e.id]=r.shift();let t="simple function";return o.run("simple2prefix",e),"prefix function"!==e.role&&"limit function"!==e.role||(t=e.role),y.propagateFunctionRole_(e,t),"prefix"}return y.CLASSIFY_FUNCTION_[e.role]||(c.isSimpleFunctionHead(e)?"simple":"")}static propagateFunctionRole_(t,e){t&&"infixop"!==t.type&&(c.isRole(t,"subsup")||c.isRole(t,"underover")||(t.role=e),y.propagateFunctionRole_(t.childNodes[0],e))}static getFunctionOp_(r,n){if(n(r))return r;for(let t,e=0;t=r.childNodes[e];e++){const r=y.getFunctionOp_(t,n);if(r)return r}return null}static tableToMatrixOrVector_(t){const r=t.childNodes[0];c.isType(r,"multiline")?y.tableToVector_(t):y.tableToMatrix_(t),t.contentNodes.forEach(r.appendContentNode.bind(r));for(let t,e=0;t=r.childNodes[e];e++)y.assignRoleToRow_(t,y.getComponentRoles_(r));return r.parent=null,r}static tableToVector_(t){const e=t.childNodes[0];e.type="vector",1!==e.childNodes.length?y.binomialForm_(e):y.tableToSquare_(t)}static binomialForm_(t){c.isBinomial(t)&&(t.role="binomial",t.childNodes[0].role="binomial",t.childNodes[1].role="binomial")}static tableToMatrix_(t){const e=t.childNodes[0];e.type="matrix",e.childNodes&&0t.match(/[^\s]/)),r=e.map(s.lookupMeaning);if(r.every(function(t){return"number"===t.type&&"integer"===t.role||"punctuation"===t.type&&"comma"===t.role}))return t.role="integer",void("0"===e[0]&&t.addAnnotation("general","basenumber"));r.every(function(t){return"number"===t.type&&"integer"===t.role||"punctuation"===t.type})?t.role="float":t.role="othernumber"}}static exprFont_(t){var e;"unknown"===t.font&&(e=[...t.textContent].map(s.lookupMeaning).reduce(function(t,e){return t&&e.font&&"unknown"!==e.font&&e.font!==t?"unknown"===t?e.font:null:t},"unknown"))&&(t.font=e)}static purgeFences_(e){const r=e.rel,n=e.comp,o=[],i=[];for(;0y.isPureRelation_(t,r))||2===e.length&&(y.testColumns_(e,1,t=>y.isEndRelation_(t,r)||y.isPureRelation_(t,r))||y.testColumns_(e,0,t=>y.isEndRelation_(t,r,!0)||y.isPureRelation_(t,r))))&&(t.role=r,!0)}static isEndRelation_(t,e,r){r=r?t.childNodes.length-1:0;return c.isType(t,"relseq")&&c.isRole(t,e)&&c.isType(t.childNodes[r],"empty")}static isPureRelation_(t,e){return c.isType(t,"relation")&&c.isRole(t,e)}static computeColumns_(e){const n=[];for(let r,t=0;r=e.childNodes[t];t++)for(let t,e=0;t=r.childNodes[e];e++)n[e]?n[e].push(t):n[e]=[t];return n}static testColumns_(t,e,r){const n=t[e];return!!n&&n.some(function(t){return t.childNodes.length&&r(t.childNodes[0])})&&n.every(function(t){return!t.childNodes.length||r(t.childNodes[0])})}setNodeFactory(t){y.getInstance().factory_=t,o.updateFactory(y.getInstance().factory_)}getNodeFactory(){return y.getInstance().factory_}identifierNode(t,e,r){if("MathML-Unit"===r)t.type="identifier",t.role="unit";else if(!e&&1===t.textContent.length&&("integer"===t.role||"latinletter"===t.role||"greekletter"===t.role)&&"normal"===t.font)return t.font="italic",o.run("simpleNamedFunction",t);return"unknown"===t.type&&(t.type="identifier"),y.exprFont_(t),o.run("simpleNamedFunction",t)}implicitNode(t){if(t=y.getInstance().getMixedNumbers_(t),1===(t=y.getInstance().combineUnits_(t)).length)return t[0];t=y.getInstance().implicitNode_(t);return o.run("combine_juxtaposition",t)}text(t,e){return y.exprFont_(t),t.type="text","MS"===e?t.role="string":"MSPACE"!==e&&!t.textContent.match(/^\s*$/)||(t.role="space"),t}row(t){return 0===(t=t.filter(function(t){return!c.isType(t,"empty")})).length?y.getInstance().factory_.makeEmptyNode():(t=y.getInstance().getFencesInRow_(t),t=y.getInstance().tablesInRow(t),t=y.getInstance().getPunctuationInRow_(t),t=y.getInstance().getTextInRow_(t),t=y.getInstance().getFunctionsInRow_(t),y.getInstance().relationsInRow_(t))}limitNode(t,e){if(!e.length)return y.getInstance().factory_.makeEmptyNode();let r,n=e[0],o="unknown";if(!e[1])return n;if(c.isLimitBase(n)){var i=(r=y.MML_TO_LIMIT_[t]).length;if(o=r.type,e=e.slice(0,r.length+1),1===i&&c.isAccent(e[1])||2===i&&c.isAccent(e[1])&&c.isAccent(e[2]))return r=y.MML_TO_BOUNDS_[t],y.getInstance().accentNode_(n,e,r.type,r.length,r.accent);if(2===i){if(c.isAccent(e[1]))return n=y.getInstance().accentNode_(n,[n,e[1]],{MSUBSUP:"subscript",MUNDEROVER:"underscore"}[t],1,!0),e[2]?y.getInstance().makeLimitNode_(n,[n,e[2]],null,"limupper"):n;if(e[2]&&c.isAccent(e[2]))return n=y.getInstance().accentNode_(n,[n,e[2]],{MSUBSUP:"superscript",MUNDEROVER:"overscore"}[t],1,!0),y.getInstance().makeLimitNode_(n,[n,e[1]],null,"limlower");e[i]||(o="limlower")}return y.getInstance().makeLimitNode_(n,e,null,o)}return r=y.MML_TO_BOUNDS_[t],y.getInstance().accentNode_(n,e,r.type,r.length,r.accent)}tablesInRow(t){let r=u.partitionNodes(t,c.tableIsMatrixOrVector),n=[];for(let t,e=0;t=r.rel[e];e++)(n=n.concat(r.comp.shift())).push(y.tableToMatrixOrVector_(t));n=n.concat(r.comp.shift()),r=u.partitionNodes(n,c.isTableOrMultiline),n=[];for(let t,e=0;t=r.rel[e];e++){const o=r.comp.shift();c.tableIsCases(t,o)&&y.tableToCases_(t,o.pop()),(n=n.concat(o)).push(t)}return n.concat(r.comp.shift())}mfenced(e,r,t,n){if(t&&0{r.push(y.getInstance().factory_.makeContentNode(e())),r.push(t)}),n=r}return e&&r?y.getInstance().horizontalFencedNode_(y.getInstance().factory_.makeContentNode(e),y.getInstance().factory_.makeContentNode(r),n):(e&&n.unshift(y.getInstance().factory_.makeContentNode(e)),r&&n.push(y.getInstance().factory_.makeContentNode(r)),y.getInstance().row(n))}fractionLikeNode(t,e,r,n){let o;if(n||!u.isZeroLength(r))return o=y.getInstance().fractionNode_(t,e),n&&o.addAnnotation("general","bevelled"),o;{const r=y.getInstance().factory_.makeBranchNode("line",[t],[]),n=y.getInstance().factory_.makeBranchNode("line",[e],[]);return o=y.getInstance().factory_.makeBranchNode("multiline",[r,n],[]),y.binomialForm_(o),y.classifyMultiline(o),o}}tensor(t,e,r,n,o){const i=y.getInstance().factory_.makeBranchNode("tensor",[t,y.getInstance().scriptNode_(e,"leftsub"),y.getInstance().scriptNode_(r,"leftsuper"),y.getInstance().scriptNode_(n,"rightsub"),y.getInstance().scriptNode_(o,"rightsuper")],[]);return i.role=t.role,i.embellished=c.isEmbellished(t),i}pseudoTensor(t,e,r){var n=t=>!c.isType(t,"empty"),o=e.filter(n).length,n=r.filter(n).length;if(!o&&!n)return t;const i=o?n?"MSUBSUP":"MSUB":"MSUP",a=[t];return o&&a.push(y.getInstance().scriptNode_(e,"rightsub",!0)),n&&a.push(y.getInstance().scriptNode_(r,"rightsuper",!0)),y.getInstance().limitNode(i,a)}font(t){return y.MATHJAX_FONTS[t]||t}proof(t,e,r){if(e.inference||e.axiom||console.log("Noise"),e.axiom){const e=y.getInstance().cleanInference(t.childNodes),n=e.length?y.getInstance().factory_.makeBranchNode("inference",r(e),[]):y.getInstance().factory_.makeEmptyNode();return n.role="axiom",n.mathmlTree=t,n}const n=y.getInstance().inference(t,e,r);return e.proof&&(n.role="proof",n.childNodes[0].role="final"),n}inference(t,e,r){if(e.inferenceRule){const e=y.getInstance().getFormulas(t,[],r);return y.getInstance().factory_.makeBranchNode("inference",[e.conclusion,e.premises],[])}const n=e.labelledRule,o=m.toArray(t.childNodes),i=[],a=("left"!==n&&"both"!==n||i.push(y.getInstance().getLabel(t,o,r,"left")),"right"!==n&&"both"!==n||i.push(y.getInstance().getLabel(t,o,r,"right")),y.getInstance().getFormulas(t,o,r)),s=y.getInstance().factory_.makeBranchNode("inference",[a.conclusion,a.premises],i);return s.mathmlTree=t,s}getLabel(t,e,r,n){const o=y.getInstance().findNestedRow(e,"prooflabel",n),i=y.getInstance().factory_.makeBranchNode("rulelabel",r(m.toArray(o.childNodes)),[]);return i.role=n,i.mathmlTree=o,i}getFormulas(t,e,r){const n=e.length?y.getInstance().findNestedRow(e,"inferenceRule"):t,o="up"===y.getSemantics(n).inferenceRule,i=o?n.childNodes[1]:n.childNodes[0],a=o?n.childNodes[0]:n.childNodes[1],s=i.childNodes[0].childNodes[0],l=m.toArray(s.childNodes[0].childNodes),c=[];let u=1;for(const t of l)u%2&&c.push(t.childNodes[0]),u++;const p=r(c),h=r(m.toArray(a.childNodes[0].childNodes))[0],d=y.getInstance().factory_.makeBranchNode("premises",p,[]),f=(d.mathmlTree=s,y.getInstance().factory_.makeBranchNode("conclusion",[h],[]));return f.mathmlTree=a.childNodes[0].childNodes[0],{conclusion:f,premises:d}}findNestedRow(t,e,r){return y.getInstance().findNestedRow_(t,e,0,r)}cleanInference(t){return m.toArray(t).filter(function(t){return"MSPACE"!==m.tagName(t)})}operatorNode(t){return"unknown"===t.type&&(t.type="operator"),o.run("multioperator",t)}implicitNode_(t){const e=y.getInstance().factory_.makeMultipleContentNodes(t.length-1,s.invisibleTimes()),r=(y.matchSpaces_(t,e),y.getInstance().infixNode_(t,e[0]));return r.role="implicit",e.forEach(function(t){t.parent=r}),r.contentNodes=e,r}infixNode_(t,e){const r=y.getInstance().factory_.makeBranchNode("infixop",t,[e],u.getEmbellishedInner(e).textContent);return r.role=e.role,o.run("propagateSimpleFunction",r)}explicitMixed_(r){var n=u.partitionNodes(r,function(t){return t.textContent===s.invisiblePlus()});if(!n.rel.length)return r;let o=[];for(let t,e=0;t=n.rel[e];e++){const s=n.comp[e],i=n.comp[e+1],a=s.length-1;if(s[a]&&i[0]&&c.isType(s[a],"number")&&!c.isRole(s[a],"mixed")&&c.isType(i[0],"fraction")){const r=y.getInstance().factory_.makeBranchNode("number",[s[a],i[0]],[]);r.role="mixed",(o=o.concat(s.slice(0,a))).push(r),i.shift()}else(o=o.concat(s)).push(t)}return o.concat(n.comp[n.comp.length-1])}concatNode_(t,e,r){if(0===e.length)return t;const n=e.map(function(t){return u.getEmbellishedInner(t).textContent}).join(" "),o=y.getInstance().factory_.makeBranchNode(r,[t],e,n);return 1c.isRole(t,"subtraction"));let n=y.getInstance().concatNode_(t,r.comp.pop(),"prefixop");for(1===n.contentNodes.length&&"addition"===n.contentNodes[0].role&&"+"===n.contentNodes[0].textContent&&(n.role="positive");0c.isType(t,"text"));if(0===r.rel.length)return t;const n=[];let o=r.comp[0];0c.isRole(t,"open");if(0===t.length){const t=n.shift();for(;0{t=t.type;return"punctuation"===t||"text"===t||"operator"===t||"relation"===t},t=u.partitionNodes(r,function(t){if(!c.isPunctuation(t))return!1;if(c.isPunctuation(t)&&!c.isRole(t,"ellipsis"))return!0;t=r.indexOf(t);if(0===t)return!r[1]||!n(r[1]);var e=r[t-1];if(t===r.length-1)return!n(e);t=r[t+1];return!n(e)||!n(t)});if(0===t.rel.length)return r;const e=[];let o=t.comp.shift(),i=(0c.isRole(t,"dummy"))?r.role="text":t.every(t=>c.isRole(t,"space"))?r.role="space":r.role="sequence",r}dummyNode_(t){const e=y.getInstance().factory_.makeMultipleContentNodes(t.length-1,s.invisibleComma());return e.forEach(function(t){t.role="dummy"}),y.getInstance().punctuatedNode_(t,e)}accentRole_(t,e){if(!c.isAccent(t))return!1;var r=t.textContent,r=s.lookupSecondary("bar",r)||s.lookupSecondary("tilde",r)||t.role;return t.role="underscore"===e?"underaccent":"overaccent",t.addAnnotation("accent",r),!0}accentNode_(t,e,r,n,o){var i=(e=e.slice(0,n+1))[1],a=e[2];let s;if(!o&&a&&((s=y.getInstance().factory_.makeBranchNode("subscript",[t,i],[])).role="subsup",e=[s,a],r="superscript"),o){const n=y.getInstance().accentRole_(i,r);a&&(r=y.getInstance().accentRole_(a,"overscore")&&!n?(e=[s=y.getInstance().factory_.makeBranchNode("overscore",[t,a],[]),i],"underscore"):(e=[s=y.getInstance().factory_.makeBranchNode("underscore",[t,i],[]),a],"overscore"),s.role="underover")}return y.getInstance().makeLimitNode_(t,e,s,r)}makeLimitNode_(t,e,r,n){if("limupper"===n&&"limlower"===t.type)return t.childNodes.push(e[1]),(e[1].parent=t).type="limboth",t;if("limlower"===n&&"limupper"===t.type)return t.childNodes.splice(1,-1,e[1]),(e[1].parent=t).type="limboth",t;const o=y.getInstance().factory_.makeBranchNode(n,e,[]),i=c.isEmbellished(t);return r&&(r.embellished=i),o.embellished=i,o.role=t.role,o}getFunctionsInRow_(t,e){const r=e||[];if(0===t.length)return r;var e=t.shift(),n=y.classifyFunction_(e,t);if(!n)return r.push(e),y.getInstance().getFunctionsInRow_(t,r);t=y.getInstance().getFunctionsInRow_(t,[]),e=y.getInstance().getFunctionArgs_(e,t,n);return r.concat(e)}getFunctionArgs_(t,e,r){let n,o,i;switch(r){case"integral":{const r=y.getInstance().getIntegralArgs_(e);if(!r.intvar&&!r.integrand.length)return r.rest.unshift(t),r.rest;const n=y.getInstance().row(r.integrand);return i=y.getInstance().integralNode_(t,n,r.intvar),r.rest.unshift(i),r.rest}case"prefix":if(e[0]&&"fenced"===e[0].type){const r=e.shift();return c.isNeutralFence(r)||(r.role="leftright"),i=y.getInstance().functionNode_(t,r),e.unshift(i),e}if((n=u.sliceNodes(e,c.isPrefixFunctionBoundary)).head.length)o=y.getInstance().row(n.head),n.div&&n.tail.unshift(n.div);else{if(!n.div||!c.isType(n.div,"appl"))return e.unshift(t),e;o=n.div}return i=y.getInstance().functionNode_(t,o),n.tail.unshift(i),n.tail;case"bigop":return(n=u.sliceNodes(e,c.isBigOpBoundary)).head.length?(o=y.getInstance().row(n.head),i=y.getInstance().bigOpNode_(t,o),n.div&&n.tail.unshift(n.div),n.tail.unshift(i),n.tail):(e.unshift(t),e);default:{if(0===e.length)return[t];const r=e[0];return"fenced"===r.type&&!c.isNeutralFence(r)&&c.isSimpleFunctionScope(r)?(r.role="leftright",y.propagateFunctionRole_(t,"simple function"),i=y.getInstance().functionNode_(t,e.shift()),e.unshift(i)):e.unshift(t),e}}}getIntegralArgs_(t,e=[]){if(0===t.length)return{integrand:e,intvar:null,rest:t};const 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r=i.tagName(t);-1!==o.IGNORETAGS.indexOf(r)||-1!==o.EMPTYTAGS.indexOf(r)&&0===t.childNodes.length||n.push(t)}return n},o.isZeroLength=function(t){if(!t)return!1;if(-1!==["negativeveryverythinmathspace","negativeverythinmathspace","negativethinmathspace","negativemediummathspace","negativethickmathspace","negativeverythickmathspace","negativeveryverythickmathspace"].indexOf(t))return!0;t=t.match(/[0-9.]+/);return!!t&&0===parseFloat(t[0])},o.addAttributes=function(e,t){if(t.hasAttributes()){var r=t.attributes;for(let t=r.length-1;0<=t;t--){const n=r[t].name;n.match(/^ext/)&&(e.attributes[n]=r[t].value,e.nobreaking=!0),-1!==o.directSpeechKeys.indexOf(n)&&(e.attributes["ext-speech"]=r[t].value,e.nobreaking=!0),n.match(/texclass$/)&&(e.attributes.texclass=r[t].value),"href"===n&&(e.attributes.href=r[t].value,e.nobreaking=!0)}}},o.getEmbellishedInner=function t(e){return 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e+"/"+t}));return[["ancestor::*/following-sibling::*",r,e(i.join(" | "))].join(" and ")]},s.removeParens=function(t){if(!t.childNodes.length||!t.childNodes[0].childNodes.length||!t.childNodes[0].childNodes[0].childNodes.length)return"";const e=t.childNodes[0].childNodes[0].childNodes[0].textContent;return e.match(/^\(.+\)$/)?e.slice(1,-1):e};const S=new Map([[3,"CSFleftsuperscript"],[4,"CSFleftsubscript"],[2,"CSFbaseline"],[1,"CSFrightsubscript"],[0,"CSFrightsuperscript"]]),O=new Map([[4,2],[3,3],[2,1],[1,4],[0,5]]);s.generateTensorRules=function(i,a=!0){var e=["11111","11110","11101","11100","10111","10110","10101","10100","01111","01110","01101","01100"];for(let o,t=0;o=e[t];t++){let t="tensor"+o,[e,r,n]=function(t){const e=[];let r="",n="",o=parseInt(t,2);for(let t=0;t<5;t++){var i="children/*["+O.get(t)+"]";if(1&o){const e=S.get(t%5);r="[t] "+e+"Verbose; [n] "+i+";"+r,n="[t] "+e+"Brief; [n] "+i+";"+n}else 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1i.generateTensorRules(t,!1),CTFrelationIterator:a.relationIterator,CTFimplicitIterator:a.implicitIterator})}},7599:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.init=e.INIT_=void 0;const n=r(5425),o=r(9577),i=r(9284);e.INIT_=!1,e.init=function(){e.INIT_||((0,o.MathspeakRules)(),(0,n.ClearspeakRules)(),(0,i.PrefixRules)(),(0,i.OtherRules)(),(0,i.BrailleRules)(),e.INIT_=!0)}},7283:function(t,o,e){Object.defineProperty(o,"__esModule",{value:!0}),o.getStore=o.addStore=o.funcStore=void 0;const n=e(1676);o.funcStore=new Map,o.addStore=function(t,e,r){var n={};if(e){const t=o.funcStore.get(e)||{};Object.assign(n,t)}o.funcStore.set(t,Object.assign(n,r))},o.getStore=function(t,e,r){return o.funcStore.get([t,e,r].join("."))||o.funcStore.get([n.DynamicCstr.DEFAULT_VALUES[n.Axis.LOCALE],e,r].join("."))||o.funcStore.get([n.DynamicCstr.BASE_LOCALE,e,r].join("."))||{}}},7598:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.oneLeft=e.leftMostUnit=e.rightMostUnit=e.unitMultipliers=void 0;const o=r(7052),n=r(5274),i=r(4356),a=(e.unitMultipliers=function(t,e){const r=t;let n=0;return function(){var t=o.AuditoryDescription.create({text:s(r[n])&&l(r[n+1])?i.LOCALE.MESSAGES.unitTimes:""},{});return n++,[t]}},["superscript","subscript","overscore","underscore"]);function s(t){for(;t;){if("unit"===t.getAttribute("role"))return!0;var e=t.tagName,r=n.evalXPath("children/*",t);t=-1!==a.indexOf(e)?r[0]:r[r.length-1]}return!1}function l(t){for(;t;){if("unit"===t.getAttribute("role"))return!0;t=n.evalXPath("children/*",t)[0]}return!1}e.rightMostUnit=s,e.leftMostUnit=l,e.oneLeft=function(t){for(;t;){if("number"===t.tagName&&"1"===t.textContent)return[t];if("infixop"!==t.tagName||"multiplication"!==t.getAttribute("role")&&"implicit"!==t.getAttribute("role"))return[];t=n.evalXPath("children/*",t)[0]}return[]}},3284:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.AbstractWalker=void 0;const o=r(7052),i=r(8290),a=r(5740),n=r(4440),s=r(6828),l=r(8496),c=r(2298),u=r(4356),p=r(2105),h=r(5656),d=r(9552),f=r(9543),m=r(8504),y=r(7730),g=r(1214),b=r(179),v=r(1204),_=r(5274);class S{constructor(t,e,r,n){this.node=t,this.generator=e,this.highlighter=r,this.modifier=!1,this.keyMapping=new Map([[l.KeyCode.UP,this.up.bind(this)],[l.KeyCode.DOWN,this.down.bind(this)],[l.KeyCode.RIGHT,this.right.bind(this)],[l.KeyCode.LEFT,this.left.bind(this)],[l.KeyCode.TAB,this.repeat.bind(this)],[l.KeyCode.DASH,this.expand.bind(this)],[l.KeyCode.SPACE,this.depth.bind(this)],[l.KeyCode.HOME,this.home.bind(this)],[l.KeyCode.X,this.summary.bind(this)],[l.KeyCode.Z,this.detail.bind(this)],[l.KeyCode.V,this.virtualize.bind(this)],[l.KeyCode.P,this.previous.bind(this)],[l.KeyCode.U,this.undo.bind(this)],[l.KeyCode.LESS,this.previousRules.bind(this)],[l.KeyCode.GREATER,this.nextRules.bind(this)]]),this.cursors=[],this.xml_=null,this.rebuilt_=null,this.focus_=null,this.active_=!1,this.node.id?this.id=this.node.id:this.node.hasAttribute(S.SRE_ID_ATTR)?this.id=this.node.getAttribute(S.SRE_ID_ATTR):(this.node.setAttribute(S.SRE_ID_ATTR,S.ID_COUNTER.toString()),this.id=S.ID_COUNTER++),this.rootNode=v.getSemanticRoot(t),this.rootId=this.rootNode.getAttribute(c.Attribute.ID),this.xmlString_=n,this.moved=b.WalkerMoves.ENTER}getXml(){return this.xml_||(this.xml_=a.parseInput(this.xmlString_)),this.xml_}getRebuilt(){return this.rebuilt_||this.rebuildStree(),this.rebuilt_}isActive(){return this.active_}activate(){this.isActive()||(this.generator.start(),this.toggleActive_())}deactivate(){this.isActive()&&(b.WalkerState.setState(this.id,this.primaryId()),this.generator.end(),this.toggleActive_())}getFocus(t=!1){return this.focus_||(this.focus_=this.singletonFocus(this.rootId)),t&&this.updateFocus(),this.focus_}setFocus(t){this.focus_=t}getDepth(){return this.levels.depth()-1}isSpeech(){return this.generator.modality===c.Attribute.SPEECH}focusDomNodes(){return this.getFocus().getDomNodes()}focusSemanticNodes(){return this.getFocus().getSemanticNodes()}speech(){var r=this.focusDomNodes();if(!r.length)return"";const n=this.specialMove();if(null!==n)return n;switch(this.moved){case b.WalkerMoves.DEPTH:return this.depth_();case b.WalkerMoves.SUMMARY:return this.summary_();case b.WalkerMoves.DETAIL:return this.detail_();default:{const n=[],a=this.focusSemanticNodes();for(let t=0,e=r.length;tt.id.toString()),this.getRebuilt(),this.node))}rebuildStree(){this.rebuilt_=new g.RebuildStree(this.getXml()),this.rootId=this.rebuilt_.stree.root.id.toString(),this.generator.setRebuilt(this.rebuilt_),this.skeleton=h.SemanticSkeleton.fromTree(this.rebuilt_.stree),this.skeleton.populate(),this.focus_=this.singletonFocus(this.rootId),this.levels=this.initLevels(),f.connectMactions(this.node,this.getXml(),this.rebuilt_.xml)}previousLevel(){var t=this.getFocus().getDomPrimary();return t?v.getAttribute(t,c.Attribute.PARENT):this.getFocus().getSemanticPrimary().parent.id.toString()}nextLevel(){var t=this.getFocus().getDomPrimary();let e,r;if(t){e=v.splitAttribute(v.getAttribute(t,c.Attribute.CHILDREN)),r=v.splitAttribute(v.getAttribute(t,c.Attribute.CONTENT));const n=v.getAttribute(t,c.Attribute.TYPE),o=v.getAttribute(t,c.Attribute.ROLE);return this.combineContentChildren(n,o,r,e)}const n=t=>t.id.toString(),o=this.getRebuilt().nodeDict[this.primaryId()];return e=o.childNodes.map(n),r=o.contentNodes.map(n),0===e.length?[]:this.combineContentChildren(o.type,o.role,r,e)}singletonFocus(t){this.getRebuilt();var e=this.retrieveVisuals(t);return this.focusFromId(t,e)}retrieveVisuals(t){if(!this.skeleton)return[t];const e=parseInt(t,10),r=this.skeleton.subtreeNodes(e);if(!r.length)return[t];r.unshift(e);const n={},o=[];_.updateEvaluator(this.getXml());for(const t of r)n[t]||(o.push(t.toString()),n[t]=!0,this.subtreeIds(t,n));return o}subtreeIds(t,e){t=_.evalXPath(`//*[@data-semantic-id="${t}"]`,this.getXml());_.evalXPath("*//@data-semantic-id",t[0]).forEach(t=>e[parseInt(t.textContent,10)]=!0)}focusFromId(t,e){return y.Focus.factory(t,e,this.getRebuilt(),this.node)}summary(){return this.moved=this.isSpeech()?b.WalkerMoves.SUMMARY:b.WalkerMoves.REPEAT,this.getFocus().clone()}detail(){return this.moved=this.isSpeech()?b.WalkerMoves.DETAIL:b.WalkerMoves.REPEAT,this.getFocus().clone()}specialMove(){return null}virtualize(t){return this.cursors.push({focus:this.getFocus(),levels:this.levels,undo:t||!this.cursors.length}),this.levels=this.levels.clone(),this.getFocus().clone()}previous(){var t=this.cursors.pop();return t?(this.levels=t.levels,t.focus):this.getFocus()}undo(){let t;for(;(t=this.cursors.pop())&&!t.undo;);return t?(this.levels=t.levels,t.focus):this.getFocus()}update(t){this.generator.setOptions(t),(0,s.setup)(t).then(()=>d.generator("Tree").getSpeech(this.node,this.getXml()))}nextRules(){const t=this.generator.getOptions();return"speech"!==t.modality?this.getFocus():(n.DOMAIN_TO_STYLES[t.domain]=t.style,t.domain="mathspeak"===t.domain?"clearspeak":"mathspeak",t.style=n.DOMAIN_TO_STYLES[t.domain],this.update(t),this.moved=b.WalkerMoves.REPEAT,this.getFocus().clone())}nextStyle(t,e){if("mathspeak"===t){const t=["default","brief","sbrief"],n=t.indexOf(e);return-1===n?e:n>=t.length-1?t[0]:t[n+1]}if("clearspeak"!==t)return e;{const t=m.ClearspeakPreferences.getLocalePreferences().en;if(!t)return"default";const o=m.ClearspeakPreferences.relevantPreferences(this.getFocus().getSemanticPrimary()),i=m.ClearspeakPreferences.findPreference(e,o),a=t[o].map(function(t){return t.split("_")[1]}),s=a.indexOf(i);if(-1===s)return e;var r=s>=a.length-1?a[0]:a[s+1];return m.ClearspeakPreferences.addPreference(e,o,r)}}previousRules(){const t=this.generator.getOptions();return"speech"!==t.modality?this.getFocus():(t.style=this.nextStyle(t.domain,t.style),this.update(t),this.moved=b.WalkerMoves.REPEAT,this.getFocus().clone())}refocus(){let t,e=this.getFocus();for(;!e.getNodes().length;){t=this.levels.peek();var r=this.up();if(!r)break;this.setFocus(r),e=this.getFocus(!0)}this.levels.push(t),this.setFocus(e)}toggleActive_(){this.active_=!this.active_}mergePrefix_(t,e=[]){var r=this.isSpeech()?this.prefix_():"",r=(r&&t.unshift(r),this.isSpeech()?this.postfix_():"");return r&&t.push(r),i.finalize(i.merge(e.concat(t)))}prefix_(){var t=this.getFocus().getDomNodes(),e=this.getFocus().getSemanticNodes();return t[0]?v.getAttribute(t[0],c.Attribute.PREFIX):f.retrievePrefix(e[0])}postfix_(){var t=this.getFocus().getDomNodes();return t[0]?v.getAttribute(t[0],c.Attribute.POSTFIX):""}depth_(){var t=p.Grammar.getInstance().getParameter("depth"),e=(p.Grammar.getInstance().setParameter("depth",!0),this.getFocus().getDomPrimary()),e=this.expandable(e)?u.LOCALE.MESSAGES.navigate.EXPANDABLE:this.collapsible(e)?u.LOCALE.MESSAGES.navigate.COLLAPSIBLE:"",r=u.LOCALE.MESSAGES.navigate.LEVEL+" "+this.getDepth(),n=this.getFocus().getSemanticNodes(),n=f.retrievePrefix(n[0]),r=[new o.AuditoryDescription({text:r,personality:{}}),new o.AuditoryDescription({text:n,personality:{}}),new o.AuditoryDescription({text:e,personality:{}})];return p.Grammar.getInstance().setParameter("depth",t),i.finalize(i.markup(r))}actionable_(t){t=null==t?void 0:t.parentNode;return t&&this.highlighter.isMactionNode(t)?t:null}summary_(){var t=this.getFocus().getSemanticPrimary().id.toString(),t=this.getRebuilt().xml.getAttribute("id")===t?this.getRebuilt().xml:a.querySelectorAllByAttrValue(this.getRebuilt().xml,"id",t)[0],t=f.retrieveSummary(t);return this.mergePrefix_([t])}detail_(){const t=this.getFocus().getSemanticPrimary().id.toString(),e=this.getRebuilt().xml.getAttribute("id")===t?this.getRebuilt().xml:a.querySelectorAllByAttrValue(this.getRebuilt().xml,"id",t)[0],r=e.getAttribute("alternative");e.removeAttribute("alternative");var n=f.computeMarkup(e),n=this.mergePrefix_([n]);return e.setAttribute("alternative",r),n}}(e.AbstractWalker=S).ID_COUNTER=0,S.SRE_ID_ATTR="sre-explorer-id"},162:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.DummyWalker=void 0;class n extends r(3284).AbstractWalker{up(){return null}down(){return null}left(){return null}right(){return null}repeat(){return null}depth(){return null}home(){return null}getDepth(){return 0}initLevels(){return null}combineContentChildren(t,e,r,n){return[]}findFocusOnLevel(t){return null}}e.DummyWalker=n},7730:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.Focus=void 0;const p=r(1204);class h{constructor(t,e){this.nodes=t,this.primary=e,this.domNodes=[],this.domPrimary_=null,this.allNodes=[]}static factory(t,e,r,n){const o=t=>p.getBySemanticId(n,t),i=r.nodeDict,a=o(t),s=e.map(o),l=e.map(function(t){return i[t]}),c=new h(l,i[t]);return c.domNodes=s,c.domPrimary_=a,c.allNodes=h.generateAllVisibleNodes_(e,s,i,n),c}static generateAllVisibleNodes_(r,n,o,i){var a=t=>p.getBySemanticId(i,t);let s=[];for(let t=0,e=r.length;t=e.length?null:e[t]}depth(){return this.level_.length}clone(){const t=new r;return t.level_=this.level_.slice(0),t}toString(){let r="";for(let t,e=0;t=this.level_[e];e++)r+="\n"+t.map(function(t){return t.toString()});return r}}},1214:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.RebuildStree=void 0;const n=r(5740),c=r(2298),o=r(3588),i=r(6537),a=r(3308),s=r(5656),l=r(7075),u=r(4795),p=r(1204);class h{constructor(t){this.mathml=t,this.factory=new i.SemanticNodeFactory,this.nodeDict={},this.mmlRoot=p.getSemanticRoot(t),this.streeRoot=this.assembleTree(this.mmlRoot),this.stree=l.SemanticTree.fromNode(this.streeRoot,this.mathml),this.xml=this.stree.xml(),a.default.getInstance().setNodeFactory(this.factory)}static addAttributes(t,e,r){r&&1===e.childNodes.length&&e.childNodes[0].nodeType!==n.NodeType.TEXT_NODE&&u.addAttributes(t,e.childNodes[0]),u.addAttributes(t,e)}static textContent(t,e,r){!r&&e.textContent?t.textContent=e.textContent:1<(r=p.splitAttribute(p.getAttribute(e,c.Attribute.OPERATOR))).length&&(t.textContent=r[1])}static isPunctuated(t){return!s.SemanticSkeleton.simpleCollapseStructure(t)&&t[1]&&s.SemanticSkeleton.contentCollapseStructure(t[1])}getTree(){return this.stree}assembleTree(t){const e=this.makeNode(t),r=p.splitAttribute(p.getAttribute(t,c.Attribute.CHILDREN)),n=p.splitAttribute(p.getAttribute(t,c.Attribute.CONTENT));if(h.addAttributes(e,t,!(r.length||n.length)),0===n.length&&0===r.length)return h.textContent(e,t),e;if(0this.setParent(t,e)),e.childNodes=r.map(t=>this.setParent(t,e));t=p.getAttribute(t,c.Attribute.COLLAPSED);return t?this.postProcess(e,t):e}makeNode(t){const e=p.getAttribute(t,c.Attribute.TYPE),r=p.getAttribute(t,c.Attribute.ROLE),n=p.getAttribute(t,c.Attribute.FONT),o=p.getAttribute(t,c.Attribute.ANNOTATION)||"",i=p.getAttribute(t,c.Attribute.ID),a=p.getAttribute(t,c.Attribute.EMBELLISHED),s=p.getAttribute(t,c.Attribute.FENCEPOINTER),l=this.createNode(parseInt(i,10));return l.type=e,l.role=r,l.font=n||"unknown",l.parseAnnotation(o),s&&(l.fencePointer=s),a&&(l.embellished=a),l}makePunctuation(t){const e=this.createNode(t);return e.updateContent((0,o.invisibleComma)()),e.role="dummy",e}makePunctuated(t,e,r){const n=this.createNode(e[0]),o=(n.type="punctuated",n.embellished=t.embellished,n.fencePointer=t.fencePointer,n.role=r,e.splice(1,1)[0].slice(1));n.contentNodes=o.map(this.makePunctuation.bind(this)),this.collapsedChildren_(e)}makeEmpty(t,e,r){const n=this.createNode(e);n.type="empty",n.embellished=t.embellished,n.fencePointer=t.fencePointer,n.role=r}makeIndex(t,e,r){if(h.isPunctuated(e))return this.makePunctuated(t,e,r),void e[0];s.SemanticSkeleton.simpleCollapseStructure(e)&&!this.nodeDict[e.toString()]&&this.makeEmpty(t,e,r)}postProcess(t,e){const r=s.SemanticSkeleton.fromString(e).array;if("subsup"===t.type){const e=this.createNode(r[1][0]);return e.type="subscript",e.role="subsup",t.type="superscript",e.embellished=t.embellished,e.fencePointer=t.fencePointer,this.makeIndex(t,r[1][2],"rightsub"),this.makeIndex(t,r[2],"rightsuper"),this.collapsedChildren_(r),t}if("subscript"===t.type)return this.makeIndex(t,r[2],"rightsub"),this.collapsedChildren_(r),t;if("superscript"===t.type)return this.makeIndex(t,r[2],"rightsuper"),this.collapsedChildren_(r),t;if("tensor"===t.type)return this.makeIndex(t,r[2],"leftsub"),this.makeIndex(t,r[3],"leftsuper"),this.makeIndex(t,r[4],"rightsub"),this.makeIndex(t,r[5],"rightsuper"),this.collapsedChildren_(r),t;if("punctuated"===t.type){if(h.isPunctuated(r)){const e=r.splice(1,1)[0].slice(1);t.contentNodes=e.map(this.makePunctuation.bind(this))}return t}if("underover"!==t.type)return t;{const e=this.createNode(r[1][0]);return"overaccent"===t.childNodes[1].role?(e.type="overscore",t.type="underscore"):(e.type="underscore",t.type="overscore"),e.role="underover",e.embellished=t.embellished,e.fencePointer=t.fencePointer,this.collapsedChildren_(r),t}}createNode(t){var e=this.factory.makeNode(t);return this.nodeDict[t.toString()]=e}collapsedChildren_(t){const i=r=>{const n=this.nodeDict[r[0]];n.childNodes=[];for(let t=1,e=r.length;tt.getSemanticPrimary().id===e)}}e.SemanticWalker=i},9806:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.SyntaxWalker=void 0;const o=r(707),n=r(3284),i=r(9797);class a extends n.AbstractWalker{constructor(t,e,r,n){super(t,e,r,n),this.node=t,this.generator=e,this.highlighter=r,this.levels=null,this.restoreState()}initLevels(){const t=new i.Levels;return t.push([this.primaryId()]),t}up(){super.up();var t=this.previousLevel();return t?(this.levels.pop(),this.singletonFocus(t)):null}down(){super.down();var t=this.nextLevel();if(0===t.length)return null;var e=this.singletonFocus(t[0]);return e&&this.levels.push(t),e}combineContentChildren(t,e,r,n){switch(t){case"relseq":case"infixop":case"multirel":return(0,o.interleaveLists)(n,r);case"prefixop":return r.concat(n);case"postfixop":return n.concat(r);case"matrix":case"vector":case"fenced":return n.unshift(r[0]),n.push(r[1]),n;case"cases":return n.unshift(r[0]),n;case"punctuated":return"text"===e?(0,o.interleaveLists)(n,r):n;case"appl":return[n[0],r[0],n[1]];case"root":return[n[1],n[0]];default:return n}}left(){super.left();var t=this.levels.indexOf(this.primaryId());if(null===t)return null;t=this.levels.get(t-1);return t?this.singletonFocus(t):null}right(){super.right();var t=this.levels.indexOf(this.primaryId());if(null===t)return null;t=this.levels.get(t+1);return t?this.singletonFocus(t):null}findFocusOnLevel(t){return this.singletonFocus(t.toString())}focusDomNodes(){return[this.getFocus().getDomPrimary()]}focusSemanticNodes(){return[this.getFocus().getSemanticPrimary()]}}e.SyntaxWalker=a},1799:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.TableWalker=void 0;const i=r(5740),o=r(8496),n=r(9806),a=r(179);class s extends n.SyntaxWalker{constructor(t,e,r,n){super(t,e,r,n),this.node=t,this.generator=e,this.highlighter=r,this.firstJump=null,this.key_=null,this.row_=0,this.currentTable_=null,this.keyMapping.set(o.KeyCode.ZERO,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.ONE,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.TWO,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.THREE,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.FOUR,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.FIVE,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.SIX,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.SEVEN,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.EIGHT,this.jumpCell.bind(this)),this.keyMapping.set(o.KeyCode.NINE,this.jumpCell.bind(this))}move(t){this.key_=t;t=super.move(t);return this.modifier=!1,t}up(){return this.moved=a.WalkerMoves.UP,this.eligibleCell_()?this.verticalMove_(!1):super.up()}down(){return 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auto}.btn-group>.btn-check:checked+.btn,.btn-group>.btn-check:focus+.btn,.btn-group>.btn:hover,.btn-group>.btn:focus,.btn-group>.btn:active,.btn-group>.btn.active,.btn-group-vertical>.btn-check:checked+.btn,.btn-group-vertical>.btn-check:focus+.btn,.btn-group-vertical>.btn:hover,.btn-group-vertical>.btn:focus,.btn-group-vertical>.btn:active,.btn-group-vertical>.btn.active{z-index:1}.btn-toolbar{display:flex;display:-webkit-flex;flex-wrap:wrap;-webkit-flex-wrap:wrap;justify-content:flex-start;-webkit-justify-content:flex-start}.btn-toolbar .input-group{width:auto}.btn-group{border-radius:var(--bs-border-radius)}.btn-group>:not(.btn-check:first-child)+.btn,.btn-group>.btn-group:not(:first-child){margin-left:calc(var(--bs-border-width) * -1)}.btn-group>.btn:not(:last-child):not(.dropdown-toggle),.btn-group>.btn.dropdown-toggle-split:first-child,.btn-group>.btn-group:not(:last-child)>.btn{border-top-right-radius:0;border-bottom-right-radius:0}.btn-group>.btn:nth-child(n + 3),.btn-group>:not(.btn-check)+.btn,.btn-group>.btn-group:not(:first-child)>.btn{border-top-left-radius:0;border-bottom-left-radius:0}.dropdown-toggle-split{padding-right:.5625rem;padding-left:.5625rem}.dropdown-toggle-split::after,.dropup .dropdown-toggle-split::after,.dropend .dropdown-toggle-split::after{margin-left:0}.dropstart .dropdown-toggle-split::before{margin-right:0}.btn-sm+.dropdown-toggle-split,.btn-group-sm>.btn+.dropdown-toggle-split{padding-right:.375rem;padding-left:.375rem}.btn-lg+.dropdown-toggle-split,.btn-group-lg>.btn+.dropdown-toggle-split{padding-right:.75rem;padding-left:.75rem}.btn-group-vertical{flex-direction:column;-webkit-flex-direction:column;align-items:flex-start;-webkit-align-items:flex-start;justify-content:center;-webkit-justify-content:center}.btn-group-vertical>.btn,.btn-group-vertical>.btn-group{width:100%}.btn-group-vertical>.btn:not(:first-child),.btn-group-vertical>.btn-group:not(:first-child){margin-top:calc(var(--bs-border-width) * 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var(--bs-nav-link-padding-x);font-size:var(--bs-nav-link-font-size);font-weight:var(--bs-nav-link-font-weight);color:var(--bs-nav-link-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background:none;border:0;transition:color 0.15s ease-in-out,background-color 0.15s ease-in-out,border-color 0.15s ease-in-out}@media (prefers-reduced-motion: reduce){.nav-link{transition:none}}.nav-link:hover,.nav-link:focus{color:var(--bs-nav-link-hover-color)}.nav-link:focus-visible{outline:0;box-shadow:0 0 0 .25rem rgba(13,110,253,0.25)}.nav-link.disabled,.nav-link:disabled{color:var(--bs-nav-link-disabled-color);pointer-events:none;cursor:default}.nav-tabs{--bs-nav-tabs-border-width: var(--bs-border-width);--bs-nav-tabs-border-color: var(--bs-border-color);--bs-nav-tabs-border-radius: var(--bs-border-radius);--bs-nav-tabs-link-hover-border-color: var(--bs-secondary-bg) var(--bs-secondary-bg) var(--bs-border-color);--bs-nav-tabs-link-active-color: var(--bs-emphasis-color);--bs-nav-tabs-link-active-bg: var(--bs-body-bg);--bs-nav-tabs-link-active-border-color: var(--bs-border-color) var(--bs-border-color) var(--bs-body-bg);border-bottom:var(--bs-nav-tabs-border-width) solid var(--bs-nav-tabs-border-color)}.nav-tabs .nav-link{margin-bottom:calc(-1 * var(--bs-nav-tabs-border-width));border:var(--bs-nav-tabs-border-width) solid transparent;border-top-left-radius:var(--bs-nav-tabs-border-radius);border-top-right-radius:var(--bs-nav-tabs-border-radius)}.nav-tabs .nav-link:hover,.nav-tabs .nav-link:focus{isolation:isolate;border-color:var(--bs-nav-tabs-link-hover-border-color)}.nav-tabs .nav-link.active,.nav-tabs .nav-item.show .nav-link{color:var(--bs-nav-tabs-link-active-color);background-color:var(--bs-nav-tabs-link-active-bg);border-color:var(--bs-nav-tabs-link-active-border-color)}.nav-tabs .dropdown-menu{margin-top:calc(-1 * 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reduce){.accordion-button::after{transition:none}}.accordion-button:hover{z-index:2}.accordion-button:focus{z-index:3;border-color:var(--bs-accordion-btn-focus-border-color);outline:0;box-shadow:var(--bs-accordion-btn-focus-box-shadow)}.accordion-header{margin-bottom:0}.accordion-item{color:var(--bs-accordion-color);background-color:var(--bs-accordion-bg);border:var(--bs-accordion-border-width) solid var(--bs-accordion-border-color)}.accordion-item:first-of-type{border-top-left-radius:var(--bs-accordion-border-radius);border-top-right-radius:var(--bs-accordion-border-radius)}.accordion-item:first-of-type .accordion-button{border-top-left-radius:var(--bs-accordion-inner-border-radius);border-top-right-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:not(:first-of-type){border-top:0}.accordion-item:last-of-type{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-item:last-of-type 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fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-active-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%236ea8fe'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e")}.breadcrumb{--bs-breadcrumb-padding-x: 0;--bs-breadcrumb-padding-y: 0;--bs-breadcrumb-margin-bottom: 1rem;--bs-breadcrumb-bg: ;--bs-breadcrumb-border-radius: ;--bs-breadcrumb-divider-color: var(--bs-secondary-color);--bs-breadcrumb-item-padding-x: .5rem;--bs-breadcrumb-item-active-color: var(--bs-secondary-color);display:flex;display:-webkit-flex;flex-wrap:wrap;-webkit-flex-wrap:wrap;padding:var(--bs-breadcrumb-padding-y) var(--bs-breadcrumb-padding-x);margin-bottom:var(--bs-breadcrumb-margin-bottom);font-size:var(--bs-breadcrumb-font-size);list-style:none;background-color:var(--bs-breadcrumb-bg);border-radius:var(--bs-breadcrumb-border-radius)}.breadcrumb-item+.breadcrumb-item{padding-left:var(--bs-breadcrumb-item-padding-x)}.breadcrumb-item+.breadcrumb-item::before{float:left;padding-right:var(--bs-breadcrumb-item-padding-x);color:var(--bs-breadcrumb-divider-color);content:var(--bs-breadcrumb-divider, "/") /* rtl: var(--bs-breadcrumb-divider, "/") */}.breadcrumb-item.active{color:var(--bs-breadcrumb-item-active-color)}.pagination{--bs-pagination-padding-x: .75rem;--bs-pagination-padding-y: .375rem;--bs-pagination-font-size:1rem;--bs-pagination-color: var(--bs-link-color);--bs-pagination-bg: var(--bs-body-bg);--bs-pagination-border-width: var(--bs-border-width);--bs-pagination-border-color: var(--bs-border-color);--bs-pagination-border-radius: var(--bs-border-radius);--bs-pagination-hover-color: var(--bs-link-hover-color);--bs-pagination-hover-bg: var(--bs-tertiary-bg);--bs-pagination-hover-border-color: var(--bs-border-color);--bs-pagination-focus-color: var(--bs-link-hover-color);--bs-pagination-focus-bg: var(--bs-secondary-bg);--bs-pagination-focus-box-shadow: 0 0 0 .25rem rgba(13,110,253,0.25);--bs-pagination-active-color: #fff;--bs-pagination-active-bg: #0d6efd;--bs-pagination-active-border-color: #0d6efd;--bs-pagination-disabled-color: var(--bs-secondary-color);--bs-pagination-disabled-bg: var(--bs-secondary-bg);--bs-pagination-disabled-border-color: var(--bs-border-color);display:flex;display:-webkit-flex;padding-left:0;list-style:none}.page-link{position:relative;display:block;padding:var(--bs-pagination-padding-y) var(--bs-pagination-padding-x);font-size:var(--bs-pagination-font-size);color:var(--bs-pagination-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-pagination-bg);border:var(--bs-pagination-border-width) solid var(--bs-pagination-border-color);transition:color 0.15s ease-in-out,background-color 0.15s ease-in-out,border-color 0.15s ease-in-out,box-shadow 0.15s ease-in-out}@media (prefers-reduced-motion: reduce){.page-link{transition:none}}.page-link:hover{z-index:2;color:var(--bs-pagination-hover-color);background-color:var(--bs-pagination-hover-bg);border-color:var(--bs-pagination-hover-border-color)}.page-link:focus{z-index:3;color:var(--bs-pagination-focus-color);background-color:var(--bs-pagination-focus-bg);outline:0;box-shadow:var(--bs-pagination-focus-box-shadow)}.page-link.active,.active>.page-link{z-index:3;color:var(--bs-pagination-active-color);background-color:var(--bs-pagination-active-bg);border-color:var(--bs-pagination-active-border-color)}.page-link.disabled,.disabled>.page-link{color:var(--bs-pagination-disabled-color);pointer-events:none;background-color:var(--bs-pagination-disabled-bg);border-color:var(--bs-pagination-disabled-border-color)}.page-item:not(:first-child) .page-link{margin-left:calc(var(--bs-border-width) * -1)}.page-item:first-child .page-link{border-top-left-radius:var(--bs-pagination-border-radius);border-bottom-left-radius:var(--bs-pagination-border-radius)}.page-item:last-child .page-link{border-top-right-radius:var(--bs-pagination-border-radius);border-bottom-right-radius:var(--bs-pagination-border-radius)}.pagination-lg{--bs-pagination-padding-x: 1.5rem;--bs-pagination-padding-y: .75rem;--bs-pagination-font-size:1.25rem;--bs-pagination-border-radius: var(--bs-border-radius-lg)}.pagination-sm{--bs-pagination-padding-x: .5rem;--bs-pagination-padding-y: .25rem;--bs-pagination-font-size:.875rem;--bs-pagination-border-radius: var(--bs-border-radius-sm)}.badge{--bs-badge-padding-x: .65em;--bs-badge-padding-y: .35em;--bs-badge-font-size:.75em;--bs-badge-font-weight: 700;--bs-badge-color: #fff;--bs-badge-border-radius: var(--bs-border-radius);display:inline-block;padding:var(--bs-badge-padding-y) var(--bs-badge-padding-x);font-size:var(--bs-badge-font-size);font-weight:var(--bs-badge-font-weight);line-height:1;color:var(--bs-badge-color);text-align:center;white-space:nowrap;vertical-align:baseline;border-radius:var(--bs-badge-border-radius)}.badge:empty{display:none}.btn .badge{position:relative;top:-1px}.alert{--bs-alert-bg: transparent;--bs-alert-padding-x: 1rem;--bs-alert-padding-y: 1rem;--bs-alert-margin-bottom: 1rem;--bs-alert-color: inherit;--bs-alert-border-color: transparent;--bs-alert-border: var(--bs-border-width) solid var(--bs-alert-border-color);--bs-alert-border-radius: var(--bs-border-radius);--bs-alert-link-color: inherit;position:relative;padding:var(--bs-alert-padding-y) var(--bs-alert-padding-x);margin-bottom:var(--bs-alert-margin-bottom);color:var(--bs-alert-color);background-color:var(--bs-alert-bg);border:var(--bs-alert-border);border-radius:var(--bs-alert-border-radius)}.alert-heading{color:inherit}.alert-link{font-weight:700;color:var(--bs-alert-link-color)}.alert-dismissible{padding-right:3rem}.alert-dismissible .btn-close{position:absolute;top:0;right:0;z-index:2;padding:1.25rem 1rem}.alert-default{--bs-alert-color: var(--bs-default-text-emphasis);--bs-alert-bg: var(--bs-default-bg-subtle);--bs-alert-border-color: var(--bs-default-border-subtle);--bs-alert-link-color: var(--bs-default-text-emphasis)}.alert-primary{--bs-alert-color: var(--bs-primary-text-emphasis);--bs-alert-bg: var(--bs-primary-bg-subtle);--bs-alert-border-color: var(--bs-primary-border-subtle);--bs-alert-link-color: var(--bs-primary-text-emphasis)}.alert-secondary{--bs-alert-color: var(--bs-secondary-text-emphasis);--bs-alert-bg: var(--bs-secondary-bg-subtle);--bs-alert-border-color: var(--bs-secondary-border-subtle);--bs-alert-link-color: var(--bs-secondary-text-emphasis)}.alert-success{--bs-alert-color: var(--bs-success-text-emphasis);--bs-alert-bg: var(--bs-success-bg-subtle);--bs-alert-border-color: var(--bs-success-border-subtle);--bs-alert-link-color: var(--bs-success-text-emphasis)}.alert-info{--bs-alert-color: var(--bs-info-text-emphasis);--bs-alert-bg: var(--bs-info-bg-subtle);--bs-alert-border-color: var(--bs-info-border-subtle);--bs-alert-link-color: var(--bs-info-text-emphasis)}.alert-warning{--bs-alert-color: var(--bs-warning-text-emphasis);--bs-alert-bg: var(--bs-warning-bg-subtle);--bs-alert-border-color: var(--bs-warning-border-subtle);--bs-alert-link-color: var(--bs-warning-text-emphasis)}.alert-danger{--bs-alert-color: var(--bs-danger-text-emphasis);--bs-alert-bg: var(--bs-danger-bg-subtle);--bs-alert-border-color: var(--bs-danger-border-subtle);--bs-alert-link-color: var(--bs-danger-text-emphasis)}.alert-light{--bs-alert-color: var(--bs-light-text-emphasis);--bs-alert-bg: var(--bs-light-bg-subtle);--bs-alert-border-color: var(--bs-light-border-subtle);--bs-alert-link-color: var(--bs-light-text-emphasis)}.alert-dark{--bs-alert-color: var(--bs-dark-text-emphasis);--bs-alert-bg: var(--bs-dark-bg-subtle);--bs-alert-border-color: var(--bs-dark-border-subtle);--bs-alert-link-color: var(--bs-dark-text-emphasis)}@keyframes progress-bar-stripes{0%{background-position-x:1rem}}.progress,.progress-stacked{--bs-progress-height: 1rem;--bs-progress-font-size:.75rem;--bs-progress-bg: var(--bs-secondary-bg);--bs-progress-border-radius: var(--bs-border-radius);--bs-progress-box-shadow: var(--bs-box-shadow-inset);--bs-progress-bar-color: #fff;--bs-progress-bar-bg: #0d6efd;--bs-progress-bar-transition: width 0.6s ease;display:flex;display:-webkit-flex;height:var(--bs-progress-height);overflow:hidden;font-size:var(--bs-progress-font-size);background-color:var(--bs-progress-bg);border-radius:var(--bs-progress-border-radius)}.progress-bar{display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;justify-content:center;-webkit-justify-content:center;overflow:hidden;color:var(--bs-progress-bar-color);text-align:center;white-space:nowrap;background-color:var(--bs-progress-bar-bg);transition:var(--bs-progress-bar-transition)}@media (prefers-reduced-motion: reduce){.progress-bar{transition:none}}.progress-bar-striped{background-image:linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-size:var(--bs-progress-height) var(--bs-progress-height)}.progress-stacked>.progress{overflow:visible}.progress-stacked>.progress>.progress-bar{width:100%}.progress-bar-animated{animation:1s linear infinite progress-bar-stripes}@media (prefers-reduced-motion: reduce){.progress-bar-animated{animation:none}}.list-group{--bs-list-group-color: var(--bs-body-color);--bs-list-group-bg: var(--bs-body-bg);--bs-list-group-border-color: var(--bs-border-color);--bs-list-group-border-width: var(--bs-border-width);--bs-list-group-border-radius: var(--bs-border-radius);--bs-list-group-item-padding-x: 1rem;--bs-list-group-item-padding-y: .5rem;--bs-list-group-action-color: var(--bs-secondary-color);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-tertiary-bg);--bs-list-group-action-active-color: var(--bs-body-color);--bs-list-group-action-active-bg: var(--bs-secondary-bg);--bs-list-group-disabled-color: var(--bs-secondary-color);--bs-list-group-disabled-bg: var(--bs-body-bg);--bs-list-group-active-color: #fff;--bs-list-group-active-bg: #0d6efd;--bs-list-group-active-border-color: #0d6efd;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;padding-left:0;margin-bottom:0;border-radius:var(--bs-list-group-border-radius)}.list-group-numbered{list-style-type:none;counter-reset:section}.list-group-numbered>.list-group-item::before{content:counters(section, ".") ". ";counter-increment:section}.list-group-item-action{width:100%;color:var(--bs-list-group-action-color);text-align:inherit}.list-group-item-action:hover,.list-group-item-action:focus{z-index:1;color:var(--bs-list-group-action-hover-color);text-decoration:none;background-color:var(--bs-list-group-action-hover-bg)}.list-group-item-action:active{color:var(--bs-list-group-action-active-color);background-color:var(--bs-list-group-action-active-bg)}.list-group-item{position:relative;display:block;padding:var(--bs-list-group-item-padding-y) var(--bs-list-group-item-padding-x);color:var(--bs-list-group-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-list-group-bg);border:var(--bs-list-group-border-width) solid var(--bs-list-group-border-color)}.list-group-item:first-child{border-top-left-radius:inherit;border-top-right-radius:inherit}.list-group-item:last-child{border-bottom-right-radius:inherit;border-bottom-left-radius:inherit}.list-group-item.disabled,.list-group-item:disabled{color:var(--bs-list-group-disabled-color);pointer-events:none;background-color:var(--bs-list-group-disabled-bg)}.list-group-item.active{z-index:2;color:var(--bs-list-group-active-color);background-color:var(--bs-list-group-active-bg);border-color:var(--bs-list-group-active-border-color)}.list-group-item+.list-group-item{border-top-width:0}.list-group-item+.list-group-item.active{margin-top:calc(-1 * var(--bs-list-group-border-width));border-top-width:var(--bs-list-group-border-width)}.list-group-horizontal{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal>.list-group-item.active{margin-top:0}.list-group-horizontal>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}@media (min-width: 576px){.list-group-horizontal-sm{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-sm>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-sm>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-sm>.list-group-item.active{margin-top:0}.list-group-horizontal-sm>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-sm>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 768px){.list-group-horizontal-md{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-md>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-md>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-md>.list-group-item.active{margin-top:0}.list-group-horizontal-md>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-md>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 992px){.list-group-horizontal-lg{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-lg>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-lg>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-lg>.list-group-item.active{margin-top:0}.list-group-horizontal-lg>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-lg>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 1200px){.list-group-horizontal-xl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xl>.list-group-item.active{margin-top:0}.list-group-horizontal-xl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xl>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 1400px){.list-group-horizontal-xxl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xxl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xxl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xxl>.list-group-item.active{margin-top:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}.list-group-flush{border-radius:0}.list-group-flush>.list-group-item{border-width:0 0 var(--bs-list-group-border-width)}.list-group-flush>.list-group-item:last-child{border-bottom-width:0}.list-group-item-default{--bs-list-group-color: var(--bs-default-text-emphasis);--bs-list-group-bg: var(--bs-default-bg-subtle);--bs-list-group-border-color: var(--bs-default-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-default-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-default-border-subtle);--bs-list-group-active-color: var(--bs-default-bg-subtle);--bs-list-group-active-bg: var(--bs-default-text-emphasis);--bs-list-group-active-border-color: var(--bs-default-text-emphasis)}.list-group-item-primary{--bs-list-group-color: var(--bs-primary-text-emphasis);--bs-list-group-bg: var(--bs-primary-bg-subtle);--bs-list-group-border-color: var(--bs-primary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-primary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-primary-border-subtle);--bs-list-group-active-color: var(--bs-primary-bg-subtle);--bs-list-group-active-bg: var(--bs-primary-text-emphasis);--bs-list-group-active-border-color: var(--bs-primary-text-emphasis)}.list-group-item-secondary{--bs-list-group-color: var(--bs-secondary-text-emphasis);--bs-list-group-bg: var(--bs-secondary-bg-subtle);--bs-list-group-border-color: var(--bs-secondary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-secondary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-secondary-border-subtle);--bs-list-group-active-color: var(--bs-secondary-bg-subtle);--bs-list-group-active-bg: var(--bs-secondary-text-emphasis);--bs-list-group-active-border-color: var(--bs-secondary-text-emphasis)}.list-group-item-success{--bs-list-group-color: var(--bs-success-text-emphasis);--bs-list-group-bg: var(--bs-success-bg-subtle);--bs-list-group-border-color: var(--bs-success-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-success-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-success-border-subtle);--bs-list-group-active-color: var(--bs-success-bg-subtle);--bs-list-group-active-bg: var(--bs-success-text-emphasis);--bs-list-group-active-border-color: var(--bs-success-text-emphasis)}.list-group-item-info{--bs-list-group-color: var(--bs-info-text-emphasis);--bs-list-group-bg: var(--bs-info-bg-subtle);--bs-list-group-border-color: var(--bs-info-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-info-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-info-border-subtle);--bs-list-group-active-color: var(--bs-info-bg-subtle);--bs-list-group-active-bg: var(--bs-info-text-emphasis);--bs-list-group-active-border-color: var(--bs-info-text-emphasis)}.list-group-item-warning{--bs-list-group-color: var(--bs-warning-text-emphasis);--bs-list-group-bg: var(--bs-warning-bg-subtle);--bs-list-group-border-color: var(--bs-warning-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-warning-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-warning-border-subtle);--bs-list-group-active-color: var(--bs-warning-bg-subtle);--bs-list-group-active-bg: var(--bs-warning-text-emphasis);--bs-list-group-active-border-color: var(--bs-warning-text-emphasis)}.list-group-item-danger{--bs-list-group-color: var(--bs-danger-text-emphasis);--bs-list-group-bg: var(--bs-danger-bg-subtle);--bs-list-group-border-color: var(--bs-danger-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-danger-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-danger-border-subtle);--bs-list-group-active-color: var(--bs-danger-bg-subtle);--bs-list-group-active-bg: var(--bs-danger-text-emphasis);--bs-list-group-active-border-color: var(--bs-danger-text-emphasis)}.list-group-item-light{--bs-list-group-color: var(--bs-light-text-emphasis);--bs-list-group-bg: var(--bs-light-bg-subtle);--bs-list-group-border-color: var(--bs-light-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-light-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-light-border-subtle);--bs-list-group-active-color: var(--bs-light-bg-subtle);--bs-list-group-active-bg: var(--bs-light-text-emphasis);--bs-list-group-active-border-color: var(--bs-light-text-emphasis)}.list-group-item-dark{--bs-list-group-color: var(--bs-dark-text-emphasis);--bs-list-group-bg: var(--bs-dark-bg-subtle);--bs-list-group-border-color: var(--bs-dark-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-dark-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-dark-border-subtle);--bs-list-group-active-color: var(--bs-dark-bg-subtle);--bs-list-group-active-bg: var(--bs-dark-text-emphasis);--bs-list-group-active-border-color: var(--bs-dark-text-emphasis)}.btn-close{--bs-btn-close-color: #000;--bs-btn-close-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23000'%3e%3cpath d='M.293.293a1 1 0 0 1 1.414 0L8 6.586 14.293.293a1 1 0 1 1 1.414 1.414L9.414 8l6.293 6.293a1 1 0 0 1-1.414 1.414L8 9.414l-6.293 6.293a1 1 0 0 1-1.414-1.414L6.586 8 .293 1.707a1 1 0 0 1 0-1.414z'/%3e%3c/svg%3e");--bs-btn-close-opacity: .5;--bs-btn-close-hover-opacity: .75;--bs-btn-close-focus-shadow: 0 0 0 .25rem rgba(13,110,253,0.25);--bs-btn-close-focus-opacity: 1;--bs-btn-close-disabled-opacity: .25;--bs-btn-close-white-filter: invert(1) grayscale(100%) brightness(200%);box-sizing:content-box;width:1em;height:1em;padding:.25em .25em;color:var(--bs-btn-close-color);background:transparent var(--bs-btn-close-bg) center/1em auto no-repeat;border:0;border-radius:.375rem;opacity:var(--bs-btn-close-opacity)}.btn-close:hover{color:var(--bs-btn-close-color);text-decoration:none;opacity:var(--bs-btn-close-hover-opacity)}.btn-close:focus{outline:0;box-shadow:var(--bs-btn-close-focus-shadow);opacity:var(--bs-btn-close-focus-opacity)}.btn-close:disabled,.btn-close.disabled{pointer-events:none;user-select:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;-o-user-select:none;opacity:var(--bs-btn-close-disabled-opacity)}.btn-close-white{filter:var(--bs-btn-close-white-filter)}[data-bs-theme="dark"] .btn-close{filter:var(--bs-btn-close-white-filter)}.toast{--bs-toast-zindex: 1090;--bs-toast-padding-x: .75rem;--bs-toast-padding-y: .5rem;--bs-toast-spacing: 1.5rem;--bs-toast-max-width: 350px;--bs-toast-font-size:.875rem;--bs-toast-color: ;--bs-toast-bg: rgba(var(--bs-body-bg-rgb), 0.85);--bs-toast-border-width: var(--bs-border-width);--bs-toast-border-color: var(--bs-border-color-translucent);--bs-toast-border-radius: var(--bs-border-radius);--bs-toast-box-shadow: var(--bs-box-shadow);--bs-toast-header-color: var(--bs-secondary-color);--bs-toast-header-bg: rgba(var(--bs-body-bg-rgb), 0.85);--bs-toast-header-border-color: var(--bs-border-color-translucent);width:var(--bs-toast-max-width);max-width:100%;font-size:var(--bs-toast-font-size);color:var(--bs-toast-color);pointer-events:auto;background-color:var(--bs-toast-bg);background-clip:padding-box;border:var(--bs-toast-border-width) solid var(--bs-toast-border-color);box-shadow:var(--bs-toast-box-shadow);border-radius:var(--bs-toast-border-radius)}.toast.showing{opacity:0}.toast:not(.show){display:none}.toast-container{--bs-toast-zindex: 1090;position:absolute;z-index:var(--bs-toast-zindex);width:max-content;width:-webkit-max-content;width:-moz-max-content;width:-ms-max-content;width:-o-max-content;max-width:100%;pointer-events:none}.toast-container>:not(:last-child){margin-bottom:var(--bs-toast-spacing)}.toast-header{display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;padding:var(--bs-toast-padding-y) var(--bs-toast-padding-x);color:var(--bs-toast-header-color);background-color:var(--bs-toast-header-bg);background-clip:padding-box;border-bottom:var(--bs-toast-border-width) solid var(--bs-toast-header-border-color);border-top-left-radius:calc(var(--bs-toast-border-radius) - var(--bs-toast-border-width));border-top-right-radius:calc(var(--bs-toast-border-radius) - var(--bs-toast-border-width))}.toast-header .btn-close{margin-right:calc(-.5 * var(--bs-toast-padding-x));margin-left:var(--bs-toast-padding-x)}.toast-body{padding:var(--bs-toast-padding-x);word-wrap:break-word}.modal{--bs-modal-zindex: 1055;--bs-modal-width: 500px;--bs-modal-padding: 1rem;--bs-modal-margin: .5rem;--bs-modal-color: ;--bs-modal-bg: var(--bs-body-bg);--bs-modal-border-color: var(--bs-border-color-translucent);--bs-modal-border-width: var(--bs-border-width);--bs-modal-border-radius: var(--bs-border-radius-lg);--bs-modal-box-shadow: 0 0.125rem 0.25rem rgba(0,0,0,0.075);--bs-modal-inner-border-radius: calc(var(--bs-border-radius-lg) - (var(--bs-border-width)));--bs-modal-header-padding-x: 1rem;--bs-modal-header-padding-y: 1rem;--bs-modal-header-padding: 1rem 1rem;--bs-modal-header-border-color: var(--bs-border-color);--bs-modal-header-border-width: var(--bs-border-width);--bs-modal-title-line-height: 1.5;--bs-modal-footer-gap: .5rem;--bs-modal-footer-bg: ;--bs-modal-footer-border-color: var(--bs-border-color);--bs-modal-footer-border-width: var(--bs-border-width);position:fixed;top:0;left:0;z-index:var(--bs-modal-zindex);display:none;width:100%;height:100%;overflow-x:hidden;overflow-y:auto;outline:0}.modal-dialog{position:relative;width:auto;margin:var(--bs-modal-margin);pointer-events:none}.modal.fade .modal-dialog{transition:transform 0.3s ease-out;transform:translate(0, -50px)}@media (prefers-reduced-motion: reduce){.modal.fade .modal-dialog{transition:none}}.modal.show .modal-dialog{transform:none}.modal.modal-static .modal-dialog{transform:scale(1.02)}.modal-dialog-scrollable{height:calc(100% - var(--bs-modal-margin) * 2)}.modal-dialog-scrollable .modal-content{max-height:100%;overflow:hidden}.modal-dialog-scrollable .modal-body{overflow-y:auto}.modal-dialog-centered{display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;min-height:calc(100% - var(--bs-modal-margin) * 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.modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-sm-down .modal-header,.modal-fullscreen-sm-down .modal-footer{border-radius:0}.modal-fullscreen-sm-down .modal-body{overflow-y:auto}}@media (max-width: 767.98px){.modal-fullscreen-md-down{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen-md-down .modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-md-down .modal-header,.modal-fullscreen-md-down .modal-footer{border-radius:0}.modal-fullscreen-md-down .modal-body{overflow-y:auto}}@media (max-width: 991.98px){.modal-fullscreen-lg-down{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen-lg-down .modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-lg-down .modal-header,.modal-fullscreen-lg-down .modal-footer{border-radius:0}.modal-fullscreen-lg-down .modal-body{overflow-y:auto}}@media (max-width: 1199.98px){.modal-fullscreen-xl-down{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen-xl-down .modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-xl-down .modal-header,.modal-fullscreen-xl-down .modal-footer{border-radius:0}.modal-fullscreen-xl-down .modal-body{overflow-y:auto}}@media (max-width: 1399.98px){.modal-fullscreen-xxl-down{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen-xxl-down .modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-xxl-down .modal-header,.modal-fullscreen-xxl-down .modal-footer{border-radius:0}.modal-fullscreen-xxl-down .modal-body{overflow-y:auto}}.tooltip{--bs-tooltip-zindex: 1080;--bs-tooltip-max-width: 200px;--bs-tooltip-padding-x: .5rem;--bs-tooltip-padding-y: .25rem;--bs-tooltip-margin: ;--bs-tooltip-font-size:.875rem;--bs-tooltip-color: var(--bs-body-bg);--bs-tooltip-bg: var(--bs-emphasis-color);--bs-tooltip-border-radius: var(--bs-border-radius);--bs-tooltip-opacity: .9;--bs-tooltip-arrow-width: .8rem;--bs-tooltip-arrow-height: 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url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23052c65'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-focus-border-color: #86b7fe;--bs-accordion-btn-focus-box-shadow: 0 0 0 .25rem rgba(13,110,253,0.25);--bs-accordion-body-padding-x: 1.25rem;--bs-accordion-body-padding-y: 1rem;--bs-accordion-active-color: var(--bs-primary-text-emphasis);--bs-accordion-active-bg: var(--bs-primary-bg-subtle)}.accordion-button{position:relative;display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;width:100%;padding:var(--bs-accordion-btn-padding-y) var(--bs-accordion-btn-padding-x);font-size:1rem;color:var(--bs-accordion-btn-color);text-align:left;background-color:var(--bs-accordion-btn-bg);border:0;border-radius:0;overflow-anchor:none;transition:var(--bs-accordion-transition)}@media 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reduce){.accordion-button::after{transition:none}}.accordion-button:hover{z-index:2}.accordion-button:focus{z-index:3;border-color:var(--bs-accordion-btn-focus-border-color);outline:0;box-shadow:var(--bs-accordion-btn-focus-box-shadow)}.accordion-header{margin-bottom:0}.accordion-item{color:var(--bs-accordion-color);background-color:var(--bs-accordion-bg);border:var(--bs-accordion-border-width) solid var(--bs-accordion-border-color)}.accordion-item:first-of-type{border-top-left-radius:var(--bs-accordion-border-radius);border-top-right-radius:var(--bs-accordion-border-radius)}.accordion-item:first-of-type .accordion-button{border-top-left-radius:var(--bs-accordion-inner-border-radius);border-top-right-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:not(:first-of-type){border-top:0}.accordion-item:last-of-type{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-item:last-of-type .accordion-button.collapsed{border-bottom-right-radius:var(--bs-accordion-inner-border-radius);border-bottom-left-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:last-of-type .accordion-collapse{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-body{padding:var(--bs-accordion-body-padding-y) var(--bs-accordion-body-padding-x)}.accordion-flush .accordion-collapse{border-width:0}.accordion-flush .accordion-item{border-right:0;border-left:0;border-radius:0}.accordion-flush .accordion-item:first-child{border-top:0}.accordion-flush .accordion-item:last-child{border-bottom:0}.accordion-flush .accordion-item .accordion-button,.accordion-flush .accordion-item .accordion-button.collapsed{border-radius:0}[data-bs-theme="dark"] .accordion-button::after{--bs-accordion-btn-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%236ea8fe'%3e%3cpath 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var(--bs-breadcrumb-padding-x);margin-bottom:var(--bs-breadcrumb-margin-bottom);font-size:var(--bs-breadcrumb-font-size);list-style:none;background-color:var(--bs-breadcrumb-bg);border-radius:var(--bs-breadcrumb-border-radius)}.breadcrumb-item+.breadcrumb-item{padding-left:var(--bs-breadcrumb-item-padding-x)}.breadcrumb-item+.breadcrumb-item::before{float:left;padding-right:var(--bs-breadcrumb-item-padding-x);color:var(--bs-breadcrumb-divider-color);content:var(--bs-breadcrumb-divider, "/") /* rtl: var(--bs-breadcrumb-divider, "/") */}.breadcrumb-item.active{color:var(--bs-breadcrumb-item-active-color)}.pagination{--bs-pagination-padding-x: .75rem;--bs-pagination-padding-y: .375rem;--bs-pagination-font-size:1rem;--bs-pagination-color: var(--bs-link-color);--bs-pagination-bg: var(--bs-body-bg);--bs-pagination-border-width: var(--bs-border-width);--bs-pagination-border-color: var(--bs-border-color);--bs-pagination-border-radius: var(--bs-border-radius);--bs-pagination-hover-color: var(--bs-link-hover-color);--bs-pagination-hover-bg: var(--bs-tertiary-bg);--bs-pagination-hover-border-color: var(--bs-border-color);--bs-pagination-focus-color: var(--bs-link-hover-color);--bs-pagination-focus-bg: var(--bs-secondary-bg);--bs-pagination-focus-box-shadow: 0 0 0 .25rem rgba(13,110,253,0.25);--bs-pagination-active-color: #fff;--bs-pagination-active-bg: #0d6efd;--bs-pagination-active-border-color: #0d6efd;--bs-pagination-disabled-color: var(--bs-secondary-color);--bs-pagination-disabled-bg: var(--bs-secondary-bg);--bs-pagination-disabled-border-color: var(--bs-border-color);display:flex;display:-webkit-flex;padding-left:0;list-style:none}.page-link{position:relative;display:block;padding:var(--bs-pagination-padding-y) var(--bs-pagination-padding-x);font-size:var(--bs-pagination-font-size);color:var(--bs-pagination-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-pagination-bg);border:var(--bs-pagination-border-width) solid var(--bs-pagination-border-color);transition:color 0.15s ease-in-out,background-color 0.15s ease-in-out,border-color 0.15s ease-in-out,box-shadow 0.15s ease-in-out}@media (prefers-reduced-motion: reduce){.page-link{transition:none}}.page-link:hover{z-index:2;color:var(--bs-pagination-hover-color);background-color:var(--bs-pagination-hover-bg);border-color:var(--bs-pagination-hover-border-color)}.page-link:focus{z-index:3;color:var(--bs-pagination-focus-color);background-color:var(--bs-pagination-focus-bg);outline:0;box-shadow:var(--bs-pagination-focus-box-shadow)}.page-link.active,.active>.page-link{z-index:3;color:var(--bs-pagination-active-color);background-color:var(--bs-pagination-active-bg);border-color:var(--bs-pagination-active-border-color)}.page-link.disabled,.disabled>.page-link{color:var(--bs-pagination-disabled-color);pointer-events:none;background-color:var(--bs-pagination-disabled-bg);border-color:var(--bs-pagination-disabled-border-color)}.page-item:not(:first-child) .page-link{margin-left:calc(var(--bs-border-width) * -1)}.page-item:first-child .page-link{border-top-left-radius:var(--bs-pagination-border-radius);border-bottom-left-radius:var(--bs-pagination-border-radius)}.page-item:last-child .page-link{border-top-right-radius:var(--bs-pagination-border-radius);border-bottom-right-radius:var(--bs-pagination-border-radius)}.pagination-lg{--bs-pagination-padding-x: 1.5rem;--bs-pagination-padding-y: .75rem;--bs-pagination-font-size:1.25rem;--bs-pagination-border-radius: var(--bs-border-radius-lg)}.pagination-sm{--bs-pagination-padding-x: .5rem;--bs-pagination-padding-y: .25rem;--bs-pagination-font-size:.875rem;--bs-pagination-border-radius: var(--bs-border-radius-sm)}.badge{--bs-badge-padding-x: .65em;--bs-badge-padding-y: .35em;--bs-badge-font-size:.75em;--bs-badge-font-weight: 700;--bs-badge-color: #fff;--bs-badge-border-radius: var(--bs-border-radius);display:inline-block;padding:var(--bs-badge-padding-y) var(--bs-badge-padding-x);font-size:var(--bs-badge-font-size);font-weight:var(--bs-badge-font-weight);line-height:1;color:var(--bs-badge-color);text-align:center;white-space:nowrap;vertical-align:baseline;border-radius:var(--bs-badge-border-radius)}.badge:empty{display:none}.btn .badge{position:relative;top:-1px}.alert{--bs-alert-bg: transparent;--bs-alert-padding-x: 1rem;--bs-alert-padding-y: 1rem;--bs-alert-margin-bottom: 1rem;--bs-alert-color: inherit;--bs-alert-border-color: transparent;--bs-alert-border: var(--bs-border-width) solid var(--bs-alert-border-color);--bs-alert-border-radius: var(--bs-border-radius);--bs-alert-link-color: inherit;position:relative;padding:var(--bs-alert-padding-y) var(--bs-alert-padding-x);margin-bottom:var(--bs-alert-margin-bottom);color:var(--bs-alert-color);background-color:var(--bs-alert-bg);border:var(--bs-alert-border);border-radius:var(--bs-alert-border-radius)}.alert-heading{color:inherit}.alert-link{font-weight:700;color:var(--bs-alert-link-color)}.alert-dismissible{padding-right:3rem}.alert-dismissible .btn-close{position:absolute;top:0;right:0;z-index:2;padding:1.25rem 1rem}.alert-default{--bs-alert-color: var(--bs-default-text-emphasis);--bs-alert-bg: var(--bs-default-bg-subtle);--bs-alert-border-color: var(--bs-default-border-subtle);--bs-alert-link-color: var(--bs-default-text-emphasis)}.alert-primary{--bs-alert-color: var(--bs-primary-text-emphasis);--bs-alert-bg: var(--bs-primary-bg-subtle);--bs-alert-border-color: var(--bs-primary-border-subtle);--bs-alert-link-color: var(--bs-primary-text-emphasis)}.alert-secondary{--bs-alert-color: var(--bs-secondary-text-emphasis);--bs-alert-bg: var(--bs-secondary-bg-subtle);--bs-alert-border-color: var(--bs-secondary-border-subtle);--bs-alert-link-color: var(--bs-secondary-text-emphasis)}.alert-success{--bs-alert-color: var(--bs-success-text-emphasis);--bs-alert-bg: var(--bs-success-bg-subtle);--bs-alert-border-color: var(--bs-success-border-subtle);--bs-alert-link-color: var(--bs-success-text-emphasis)}.alert-info{--bs-alert-color: var(--bs-info-text-emphasis);--bs-alert-bg: var(--bs-info-bg-subtle);--bs-alert-border-color: var(--bs-info-border-subtle);--bs-alert-link-color: var(--bs-info-text-emphasis)}.alert-warning{--bs-alert-color: var(--bs-warning-text-emphasis);--bs-alert-bg: var(--bs-warning-bg-subtle);--bs-alert-border-color: var(--bs-warning-border-subtle);--bs-alert-link-color: var(--bs-warning-text-emphasis)}.alert-danger{--bs-alert-color: var(--bs-danger-text-emphasis);--bs-alert-bg: var(--bs-danger-bg-subtle);--bs-alert-border-color: var(--bs-danger-border-subtle);--bs-alert-link-color: var(--bs-danger-text-emphasis)}.alert-light{--bs-alert-color: var(--bs-light-text-emphasis);--bs-alert-bg: var(--bs-light-bg-subtle);--bs-alert-border-color: var(--bs-light-border-subtle);--bs-alert-link-color: var(--bs-light-text-emphasis)}.alert-dark{--bs-alert-color: var(--bs-dark-text-emphasis);--bs-alert-bg: var(--bs-dark-bg-subtle);--bs-alert-border-color: var(--bs-dark-border-subtle);--bs-alert-link-color: var(--bs-dark-text-emphasis)}@keyframes progress-bar-stripes{0%{background-position-x:1rem}}.progress,.progress-stacked{--bs-progress-height: 1rem;--bs-progress-font-size:.75rem;--bs-progress-bg: var(--bs-secondary-bg);--bs-progress-border-radius: var(--bs-border-radius);--bs-progress-box-shadow: var(--bs-box-shadow-inset);--bs-progress-bar-color: #fff;--bs-progress-bar-bg: #0d6efd;--bs-progress-bar-transition: width 0.6s ease;display:flex;display:-webkit-flex;height:var(--bs-progress-height);overflow:hidden;font-size:var(--bs-progress-font-size);background-color:var(--bs-progress-bg);border-radius:var(--bs-progress-border-radius)}.progress-bar{display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;justify-content:center;-webkit-justify-content:center;overflow:hidden;color:var(--bs-progress-bar-color);text-align:center;white-space:nowrap;background-color:var(--bs-progress-bar-bg);transition:var(--bs-progress-bar-transition)}@media (prefers-reduced-motion: reduce){.progress-bar{transition:none}}.progress-bar-striped{background-image:linear-gradient(45deg, rgba(255,255,255,0.15) 25%, transparent 25%, transparent 50%, rgba(255,255,255,0.15) 50%, rgba(255,255,255,0.15) 75%, transparent 75%, transparent);background-size:var(--bs-progress-height) var(--bs-progress-height)}.progress-stacked>.progress{overflow:visible}.progress-stacked>.progress>.progress-bar{width:100%}.progress-bar-animated{animation:1s linear infinite progress-bar-stripes}@media (prefers-reduced-motion: reduce){.progress-bar-animated{animation:none}}.list-group{--bs-list-group-color: var(--bs-body-color);--bs-list-group-bg: var(--bs-body-bg);--bs-list-group-border-color: var(--bs-border-color);--bs-list-group-border-width: var(--bs-border-width);--bs-list-group-border-radius: var(--bs-border-radius);--bs-list-group-item-padding-x: 1rem;--bs-list-group-item-padding-y: .5rem;--bs-list-group-action-color: var(--bs-secondary-color);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-tertiary-bg);--bs-list-group-action-active-color: var(--bs-body-color);--bs-list-group-action-active-bg: var(--bs-secondary-bg);--bs-list-group-disabled-color: var(--bs-secondary-color);--bs-list-group-disabled-bg: var(--bs-body-bg);--bs-list-group-active-color: #fff;--bs-list-group-active-bg: #0d6efd;--bs-list-group-active-border-color: #0d6efd;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;padding-left:0;margin-bottom:0;border-radius:var(--bs-list-group-border-radius)}.list-group-numbered{list-style-type:none;counter-reset:section}.list-group-numbered>.list-group-item::before{content:counters(section, ".") ". ";counter-increment:section}.list-group-item-action{width:100%;color:var(--bs-list-group-action-color);text-align:inherit}.list-group-item-action:hover,.list-group-item-action:focus{z-index:1;color:var(--bs-list-group-action-hover-color);text-decoration:none;background-color:var(--bs-list-group-action-hover-bg)}.list-group-item-action:active{color:var(--bs-list-group-action-active-color);background-color:var(--bs-list-group-action-active-bg)}.list-group-item{position:relative;display:block;padding:var(--bs-list-group-item-padding-y) var(--bs-list-group-item-padding-x);color:var(--bs-list-group-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-list-group-bg);border:var(--bs-list-group-border-width) solid var(--bs-list-group-border-color)}.list-group-item:first-child{border-top-left-radius:inherit;border-top-right-radius:inherit}.list-group-item:last-child{border-bottom-right-radius:inherit;border-bottom-left-radius:inherit}.list-group-item.disabled,.list-group-item:disabled{color:var(--bs-list-group-disabled-color);pointer-events:none;background-color:var(--bs-list-group-disabled-bg)}.list-group-item.active{z-index:2;color:var(--bs-list-group-active-color);background-color:var(--bs-list-group-active-bg);border-color:var(--bs-list-group-active-border-color)}.list-group-item+.list-group-item{border-top-width:0}.list-group-item+.list-group-item.active{margin-top:calc(-1 * var(--bs-list-group-border-width));border-top-width:var(--bs-list-group-border-width)}.list-group-horizontal{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal>.list-group-item.active{margin-top:0}.list-group-horizontal>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}@media (min-width: 576px){.list-group-horizontal-sm{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-sm>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-sm>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-sm>.list-group-item.active{margin-top:0}.list-group-horizontal-sm>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-sm>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 768px){.list-group-horizontal-md{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-md>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-md>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-md>.list-group-item.active{margin-top:0}.list-group-horizontal-md>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-md>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 992px){.list-group-horizontal-lg{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-lg>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-lg>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-lg>.list-group-item.active{margin-top:0}.list-group-horizontal-lg>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-lg>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 1200px){.list-group-horizontal-xl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xl>.list-group-item.active{margin-top:0}.list-group-horizontal-xl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xl>.list-group-item+.list-group-item.active{margin-left:calc(-1 * var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media (min-width: 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var(--bs-list-group-border-width)}.list-group-flush>.list-group-item:last-child{border-bottom-width:0}.list-group-item-default{--bs-list-group-color: var(--bs-default-text-emphasis);--bs-list-group-bg: var(--bs-default-bg-subtle);--bs-list-group-border-color: var(--bs-default-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-default-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-default-border-subtle);--bs-list-group-active-color: var(--bs-default-bg-subtle);--bs-list-group-active-bg: var(--bs-default-text-emphasis);--bs-list-group-active-border-color: var(--bs-default-text-emphasis)}.list-group-item-primary{--bs-list-group-color: var(--bs-primary-text-emphasis);--bs-list-group-bg: var(--bs-primary-bg-subtle);--bs-list-group-border-color: var(--bs-primary-border-subtle);--bs-list-group-action-hover-color: 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var(--bs-secondary-text-emphasis);--bs-list-group-active-border-color: var(--bs-secondary-text-emphasis)}.list-group-item-success{--bs-list-group-color: var(--bs-success-text-emphasis);--bs-list-group-bg: var(--bs-success-bg-subtle);--bs-list-group-border-color: var(--bs-success-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-success-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-success-border-subtle);--bs-list-group-active-color: var(--bs-success-bg-subtle);--bs-list-group-active-bg: var(--bs-success-text-emphasis);--bs-list-group-active-border-color: var(--bs-success-text-emphasis)}.list-group-item-info{--bs-list-group-color: var(--bs-info-text-emphasis);--bs-list-group-bg: var(--bs-info-bg-subtle);--bs-list-group-border-color: var(--bs-info-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-info-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-info-border-subtle);--bs-list-group-active-color: var(--bs-info-bg-subtle);--bs-list-group-active-bg: var(--bs-info-text-emphasis);--bs-list-group-active-border-color: var(--bs-info-text-emphasis)}.list-group-item-warning{--bs-list-group-color: var(--bs-warning-text-emphasis);--bs-list-group-bg: var(--bs-warning-bg-subtle);--bs-list-group-border-color: var(--bs-warning-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-warning-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-warning-border-subtle);--bs-list-group-active-color: var(--bs-warning-bg-subtle);--bs-list-group-active-bg: var(--bs-warning-text-emphasis);--bs-list-group-active-border-color: var(--bs-warning-text-emphasis)}.list-group-item-danger{--bs-list-group-color: var(--bs-danger-text-emphasis);--bs-list-group-bg: var(--bs-danger-bg-subtle);--bs-list-group-border-color: var(--bs-danger-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-danger-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-danger-border-subtle);--bs-list-group-active-color: var(--bs-danger-bg-subtle);--bs-list-group-active-bg: var(--bs-danger-text-emphasis);--bs-list-group-active-border-color: var(--bs-danger-text-emphasis)}.list-group-item-light{--bs-list-group-color: var(--bs-light-text-emphasis);--bs-list-group-bg: var(--bs-light-bg-subtle);--bs-list-group-border-color: var(--bs-light-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-light-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-light-border-subtle);--bs-list-group-active-color: var(--bs-light-bg-subtle);--bs-list-group-active-bg: var(--bs-light-text-emphasis);--bs-list-group-active-border-color: var(--bs-light-text-emphasis)}.list-group-item-dark{--bs-list-group-color: var(--bs-dark-text-emphasis);--bs-list-group-bg: var(--bs-dark-bg-subtle);--bs-list-group-border-color: var(--bs-dark-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-dark-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-dark-border-subtle);--bs-list-group-active-color: var(--bs-dark-bg-subtle);--bs-list-group-active-bg: var(--bs-dark-text-emphasis);--bs-list-group-active-border-color: var(--bs-dark-text-emphasis)}.btn-close{--bs-btn-close-color: #000;--bs-btn-close-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' 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diff --git a/docs/deps/data-deps.txt b/docs/deps/data-deps.txt
index ca4dfd9c..a4ab73a2 100644
--- a/docs/deps/data-deps.txt
+++ b/docs/deps/data-deps.txt
@@ -11,3 +11,4 @@
 
 
 
+
diff --git a/docs/index.html b/docs/index.html
index c236f4dd..fa924c6d 100644
--- a/docs/index.html
+++ b/docs/index.html
@@ -10,7 +10,7 @@
 
 
 
-
+
 
 
 
@@ -22,7 +22,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -98,7 +98,7 @@ 
Citation

 

 
Developers

 
 

@@ -120,7 +120,7 @@ 
Dev status

 

 
 

-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     
diff --git a/docs/news/index.html b/docs/news/index.html
index 27c58804..a3614952 100644
--- a/docs/news/index.html
+++ b/docs/news/index.html
@@ -1,5 +1,5 @@
 
-Changelog • spdep
+Changelog • spdep
     Skip to contents
 
 
@@ -7,7 +7,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -58,7 +58,7 @@ 
Ver
     

 
Version 1.3-10 (2025-01-20)
CRAN release: 2025-01-20

 
  • R_NO_REMAP problem with R < 4.4.1 fixed by replacing COPY_TO_USER_STRING by Rf_mkChar, because include/Rdefines.h before revision 86416 set COPY_TO_USER_STRING as mkChar which is not defined as Rf_mkChar when R_NO_REMAP is defined, #176, thanks to Edzer Pebesma
    • 
-
  • disambiguate which skater in examples to satisfy pkgdown, which used rgeoda::skater; other patches to examples to satisfy pkgdown
    • 
+
  • disambiguate which skater in examples to satisfy pkgdown, which used rgeoda::skater; other patches to examples to satisfy pkgdown
    • 
 
  • use inherits in skater
    • 
 

     

@@ -103,7 +103,7 @@ 
Versi
 

     

 
Version 1.3-3 (2024-02-07)
CRAN release: 2024-02-07

-
  • change lm.LMtests to lm.RStests and re-name Lagrange multiplier to Rao’s score; add GNM_ prefix to test names if the input object inherits from SlX created by spatialreg::lmSLX (Koley, forthcoming)
    • 
+
    • change lm.LMtests to lm.RStests and re-name Lagrange multiplier to Rao’s score; add GNM_ prefix to test names if the input object inherits from SlX created by spatialreg::lmSLX (Koley, forthcoming)
      • 
 
    • add SD.RStests implementation of Rao’s score tests for spatial Durbin models (Koley and Bera, 2024) and for SDEM models (Koley, forthcoming)
      • 
 
    • #143 row.names pass-through in poly2nb corrected, harmonised row.names pass-through also in nbdists and dnearneigh
      • 
 
    • #139 add na.action argument to geary.test, geary.mc and globalG.test
      • 
@@ -236,7 +236,7 @@ 
      Versi
 

 
 

-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/pkgdown.yml b/docs/pkgdown.yml
index f1c0b675..044af2e6 100644
--- a/docs/pkgdown.yml
+++ b/docs/pkgdown.yml
@@ -1,13 +1,13 @@
-pandoc: 3.1.11.1
-pkgdown: 2.1.3
+pandoc: 3.6.3
+pkgdown: 2.1.1
 pkgdown_sha: ~
 articles:
   CO69: CO69.html
-  nb_sf: nb_sf.html
   nb: nb.html
+  nb_sf: nb_sf.html
   sids: sids.html
   subgraphs: subgraphs.html
-last_built: 2025-06-10T07:28Z
+last_built: 2025-07-10T18:01Z
 urls:
   reference: https://r-spatial.github.io/spdep/reference
   article: https://r-spatial.github.io/spdep/articles
diff --git a/docs/reference/COL.OLD.html b/docs/reference/COL.OLD.html
index 6d47346a..c0796961 100644
--- a/docs/reference/COL.OLD.html
+++ b/docs/reference/COL.OLD.html
@@ -1,5 +1,5 @@
 
-Columbus OH spatial analysis data set - old numbering — oldcol • spdepColumbus OH spatial analysis data set - old numbering — oldcol • spdepspdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -162,7 +162,7 @@ 
Note

 

 
 

-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/EBImoran.mc.html b/docs/reference/EBImoran.mc.html
index 31f39d0e..0317b0c8 100644
--- a/docs/reference/EBImoran.mc.html
+++ b/docs/reference/EBImoran.mc.html
@@ -1,5 +1,5 @@
 
-Permutation test for empirical Bayes index — EBImoran.mc • spdep
+Permutation test for empirical Bayes index — EBImoran.mc • spdep
     Skip to contents
 
 
@@ -7,7 +7,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -186,7 +186,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/EBest-1.png b/docs/reference/EBest-1.png
index 8ec6b735..6472e6a0 100644
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diff --git a/docs/reference/EBest.html b/docs/reference/EBest.html
index 44b28e29..16c05d5e 100644
--- a/docs/reference/EBest.html
+++ b/docs/reference/EBest.html
@@ -1,5 +1,5 @@
 
-Global Empirical Bayes estimator — EBest • spdep
+Global Empirical Bayes estimator — EBest • spdep
     Skip to contents
 
 
@@ -7,7 +7,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -200,7 +200,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/EBlocal-1.png b/docs/reference/EBlocal-1.png
index 1b237319..f78c30e2 100644
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diff --git a/docs/reference/EBlocal.html b/docs/reference/EBlocal.html
index 301aa3fd..eb2cee9b 100644
--- a/docs/reference/EBlocal.html
+++ b/docs/reference/EBlocal.html
@@ -1,5 +1,5 @@
 
-Local Empirical Bayes estimator — EBlocal • spdep
+Local Empirical Bayes estimator — EBlocal • spdep
     Skip to contents
 
 
@@ -7,7 +7,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -128,7 +128,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/LOSH-1.png b/docs/reference/LOSH-1.png
index 52c40c30..21fde589 100644
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diff --git a/docs/reference/LOSH.cs-1.png b/docs/reference/LOSH.cs-1.png
index 52c40c30..21fde589 100644
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diff --git a/docs/reference/LOSH.cs.html b/docs/reference/LOSH.cs.html
index 61df579e..8b2c13f9 100644
--- a/docs/reference/LOSH.cs.html
+++ b/docs/reference/LOSH.cs.html
@@ -1,5 +1,5 @@
 
-Chi-square based test for local spatial heteroscedasticity — LOSH.cs • spdep
+Chi-square based test for local spatial heteroscedasticity — LOSH.cs • spdep
     Skip to contents
 
 
@@ -7,7 +7,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -134,7 +134,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/LOSH.html b/docs/reference/LOSH.html
index e58c6ad6..cf3d728f 100644
--- a/docs/reference/LOSH.html
+++ b/docs/reference/LOSH.html
@@ -1,5 +1,5 @@
 
-Local spatial heteroscedasticity — LOSH • spdepLocal spatial heteroscedasticity — LOSH • spdepspdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -142,7 +142,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/LOSH.mc-1.png b/docs/reference/LOSH.mc-1.png
index bc7f37de..611fec2c 100644
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diff --git a/docs/reference/LOSH.mc.html b/docs/reference/LOSH.mc.html
index fb5bc559..e3f82e21 100644
--- a/docs/reference/LOSH.mc.html
+++ b/docs/reference/LOSH.mc.html
@@ -1,5 +1,5 @@
 
-Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc • spdep
+Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc • spdep
     Skip to contents
 
 
@@ -7,7 +7,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -130,28 +130,28 @@ 
Examples    resLOSH_mc <- LOSH.mc(columbus$CRIME, nb2listw(col.gal.nb), 2, 100)
     summary(resLOSH_mc)
 #>        Hi             x_bar_i            ei                 Pr()         
-#>  Min.   :0.03438   Min.   :13.85   Min.   :2.982e-02   Min.   :0.009901  
-#>  1st Qu.:0.23838   1st Qu.:24.71   1st Qu.:7.011e+00   1st Qu.:0.079208  
-#>  Median :0.66689   Median :35.90   Median :5.211e+01   Median :0.653465  
-#>  Mean   :1.06592   Mean   :34.88   Mean   :1.519e+02   Mean   :0.552233  
-#>  3rd Qu.:1.59680   3rd Qu.:45.39   3rd Qu.:1.051e+02   3rd Qu.:0.900990  
-#>  Max.   :4.68765   Max.   :54.91   Max.   :2.455e+03   Max.   :0.990099  
+#>  Min.   :0.03438   Min.   :13.85   Min.   :   0.0298   Min.   :0.009901  
+#>  1st Qu.:0.23838   1st Qu.:24.71   1st Qu.:   7.0114   1st Qu.:0.118812  
+#>  Median :0.66689   Median :35.90   Median :  52.1094   Median :0.673267  
+#>  Mean   :1.06592   Mean   :34.88   Mean   : 151.9232   Mean   :0.551424  
+#>  3rd Qu.:1.59680   3rd Qu.:45.39   3rd Qu.: 105.0551   3rd Qu.:0.900990  
+#>  Max.   :4.68765   Max.   :54.91   Max.   :2455.2201   Max.   :0.990099  
     resLOSH_cs <- LOSH.cs(columbus$CRIME, nb2listw(col.gal.nb))
     summary(resLOSH_cs)
 #>        Hi               E.Hi       Var.Hi            Z.Hi        
 #>  Min.   :0.03438   Min.   :1   Min.   :0.4972   Min.   :0.04356  
-#>  1st Qu.:0.23838   1st Qu.:1   1st Qu.:0.9136   1st Qu.:0.35070  
-#>  Median :0.66689   Median :1   Median :1.4342   Median :1.19176  
+#>  1st Qu.:0.23838   1st Qu.:1   1st Qu.:0.9136   1st Qu.:0.35069  
+#>  Median :0.66689   Median :1   Median :1.4342   Median :1.19175  
 #>  Mean   :1.06592   Mean   :1   Mean   :1.4758   Mean   :1.89447  
 #>  3rd Qu.:1.59680   3rd Qu.:1   3rd Qu.:1.9547   3rd Qu.:2.65120  
 #>  Max.   :4.68765   Max.   :1   Max.   :2.9958   Max.   :7.25681  
 #>     x_bar_i            ei                 Pr()       
-#>  Min.   :13.85   Min.   :2.982e-02   Min.   :0.0190  
-#>  1st Qu.:24.71   1st Qu.:7.011e+00   1st Qu.:0.2050  
-#>  Median :35.90   Median :5.211e+01   Median :0.5264  
-#>  Mean   :34.88   Mean   :1.519e+02   Mean   :0.4507  
-#>  3rd Qu.:45.39   3rd Qu.:1.051e+02   3rd Qu.:0.6529  
-#>  Max.   :54.91   Max.   :2.455e+03   Max.   :0.9540  
+#>  Min.   :13.85   Min.   :   0.0298   Min.   :0.0190  
+#>  1st Qu.:24.71   1st Qu.:   7.0114   1st Qu.:0.2050  
+#>  Median :35.90   Median :  52.1094   Median :0.5264  
+#>  Mean   :34.88   Mean   : 151.9232   Mean   :0.4507  
+#>  3rd Qu.:45.39   3rd Qu.: 105.0551   3rd Qu.:0.6529  
+#>  Max.   :54.91   Max.   :2455.2201   Max.   :0.9540  
     plot(resLOSH_mc[,"Pr()"], resLOSH_cs[,"Pr()"])
 
 

@@ -165,7 +165,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/SD.RStests.html b/docs/reference/SD.RStests.html
index 83b7e1ec..f9a80111 100644
--- a/docs/reference/SD.RStests.html
+++ b/docs/reference/SD.RStests.html
@@ -1,5 +1,5 @@
 
-Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests • spdepRao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests • spdep
     Skip to contents
@@ -9,7 +9,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -124,7 +124,8 @@ 
See alsoExamples

     
columbus <- sf::st_read(system.file("shapes/columbus.gpkg", package="spData")[1])
 #> Reading layer `columbus' from data source 
-#>   `/home/rsb/lib/r_libs/spData/shapes/columbus.gpkg' using driver `GPKG'
+#>   `C:\Users\rzomor2\AppData\Local\R\win-library\4.4\spData\shapes\columbus.gpkg' 
+#>   using driver `GPKG'
 #> Simple feature collection with 49 features and 20 fields
 #> Geometry type: POLYGON
 #> Dimension:     XY
@@ -169,11 +170,11 @@ 
Examples#> SDM_adjRSWX  12.233108         6 0.05697 .
 #> SDM_Joint    12.951730         7 0.07329 .
 #> ---
-#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
-all.equal(unname(res$SDM_Joint$statistic),
+#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+all.equal(unname(res$SDM_Joint$statistic),
  unname(res$SDM_RSlag$statistic + res$SDM_adjRSWX$statistic))
 #> [1] TRUE
-all.equal(unname(res$SDM_Joint$statistic),
+all.equal(unname(res$SDM_Joint$statistic),
  unname(res$SDM_adjRSlag$statistic + res$SDM_RSWX$statistic))
 #> [1] TRUE
 res <- SD.RStests(lm_obj, col.listw, test="SDEM")
@@ -194,8 +195,8 @@ 
Examples#> SDEM_RSWX  12.904287         6 0.04458 *
 #> SDEM_Joint 12.951730         7 0.07329 .
 #> ---
-#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
-all.equal(unname(res$SDEM_Joint$statistic),
+#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+all.equal(unname(res$SDEM_Joint$statistic),
  unname(res$SDEM_RSerr$statistic + res$SDEM_RSWX$statistic))
 #> [1] TRUE
 summary(SD.RStests(lm_obj, nb2listw(col.gal.nb, style="C"), test="all"))
@@ -221,7 +222,7 @@ 
Examples#> SDEM_RSWX    12.2469692         7 0.09272 .
 #> SDEM_Joint   12.2499705         8 0.14039  
 #> ---
-#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
 summary(SD.RStests(lm_obj, col.listw, test="all", Durbin= ~ INC))
 #> 	Rao's score test spatial Durbin diagnostics
 #> data:  
@@ -257,7 +258,7 @@ 
Examples#> SDEM_RSWX       6.0609         2 0.048295 * 
 #> SDEM_Joint     10.6720         3 0.013638 * 
 #> ---
-#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
 columbusNA <- columbus
 columbusNA$HOVAL[15] <- NA
 lm_objNA <- lm(CRIME ~ INC + HOVAL, data=columbusNA)
@@ -277,7 +278,7 @@ 
Examples#> SDEM_RSWX       6.0812         2 0.047807 * 
 #> SDEM_Joint     10.5527         3 0.014407 * 
 #> ---
-#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
 

     

   

 
     

diff --git a/docs/reference/aggregate.nb-1.png b/docs/reference/aggregate.nb-1.png
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diff --git a/docs/reference/aggregate.nb.html b/docs/reference/aggregate.nb.html
index e02b0621..5ed4e718 100644
--- a/docs/reference/aggregate.nb.html
+++ b/docs/reference/aggregate.nb.html
@@ -1,5 +1,5 @@
 
-Aggregate a spatial neighbours object — aggregate.nb • spdep
+Aggregate a spatial neighbours object — aggregate.nb • spdep
     Skip to contents
 
 
@@ -7,7 +7,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -106,7 +106,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/airdist.html b/docs/reference/airdist.html
index e4aa6803..3dfffa7d 100644
--- a/docs/reference/airdist.html
+++ b/docs/reference/airdist.html
@@ -1,5 +1,5 @@
 
-Measure distance from plot — airdist • spdep
+Measure distance from plot — airdist • spdep
     Skip to contents
 
 
@@ -7,7 +7,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -85,7 +85,7 @@ 
See also
 
 

-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/autocov_dist-1.png b/docs/reference/autocov_dist-1.png
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index 01be1e7e..7adf6244 100644
--- a/docs/reference/autocov_dist.html
+++ b/docs/reference/autocov_dist.html
@@ -1,5 +1,5 @@
 
-Distance-weighted autocovariate — autocov_dist • spdep
+Distance-weighted autocovariate — autocov_dist • spdep
     Skip to contents
 
 
@@ -7,7 +7,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -158,7 +158,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/bhicv.html b/docs/reference/bhicv.html
index 1be61702..73ae9c5d 100644
--- a/docs/reference/bhicv.html
+++ b/docs/reference/bhicv.html
@@ -1,5 +1,5 @@
 
-Data set with 4 life condition indices of Belo Horizonte region — bhicv • spdepData set with 4 life condition indices of Belo Horizonte region — bhicv • spdep
     Skip to contents
@@ -9,7 +9,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -91,7 +91,7 @@ 
Examples    bh <- st_read(target)
 }
 #> Reading layer `bhicv' from data source 
-#>   `/tmp/Rtmp5vVziX/temp_libpath224d25059ed81/spdep/etc/shapes/bhicv.gpkg.zip' 
+#>   `C:\Users\rzomor2\AppData\Local\Temp\RtmpErQTm3\temp_libpath1a5cde63ff3\spdep\etc\shapes\bhicv.gpkg.zip' 
 #>   using driver `GPKG'
 #> Simple feature collection with 98 features and 8 fields
 #> Geometry type: POLYGON
@@ -109,7 +109,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/card.html b/docs/reference/card.html
index 3274349f..141f5fc7 100644
--- a/docs/reference/card.html
+++ b/docs/reference/card.html
@@ -1,5 +1,5 @@
 
-Cardinalities for neighbours lists — card • spdepCardinalities for neighbours lists — card • spdep
     Skip to contents
@@ -9,7 +9,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -101,7 +101,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/cell2nb-1.png b/docs/reference/cell2nb-1.png
index c1b6f24c..4de0aa47 100644
Binary files a/docs/reference/cell2nb-1.png and b/docs/reference/cell2nb-1.png differ
diff --git a/docs/reference/cell2nb.html b/docs/reference/cell2nb.html
index a7418810..bfa48373 100644
--- a/docs/reference/cell2nb.html
+++ b/docs/reference/cell2nb.html
@@ -1,5 +1,5 @@
 
-Generate neighbours list for grid cells — cell2nb • spdepGenerate neighbours list for grid cells — cell2nb • spdepspdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -194,7 +194,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/choynowski-1.png b/docs/reference/choynowski-1.png
index ed91db5c..4abef4f5 100644
Binary files a/docs/reference/choynowski-1.png and b/docs/reference/choynowski-1.png differ
diff --git a/docs/reference/choynowski.html b/docs/reference/choynowski.html
index 44f5f8dc..ee77648f 100644
--- a/docs/reference/choynowski.html
+++ b/docs/reference/choynowski.html
@@ -1,5 +1,5 @@
 
-Choynowski probability map values — choynowski • spdep
+Choynowski probability map values — choynowski • spdep
     Skip to contents
 
 
@@ -7,7 +7,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -138,7 +138,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/columbus.html b/docs/reference/columbus.html
index 070d8d0d..79049467 100644
--- a/docs/reference/columbus.html
+++ b/docs/reference/columbus.html
@@ -1,5 +1,5 @@
 
-Columbus OH spatial analysis data set — columbus • spdep
+Columbus OH spatial analysis data set — columbus • spdep
     Skip to contents
 
 
@@ -7,7 +7,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -66,7 +66,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/compon-1.png b/docs/reference/compon-1.png
index 89591823..124c658e 100644
Binary files a/docs/reference/compon-1.png and b/docs/reference/compon-1.png differ
diff --git a/docs/reference/compon.html b/docs/reference/compon.html
index d084f94b..845e7cc0 100644
--- a/docs/reference/compon.html
+++ b/docs/reference/compon.html
@@ -1,5 +1,5 @@
 
-Depth First Search on Neighbor Lists — Graph Components • spdep
+Depth First Search on Neighbor Lists — Graph Components • spdep
     Skip to contents
 
 
@@ -7,7 +7,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -59,7 +59,7 @@ 
Arguments
     
Details

-    
If attr(nb.obj, "sym") is FALSE and igraph::components is available, the components of the directed graph will be found by a simple breadth-first search; if igraph::components is not available, the object will be made symmetric (which may be time-consuming with large numbers of neighbours) and the components found by depth-first search. If attr(nb.obj, "sym") is TRUE, the components of the directed graph will be found by depth-first search. The time complexity of algorithms used in native code and through igraph::components is linear in the sum of the number of nodes and the number of edges in the graph, see https://github.com/r-spatial/spdep/issues/160 for details; very dense neighbour objects will have large numbers of edges.

+    
If attr(nb.obj, "sym") is FALSE and igraph::components is available, the components of the directed graph will be found by a simple breadth-first search; if igraph::components is not available, the object will be made symmetric (which may be time-consuming with large numbers of neighbours) and the components found by depth-first search. If attr(nb.obj, "sym") is TRUE, the components of the directed graph will be found by depth-first search. The time complexity of algorithms used in native code and through igraph::components is linear in the sum of the number of nodes and the number of edges in the graph, see https://github.com/r-spatial/spdep/issues/160 for details; very dense neighbour objects will have large numbers of edges.

     

     

     
Value

@@ -100,44 +100,24 @@ 
Examples
 run <- FALSE
 if (require("igraph", quietly=TRUE) && require("spatialreg", quietly=TRUE)) run <- TRUE
-#> 
-#> Attaching package: ‘igraph’
-#> The following objects are masked from ‘package:stats’:
-#> 
-#>     decompose, spectrum
-#> The following object is masked from ‘package:base’:
-#> 
-#>     union
-#> 
-#> Attaching package: ‘spatialreg’
-#> The following objects are masked from ‘package:spdep’:
-#> 
-#>     get.ClusterOption, get.VerboseOption, get.ZeroPolicyOption,
-#>     get.coresOption, get.mcOption, set.ClusterOption,
-#>     set.VerboseOption, set.ZeroPolicyOption, set.coresOption,
-#>     set.mcOption
 if (run) {
 B <- as(nb2listw(col2, style="B", zero.policy=TRUE), "CsparseMatrix")
-g1 <- graph_from_adjacency_matrix(B, mode="undirected")
-c1 <- components(g1)
+g1 <- graph_from_adjacency_matrix(B, mode="undirected")
+c1 <- components(g1)
 print(c1$no == res$nc)
 }
-#> [1] TRUE
 if (run) {
-print(all.equal(c1$membership, res$comp.id))
+print(all.equal(c1$membership, res$comp.id))
 }
-#> [1] "names for target but not for current"
 if (run) {
-print(all.equal(c1$csize, c(table(res$comp.id)), check.attributes=FALSE))
+print(all.equal(c1$csize, c(table(res$comp.id)), check.attributes=FALSE))
 }
-#> [1] TRUE
 if (run) {
 W <- as(nb2listw(col2, style="W", zero.policy=TRUE), "CsparseMatrix")
-g1W <- graph_from_adjacency_matrix(W, mode="directed", weighted="W")
-c1W <- components(g1W, mode="weak")
-print(all.equal(c1W$membership, res$comp.id, check.attributes=FALSE))
+g1W <- graph_from_adjacency_matrix(W, mode="directed", weighted="W")
+c1W <- components(g1W, mode="weak")
+print(all.equal(c1W$membership, res$comp.id, check.attributes=FALSE))
 }
-#> [1] TRUE
 # \donttest{
 if (run) {
 data(house, package="spData")
@@ -145,25 +125,16 @@ 
Examplesk6 <- knn2nb(knearneigh(house, k=6))
 is.symmetric.nb(k6)
 }
-#> [1] FALSE
 if (run) {
 print(k6)
 }
-#> Neighbour list object:
-#> Number of regions: 25357 
-#> Number of nonzero links: 152142 
-#> Percentage nonzero weights: 0.02366211 
-#> Average number of links: 6 
-#> Non-symmetric neighbours list
 if (run) {
 length(k6) + sum(card(k6))
 }
-#> [1] 177499
 if (run) {
 # no pre-computed graph components
 str(attr(k6, "ncomp"))
 }
-#>  NULL
 if (run) {
 # raising the subgraph compute ceiling to above |N|+|E| computes and stores the
 # object in the neighbour object
@@ -171,42 +142,24 @@ 
Examplesk6 <- knn2nb(knearneigh(house, k=6))
 str(attr(k6, "ncomp"))
 }
-#> Warning: neighbour object has 47 sub-graphs
-#> List of 2
-#>  $ nc     : num 47
-#>  $ comp.id: num [1:25357] 1 1 1 1 1 1 1 1 1 1 ...
 if (run) {
 print(k6)
 }
-#> Neighbour list object:
-#> Number of regions: 25357 
-#> Number of nonzero links: 152142 
-#> Percentage nonzero weights: 0.02366211 
-#> Average number of links: 6 
-#> 47 disjoint connected subgraphs
-#> Non-symmetric neighbours list
 if (run) {
 system.time(udir <- n.comp.nb(make.sym.nb(k6)))
 }
-#>    user  system elapsed 
-#>   2.303   0.001   2.313 
 if (run) {
 system.time(dir <- n.comp.nb(k6))
 }
-#>    user  system elapsed 
-#>   0.769   0.000   0.771 
 if (run) {
 udir$nc
 }
-#> [1] 47
 if (run) {
 dir$nc
 }
-#> [1] 47
 if (run) {
-all.equal(dir, udir)
+all.equal(dir, udir)
 }
-#> [1] TRUE
 # }
 

     

@@ -219,7 +172,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/diffnb-1.png b/docs/reference/diffnb-1.png
index 14c4a15e..d34d19b1 100644
Binary files a/docs/reference/diffnb-1.png and b/docs/reference/diffnb-1.png differ
diff --git a/docs/reference/diffnb.html b/docs/reference/diffnb.html
index dfaa1ebc..ffbd1477 100644
--- a/docs/reference/diffnb.html
+++ b/docs/reference/diffnb.html
@@ -1,5 +1,5 @@
 
-Differences between neighbours lists — diffnb • spdep
+Differences between neighbours lists — diffnb • spdep
     Skip to contents
 
 
@@ -7,7 +7,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -77,8 +77,8 @@ 
Author<
 
     

     
Examples

-    
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
-coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE)
+    
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
+coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE)
 rn <- row.names(columbus)
 knn1 <- knearneigh(coords, 1)
 knn2 <- knearneigh(coords, 2)
@@ -89,20 +89,18 @@ 
Examples#> Warning: neighbour object has 10 sub-graphs
 diffsl <- diffnb(nb2, nb1, legacy=FALSE)
 #> Warning: neighbour object has 10 sub-graphs
-#> Warning: neighbour object has 10 sub-graphs
-#> Warning: neighbour object has 10 sub-graphs
-all.equal(diffs, diffsl)
-#> [1] "Attributes: < Component “call”: target, current do not match when deparsed >"
+all.equal(diffs, diffsl)
+#> [1] "Attributes: < Component \"call\": target, current do not match when deparsed >"
 # call attribute fifference expected
 diffsd <- union.nb(setdiff.nb(nb1, nb2), setdiff.nb(nb2, nb1))
 #> Warning: neighbour object has 49 sub-graphs
 #> Warning: neighbour object has 10 sub-graphs
 #> Warning: neighbour object has 10 sub-graphs
-all.equal(diffs, diffsd)
-#> [1] "Attributes: < Component “call”: target, current do not match when deparsed >"
+all.equal(diffs, diffsd)
+#> [1] "Attributes: < Component \"call\": target, current do not match when deparsed >"
 # call attribute fifference expected
 opar <- par(no.readonly=TRUE)
-plot(st_geometry(columbus), border="grey", reset=FALSE,
+plot(st_geometry(columbus), border="grey", reset=FALSE,
  main="Plot of first (black) and second (red)\nnearest neighbours")
 plot(nb1, coords, add=TRUE)
 plot(diffs, coords, add=TRUE, col="red", lty=2)
@@ -119,7 +117,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/dnearneigh-1.png b/docs/reference/dnearneigh-1.png
index c265d134..abd4d36a 100644
Binary files a/docs/reference/dnearneigh-1.png and b/docs/reference/dnearneigh-1.png differ
diff --git a/docs/reference/dnearneigh-2.png b/docs/reference/dnearneigh-2.png
index ae9eaa40..dc4e325f 100644
Binary files a/docs/reference/dnearneigh-2.png and b/docs/reference/dnearneigh-2.png differ
diff --git a/docs/reference/dnearneigh.html b/docs/reference/dnearneigh.html
index 389aa5d4..01d0f4d1 100644
--- a/docs/reference/dnearneigh.html
+++ b/docs/reference/dnearneigh.html
@@ -1,5 +1,5 @@
 
-Neighbourhood contiguity by distance — dnearneigh • spdep
+Neighbourhood contiguity by distance — dnearneigh • spdep
     Skip to contents
 
 
@@ -7,7 +7,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -74,7 +74,7 @@ 
Arguments, (GE: greater than or equal to, LE: less than or equal to) that is the finite and closed interval [d1, d2], d1 <= x <= d2. The first element may also be "GT" (GT: greater than), the second "LT" (LT: less than) for finite, open intervals excluding the bounds; the first bound default was changed from "GT" to "GE" in release 1.1-7. When creating multiple distance bands, finite, half-open right-closed intervals may be used until the final interval to avoid overlapping on bounds: "GE", "LT", that is [d1, d2), d1 <= x < d2

 
   
use_kd_tree

-
default TRUE, if TRUE, use dbscan frNN if available (permitting 3D distances).

+
default TRUE, if TRUE, use dbscan frNN if available (permitting 3D distances).

 
   
symtest

 
Default FALSE; before release 1.1-7, TRUE - run symmetry check on output object, costly with large numbers of points.

@@ -105,8 +105,8 @@ 
See also
     
Examples

-    
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
-coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE)
+    
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
+coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE)
 rn <- row.names(columbus)
 k1 <- knn2nb(knearneigh(coords))
 #> Warning: neighbour object has 13 sub-graphs
@@ -129,12 +129,12 @@ 
Examples#> 1 most connected region:
 #> 28 with 11 links
 opar <- par(no.readonly=TRUE)
-plot(st_geometry(columbus), border="grey", reset=FALSE,
+plot(st_geometry(columbus), border="grey", reset=FALSE,
  main=paste("Distance based neighbours 0-",  format(all.linked), sep=""))
 plot(col.nb.0.all, coords, add=TRUE)
 
 par(opar)
-(sfc_obj <- st_centroid(st_geometry(columbus)))
+(sfc_obj <- st_centroid(st_geometry(columbus)))
 #> Geometry set for 49 features 
 #> Geometry type: POINT
 #> Dimension:     XY
@@ -148,7 +148,7 @@ 
Examples#> POINT (9.007982 13.29637)
 col.nb.0.all_sf <- dnearneigh(sfc_obj, 0, all.linked, row.names=rn)
 #> Warning: neighbour object has 2 sub-graphs
-all.equal(col.nb.0.all, col.nb.0.all_sf, check.attributes=FALSE)
+all.equal(col.nb.0.all, col.nb.0.all_sf, check.attributes=FALSE)
 #> [1] TRUE
 data(state)
 us48.fipsno <- read.geoda(system.file("etc/weights/us48.txt",
@@ -214,22 +214,22 @@ 
Examples#gc.nb <- dnearneigh(xy1, 0, all.linked)
 #summary(gc.nb, xy1, scale=0.5)
 
-xy1 <- st_as_sf((as.data.frame(state.center))[m50.48,], coords=1:2,
-  crs=st_crs("OGC:CRS84"))
-old_use_s2 <- sf_use_s2()
-sf_use_s2(TRUE)
+xy1 <- st_as_sf((as.data.frame(state.center))[m50.48,], coords=1:2,
+  crs=st_crs("OGC:CRS84"))
+old_use_s2 <- sf_use_s2()
+sf_use_s2(TRUE)
 gck1b <- knn2nb(knearneigh(xy1, k=1))
 #> Warning: neighbour object has 11 sub-graphs
 system.time(o <- nbdists(gck1b, xy1))
 #>    user  system elapsed 
-#>   0.013   0.000   0.012 
+#>       0       0       0 
 (all.linked <- max(unlist(o)))
 #> [1] 522.4464
 # use s2 brute-force dwithin_matrix approach for s2 <= 1.0.7
 system.time(gc.nb.dwithin <- dnearneigh(xy1, 0, all.linked, use_s2=TRUE, dwithin=TRUE))
 #> Warning: neighbour object has 3 sub-graphs
 #>    user  system elapsed 
-#>   0.025   0.000   0.025 
+#>    0.00    0.00    0.01 
 summary(gc.nb, xy1, scale=0.5)
 #> Neighbour list object:
 #> Number of regions: 48 
@@ -251,13 +251,13 @@ 
Examples}
 #> Warning: neighbour object has 3 sub-graphs
 #>    user  system elapsed 
-#>   0.022   0.000   0.022 
+#>       0       0       0 
 if (packageVersion("s2") > "1.0.7") {
 system.time(gc.nb.dwithin <- dnearneigh(xy1, 0, all.linked, use_s2=TRUE, dwithin=TRUE))
 }
 #> Warning: neighbour object has 3 sub-graphs
 #>    user  system elapsed 
-#>   0.024   0.000   0.024 
+#>    0.00    0.00    0.02 
 if (packageVersion("s2") > "1.0.7") {
 summary(gc.nb.dwithin, xy1, scale=0.5)
 }
@@ -300,7 +300,7 @@ 
Examplessystem.time(gc.nb.legacy <- dnearneigh(xy1, 0, all.linked, use_s2=FALSE))
 #> Warning: neighbour object has 3 sub-graphs
 #>    user  system elapsed 
-#>   0.012   0.000   0.013 
+#>    0.02    0.00    0.00 
 summary(gc.nb, xy1, scale=0.5)
 #> Neighbour list object:
 #> Number of regions: 48 
@@ -316,16 +316,16 @@ 
Examples#> 2 4 8 41 45 with 1 link
 #> 2 most connected regions:
 #> 7 28 with 10 links
-if (packageVersion("s2") > "1.0.7") all.equal(gc.nb.closest, gc.nb.dwithin, check.attributes=FALSE)
+if (packageVersion("s2") > "1.0.7") all.equal(gc.nb.closest, gc.nb.dwithin, check.attributes=FALSE)
 #> [1] TRUE
 # legacy is ellipsoidal, s2 spherical, so minor differences expected
-if (packageVersion("s2") > "1.0.7") all.equal(gc.nb, gc.nb.closest, check.attributes=FALSE)
+if (packageVersion("s2") > "1.0.7") all.equal(gc.nb, gc.nb.closest, check.attributes=FALSE)
 #> [1] "Component 2: Mean relative difference: 1"    
 #> [2] "Component 29: Numeric: lengths (2, 1) differ"
-all.equal(gc.nb, gc.nb.dwithin, check.attributes=FALSE)
+all.equal(gc.nb, gc.nb.dwithin, check.attributes=FALSE)
 #> [1] "Component 2: Mean relative difference: 1"    
 #> [2] "Component 29: Numeric: lengths (2, 1) differ"
-sf_use_s2(old_use_s2)
+sf_use_s2(old_use_s2)
 # example of reading points with readr::read_csv() yielding a tibble
 load(system.file("etc/misc/coords.rda", package="spdep"))
 class(coords)
@@ -350,7 +350,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/droplinks.html b/docs/reference/droplinks.html
index ac9f5dc3..f6fe5b4b 100644
--- a/docs/reference/droplinks.html
+++ b/docs/reference/droplinks.html
@@ -1,5 +1,5 @@
 
-Drop and add links in a neighbours list — droplinks • spdep
+Drop and add links in a neighbours list — droplinks • spdep
     Skip to contents
 
 
@@ -7,7 +7,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -105,39 +105,34 @@ 
Examples  wmat <- listw2mat(listw)
   for (j in 1:length(rho)) {
     mat <- diag(ns[i]*ns[i]) - rho[j] * wmat
-    res <- diag(solve(t(mat) %*% mat))
+    res <- diag(solve(t(mat) %*% mat))
     mns[i,j] <- mean(res)
     mxs[i,j] <- max(res)
   }
 }
 #> Warning: some observations have no neighbours
-#> Warning: some observations have no neighbours
-#> Warning: some observations have no neighbours
-#> Warning: some observations have no neighbours
-#> Warning: some observations have no neighbours
-#> Warning: some observations have no neighbours
-#> Warning: some observations have no neighbours
-#> Warning: some observations have no neighbours
+#> Error in n.comp.nb(nb): n.comp.nb: recursive nodeid out of bounds
+#> install spatialreg and igraph to avoid legacy issue
 print(mns)
-#>         0.2      0.5      0.95     0.999          1
-#> 5  1.038271 1.312627  9.486051  30.81487   32.04915
-#> 7  1.036443 1.295621 10.899580  83.25437   92.09812
-#> 9  1.035356 1.285145 10.798611 160.90951  195.02166
-#> 11 1.034639 1.278279 10.383083 254.83998  347.71145
-#> 13 1.034132 1.273442  9.968389 353.66366  555.88699
-#> 15 1.033753 1.269852  9.619387 447.19245  824.46560
-#> 17 1.033460 1.267082  9.337167 528.49015 1157.77630
-#> 19 1.033227 1.264879  9.109487 594.23907 1559.69614
+#>    0.2 0.5 0.95 0.999 1
+#> 5    0   0    0     0 0
+#> 7    0   0    0     0 0
+#> 9    0   0    0     0 0
+#> 11   0   0    0     0 0
+#> 13   0   0    0     0 0
+#> 15   0   0    0     0 0
+#> 17   0   0    0     0 0
+#> 19   0   0    0     0 0
 print(mxs)
-#>         0.2      0.5     0.95     0.999          1
-#> 5  1.048834 1.401934 12.00215  39.22742   40.79967
-#> 7  1.048834 1.402174 14.66823 106.90031  118.01556
-#> 9  1.048834 1.402176 15.49606 207.28928  249.74893
-#> 11 1.048834 1.402176 15.75744 329.22973  443.97194
-#> 13 1.048834 1.402176 15.83957 458.75739  707.14827
-#> 15 1.048834 1.402176 15.86474 583.50722 1044.75562
-#> 17 1.048834 1.402176 15.87225 695.10288 1461.57017
-#> 19 1.048834 1.402176 15.87445 789.50575 1961.84025
+#>    0.2 0.5 0.95 0.999 1
+#> 5    0   0    0     0 0
+#> 7    0   0    0     0 0
+#> 9    0   0    0     0 0
+#> 11   0   0    0     0 0
+#> 13   0   0    0     0 0
+#> 15   0   0    0     0 0
+#> 17   0   0    0     0 0
+#> 19   0   0    0     0 0
 
 # }
 
@@ -152,7 +147,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/edit.nb.html b/docs/reference/edit.nb.html
index 2f68f8c8..6f8887a9 100644
--- a/docs/reference/edit.nb.html
+++ b/docs/reference/edit.nb.html
@@ -1,5 +1,5 @@
 
-Interactive editing of neighbours lists — edit.nb • spdepInteractive editing of neighbours lists — edit.nb • spdepspdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -100,12 +100,11 @@ 
See also
     
Examples

-    
# \dontrun{
-columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
+    
if (FALSE) { # \dontrun{
+columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
 class(columbus)
-#> [1] "sf"         "data.frame"
 if (FALSE) nnb1 <- edit.nb(col.gal.nb, polys=as(columbus, "Spatial"))
-# }
+} # }
 

     

   

 
     

diff --git a/docs/reference/eire.html b/docs/reference/eire.html
index bff336c0..1a4d99e1 100644
--- a/docs/reference/eire.html
+++ b/docs/reference/eire.html
@@ -1,5 +1,5 @@
 
-Eire data sets — eire • spdep
+Eire data sets — eire • spdep
     Skip to contents
 
 
@@ -7,7 +7,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -59,7 +59,7 @@ 
Usage
 

 
 

-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/geary.html b/docs/reference/geary.html
index 411755b3..a092a7d0 100644
--- a/docs/reference/geary.html
+++ b/docs/reference/geary.html
@@ -1,5 +1,5 @@
 
-Compute Geary's C — geary • spdepCompute Geary's C — geary • spdepspdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -136,7 +136,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/geary.mc.html b/docs/reference/geary.mc.html
index d9287d65..f527af1c 100644
--- a/docs/reference/geary.mc.html
+++ b/docs/reference/geary.mc.html
@@ -1,5 +1,5 @@
 
-Permutation test for Geary's C statistic — geary.mc • spdep
+Permutation test for Geary's C statistic — geary.mc • spdep
     Skip to contents
 
 
@@ -7,7 +7,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -261,7 +261,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/geary.test.html b/docs/reference/geary.test.html
index 7ab432ad..ccb256e3 100644
--- a/docs/reference/geary.test.html
+++ b/docs/reference/geary.test.html
@@ -1,5 +1,5 @@
 
-Geary's C test for spatial autocorrelation — geary.test • spdep
+Geary's C test for spatial autocorrelation — geary.test • spdep
     Skip to contents
 
 
@@ -7,7 +7,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -294,7 +294,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/globalG.test.html b/docs/reference/globalG.test.html
index 7d1dab15..750103ae 100644
--- a/docs/reference/globalG.test.html
+++ b/docs/reference/globalG.test.html
@@ -1,5 +1,5 @@
 
-Global G test for spatial autocorrelation — globalG.test • spdep
+Global G test for spatial autocorrelation — globalG.test • spdep
     Skip to contents
 
 
@@ -7,7 +7,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -124,7 +124,7 @@ 
See also
     
Examples

-    
nc.sids <- st_read(system.file("shapes/sids.gpkg", package="spData")[1], quiet=TRUE)
+    
nc.sids <- st_read(system.file("shapes/sids.gpkg", package="spData")[1], quiet=TRUE)
 sidsrate79 <- (1000*nc.sids$SID79)/nc.sids$BIR79
 dists <- c(10, 20, 30, 33, 40, 50, 60, 70, 80, 90, 100)
 ndists <- length(dists)
@@ -227,7 +227,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/graphneigh-1.png b/docs/reference/graphneigh-1.png
index a9624ecc..8c380e4f 100644
Binary files a/docs/reference/graphneigh-1.png and b/docs/reference/graphneigh-1.png differ
diff --git a/docs/reference/graphneigh-2.png b/docs/reference/graphneigh-2.png
index 423708f8..9fc5637c 100644
Binary files a/docs/reference/graphneigh-2.png and b/docs/reference/graphneigh-2.png differ
diff --git a/docs/reference/graphneigh.html b/docs/reference/graphneigh.html
index eed8b626..f3685e00 100644
--- a/docs/reference/graphneigh.html
+++ b/docs/reference/graphneigh.html
@@ -1,5 +1,5 @@
 
-Graph based spatial weights — graphneigh • spdepGraph based spatial weights — graphneigh • spdepspdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -183,60 +183,54 @@ 
See also
     
Examples

-    
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
-sf_obj <- st_centroid(st_geometry(columbus), of_largest_polygon)
+    
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
+sf_obj <- st_centroid(st_geometry(columbus), of_largest_polygon)
 sp_obj <- as(sf_obj, "Spatial")
-coords <- st_coordinates(sf_obj)
+coords <- st_coordinates(sf_obj)
 suppressMessages(col.tri.nb <- tri2nb(coords))
 col.gab.nb <- graph2nb(gabrielneigh(coords), sym=TRUE)
 col.rel.nb <- graph2nb(relativeneigh(coords), sym=TRUE)
 par(mfrow=c(2,2))
-plot(st_geometry(columbus), border="grey")
+plot(st_geometry(columbus), border="grey")
 plot(col.tri.nb,coords,add=TRUE)
 title(main="Delaunay Triangulation", cex.main=0.6)
-plot(st_geometry(columbus), border="grey")
+plot(st_geometry(columbus), border="grey")
 plot(col.gab.nb, coords, add=TRUE)
 title(main="Gabriel Graph", cex.main=0.6)
-plot(st_geometry(columbus), border="grey")
+plot(st_geometry(columbus), border="grey")
 plot(col.rel.nb, coords, add=TRUE)
 title(main="Relative Neighbor Graph", cex.main=0.6)
-plot(st_geometry(columbus), border="grey")
+plot(st_geometry(columbus), border="grey")
+
 if (require("dbscan", quietly=TRUE)) {
   col.soi.nb <- graph2nb(soi.graph(col.tri.nb,coords), sym=TRUE)
   plot(col.soi.nb, coords, add=TRUE)
   title(main="Sphere of Influence Graph", cex.main=0.6)
 }
-#> 
-#> Attaching package: ‘dbscan’
-#> The following object is masked from ‘package:stats’:
-#> 
-#>     as.dendrogram
-
 par(mfrow=c(1,1))
 col.tri.nb_sf <- tri2nb(sf_obj)
-all.equal(col.tri.nb, col.tri.nb_sf, check.attributes=FALSE)
+all.equal(col.tri.nb, col.tri.nb_sf, check.attributes=FALSE)
 #> [1] TRUE
 col.tri.nb_sp <- tri2nb(sp_obj)
-all.equal(col.tri.nb, col.tri.nb_sp, check.attributes=FALSE)
+all.equal(col.tri.nb, col.tri.nb_sp, check.attributes=FALSE)
 #> [1] TRUE
 if (require("dbscan", quietly=TRUE)) {
   col.soi.nb_sf <- graph2nb(soi.graph(col.tri.nb, sf_obj), sym=TRUE)
-  all.equal(col.soi.nb, col.soi.nb_sf, check.attributes=FALSE)
+  all.equal(col.soi.nb, col.soi.nb_sf, check.attributes=FALSE)
   col.soi.nb_sp <- graph2nb(soi.graph(col.tri.nb, sp_obj), sym=TRUE)
-  all.equal(col.soi.nb, col.soi.nb_sp, check.attributes=FALSE)
+  all.equal(col.soi.nb, col.soi.nb_sp, check.attributes=FALSE)
 }
-#> [1] TRUE
 col.gab.nb_sp <- graph2nb(gabrielneigh(sp_obj), sym=TRUE)
-all.equal(col.gab.nb, col.gab.nb_sp, check.attributes=FALSE)
+all.equal(col.gab.nb, col.gab.nb_sp, check.attributes=FALSE)
 #> [1] TRUE
 col.gab.nb_sf <- graph2nb(gabrielneigh(sf_obj), sym=TRUE)
-all.equal(col.gab.nb, col.gab.nb_sf, check.attributes=FALSE)
+all.equal(col.gab.nb, col.gab.nb_sf, check.attributes=FALSE)
 #> [1] TRUE
 col.rel.nb_sp <- graph2nb(relativeneigh(sp_obj), sym=TRUE)
-all.equal(col.rel.nb, col.rel.nb_sp, check.attributes=FALSE)
+all.equal(col.rel.nb, col.rel.nb_sp, check.attributes=FALSE)
 #> [1] TRUE
 col.rel.nb_sf <- graph2nb(relativeneigh(sf_obj), sym=TRUE)
-all.equal(col.rel.nb, col.rel.nb_sf, check.attributes=FALSE)
+all.equal(col.rel.nb, col.rel.nb_sf, check.attributes=FALSE)
 #> [1] TRUE
 dx <- rep(0.25*0:4,5)
 dy <- c(rep(0,5),rep(0.25,5),rep(0.5,5), rep(0.75,5),rep(1,5))
@@ -307,7 +301,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/grid2nb-1.png b/docs/reference/grid2nb-1.png
index 80b0c025..4fc6c1c7 100644
Binary files a/docs/reference/grid2nb-1.png and b/docs/reference/grid2nb-1.png differ
diff --git a/docs/reference/grid2nb.html b/docs/reference/grid2nb.html
index 5003130e..4ac703fc 100644
--- a/docs/reference/grid2nb.html
+++ b/docs/reference/grid2nb.html
@@ -1,5 +1,5 @@
 
-Construct neighbours for a GridTopology — grid2nb • spdepConstruct neighbours for a GridTopology — grid2nb • spdep
     Skip to contents
@@ -9,7 +9,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -157,7 +157,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/hotspotmap.html b/docs/reference/hotspotmap.html
index 906cf87b..5bbbf618 100644
--- a/docs/reference/hotspotmap.html
+++ b/docs/reference/hotspotmap.html
@@ -1,5 +1,5 @@
 
-Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot • spdep
+Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot • spdep
     Skip to contents
 
 
@@ -7,7 +7,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -176,7 +176,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/include.self.html b/docs/reference/include.self.html
index 51e425b3..2ebf575a 100644
--- a/docs/reference/include.self.html
+++ b/docs/reference/include.self.html
@@ -1,5 +1,5 @@
 
-Include self in neighbours list — include.self • spdep
+Include self in neighbours list — include.self • spdep
     Skip to contents
 
 
@@ -7,7 +7,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -73,9 +73,9 @@ 
See also
     
Examples

-    
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
+    
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
 col.gal.nb <- read.gal(system.file("weights/columbus.gal", package="spData")[1])
-coords <- st_coordinates(st_centroid(columbus))
+coords <- st_coordinates(st_centroid(columbus))
 #> Warning: st_centroid assumes attributes are constant over geometries
 summary(col.gal.nb, coords)
 #> Neighbour list object:
@@ -130,7 +130,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.

 

 
     

diff --git a/docs/reference/index.html b/docs/reference/index.html
index e35fbf2d..5b06b80c 100644
--- a/docs/reference/index.html
+++ b/docs/reference/index.html
@@ -1,5 +1,5 @@
 
-Package index • spdep
+Package index • spdep
     Skip to contents
 
 
@@ -7,7 +7,7 @@
 
     spdep
 
-    1.3-13
+    1.4-1
 
 
     
   
@@ -52,54 +52,6 @@ 
All functionsoldcol
-
-        
-        
Columbus OH spatial analysis data set - old numbering

-

- - EBImoran.mc() - -
-
Permutation test for empirical Bayes index
-
- - EBest() - -
-
Global Empirical Bayes estimator
-
- - EBlocal() - -
-
Local Empirical Bayes estimator
-
- - LOSH() - -
-
Local spatial heteroscedasticity
-
- - LOSH.cs() - -
-
Chi-square based test for local spatial heteroscedasticity
-
- - LOSH.mc() - -
-
Bootstrapping-based test for local spatial heteroscedasticity
-
- - SD.RStests() have_factor_preds_mf() warn_factor_preds() - -
-
Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models
-
- aggregate(<nb>)
@@ -142,6 +94,12 @@

All functionsoldcol + + +
Columbus OH spatial analysis data set - old numbering
+

+ columbus
@@ -172,6 +130,24 @@

All functionsEBest() + + +
Global Empirical Bayes estimator
+

+ + EBImoran.mc() + +
+
Permutation test for empirical Bayes index
+
+ + EBlocal() + +
+
Local Empirical Bayes estimator
+
+ edit(<nb>)
@@ -184,16 +160,16 @@

All functionsgeary() + geary.mc() -
Compute Geary's C
+
Permutation test for Geary's C statistic

- geary.mc() + geary()
-
Permutation test for Geary's C statistic
+
Compute Geary's C
geary.test() @@ -268,16 +244,16 @@

All functionslee() + lee.mc()

-
Compute Lee's statistic
+
Permutation test for Lee's L statistic
- lee.mc() + lee()
-
Permutation test for Lee's L statistic
+
Compute Lee's statistic
lee.test() @@ -298,10 +274,10 @@

All functionslm.RStests() lm.LMtests() print(<RStestlist>) summary(<RStestlist>) print(<RStestlist.summary>) + lm.morantest.exact() print(<moranex>)

-
Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models
+
Exact global Moran's I test
lm.morantest() @@ -310,16 +286,16 @@

All functionslm.morantest.exact() print(<moranex>) + lm.morantest.sad() print(<moransad>) summary(<moransad>) print(<summary.moransad>)

-
Exact global Moran's I test
+
Saddlepoint approximation of global Moran's I test
- lm.morantest.sad() print(<moransad>) summary(<moransad>) print(<summary.moransad>) + lm.RStests() lm.LMtests() print(<RStestlist>) summary(<RStestlist>) print(<RStestlist.summary>)
-
Saddlepoint approximation of global Moran's I test
+
Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models
localC() localC_perm() @@ -340,52 +316,64 @@

All functionslocal_joincount_bv() + localmoran.exact() localmoran.exact.alt() print(<localmoranex>) as.data.frame(<localmoranex>)

-
Calculate the local bivariate join count
+
Exact local Moran's Ii tests
- local_joincount_uni() + localmoran() localmoran_perm()
-
Calculate the local univariate join count
+
Local Moran's I statistic
- localmoran() localmoran_perm() + localmoran.sad() print(<localmoransad>) summary(<localmoransad>) print(<summary.localmoransad>) listw2star()
-
Local Moran's I statistic
+
Saddlepoint approximation of local Moran's Ii tests
- localmoran.exact() localmoran.exact.alt() print(<localmoranex>) as.data.frame(<localmoranex>) + localmoran_bv()
-
Exact local Moran's Ii tests
+
Compute the Local Bivariate Moran's I Statistic
- localmoran.sad() print(<localmoransad>) summary(<localmoransad>) print(<summary.localmoransad>) listw2star() + local_joincount_bv()
-
Saddlepoint approximation of local Moran's Ii tests
+
Calculate the local bivariate join count
- localmoran_bv() + local_joincount_uni()
-
Compute the Local Bivariate Moran's I Statistic
+
Calculate the local univariate join count
- mat2listw() + LOSH.cs()
-
Convert a square spatial weights matrix to a weights list object
+
Chi-square based test for local spatial heteroscedasticity
- moran() + LOSH.mc()
-
Compute Moran's I
+
Bootstrapping-based test for local spatial heteroscedasticity
+
+ + LOSH() + +
+
Local spatial heteroscedasticity
+
+ + mat2listw() + +
+
Convert a square spatial weights matrix to a weights list object
moran.mc() @@ -400,6 +388,12 @@

All functionsmoran() + +

+
Compute Moran's I
+
+ moran.test()
@@ -418,22 +412,16 @@

All functionsnb2INLA() - - -
Output spatial neighbours for INLA
-

- - nb2WB() listw2WB() + nb2blocknb()
-
Output spatial weights for WinBUGS
+
Block up neighbour list for location-less observations
- nb2blocknb() + nb2INLA()
-
Block up neighbour list for location-less observations
+
Output spatial neighbours for INLA
nb2lines() listw2lines() df2sn() @@ -460,6 +448,12 @@

All functionsnb2WB() listw2WB() + +

+
Output spatial weights for WinBUGS
+
+ nbcost() nbcosts()
@@ -550,6 +544,12 @@

All functionsSD.RStests() have_factor_preds_mf() warn_factor_preds() + + +
Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models
+

+ set.mcOption() get.mcOption() set.coresOption() get.coresOption() set.ClusterOption() get.ClusterOption()
@@ -659,7 +659,7 @@

All functions -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/joincount.mc.html b/docs/reference/joincount.mc.html index 44aab42b..8403d063 100644 --- a/docs/reference/joincount.mc.html +++ b/docs/reference/joincount.mc.html @@ -1,5 +1,5 @@ -Permutation test for same colour join count statistics — joincount.mc • spdep +Permutation test for same colour join count statistics — joincount.mc • spdep Skip to contents @@ -7,7 +7,7 @@ spdep - 1.3-13 + 1.4-1 @@ -55,7 +55,7 @@

Usage

Arguments

fx
-

a factor of the same length as the neighbours and weights objects in listw

+

a factor of the same length as the neighbours and weights objects in listw; use of an ordered factor is not well understood

listw

a listw object created for example by nb2listw

@@ -184,7 +184,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/joincount.multi-1.png b/docs/reference/joincount.multi-1.png index e2eb8724..f2d015dc 100644 Binary files a/docs/reference/joincount.multi-1.png and b/docs/reference/joincount.multi-1.png differ diff --git a/docs/reference/joincount.multi.html b/docs/reference/joincount.multi.html index bc5555ba..ddffb598 100644 --- a/docs/reference/joincount.multi.html +++ b/docs/reference/joincount.multi.html @@ -1,5 +1,5 @@ -BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi • spdep +BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi • spdep Skip to contents @@ -7,7 +7,7 @@ spdep - 1.3-13 + 1.4-1 @@ -57,7 +57,7 @@

Usage

Arguments

fx
-

a factor of the same length as the neighbours and weights objects in listw

+

a factor of the same length as the neighbours and weights objects in listw; use of an ordered factor is not well understood

listw

a listw object created for example by nb2listw

@@ -101,7 +101,7 @@

See also

Examples

- 
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
+    
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
 HICRIME <- cut(columbus$CRIME, breaks=c(0,35,80), labels=c("low","high"))
 (nb <- poly2nb(columbus))
 #> Neighbour list object:
@@ -116,9 +116,9 @@ 
Examples#> high:high    54.000   27.694   18.219  6.1630
 #> high:low     29.000   60.204   26.630 -6.0468
 #> Jtot         29.000   60.204   26.630 -6.0468
-col_geoms <- st_geometry(columbus)
-col_geoms[21] <- st_buffer(col_geoms[21], dist=-0.05)
-st_geometry(columbus) <- col_geoms
+col_geoms <- st_geometry(columbus)
+col_geoms[21] <- st_buffer(col_geoms[21], dist=-0.05)
+st_geometry(columbus) <- col_geoms
 (nb <- poly2nb(columbus))
 #> Warning: some observations have no neighbours;
 #> if this seems unexpected, try increasing the snap argument.
@@ -139,111 +139,45 @@ 
Examples#> high:high    52.000   28.138   18.342  5.5716
 #> high:low     28.000   61.170   25.882 -6.5200
 #> Jtot         28.000   61.170   33.190 -5.7577
-# \dontrun{
+if (FALSE) { # \dontrun{
 data(oldcol)
 HICRIME <- cut(COL.OLD$CRIME, breaks=c(0,35,80), labels=c("low","high"))
 names(HICRIME) <- rownames(COL.OLD)
 joincount.multi(HICRIME, nb2listw(COL.nb, style="B"))
-#>           Joincount Expected Variance z-value
-#> low:low      34.000   29.592   18.895  1.0141
-#> high:high    54.000   27.224   17.888  6.3307
-#> high:low     28.000   59.184   26.233 -6.0884
-#> Jtot         28.000   59.184   26.233 -6.0884
 data(hopkins, package="spData")
 image(1:32, 1:32, hopkins[5:36,36:5], breaks=c(-0.5, 3.5, 20),
  col=c("white", "black"))
 box()
-
 hopkins.rook.nb <- cell2nb(32, 32, type="rook")
 unlist(spweights.constants(nb2listw(hopkins.rook.nb, style="B")))
-#>       n      n1      n2      n3      nn      S0      S1      S2 
-#>    1024    1023    1022    1021 1048576    3968    7936   61984 
 hopkins.queen.nb <- cell2nb(32, 32, type="queen")
 hopkins.bishop.nb <- diffnb(hopkins.rook.nb, hopkins.queen.nb, verbose=FALSE)
-#> Warning: neighbour object has 2 sub-graphs
 hopkins4 <- hopkins[5:36,36:5]
 hopkins4[which(hopkins4 > 3, arr.ind=TRUE)] <- 4
 hopkins4.f <- factor(hopkins4)
 table(hopkins4.f)
-#> hopkins4.f
-#>   0   1   2   3   4 
-#> 657 215  98  30  24 
 joincount.multi(hopkins4.f, nb2listw(hopkins.rook.nb, style="B"))
-#>       Joincount   Expected   Variance z-value
-#> 0:0   864.00000  816.27273  116.05233  4.4304
-#> 1:1    94.00000   87.14015   55.25216  0.9229
-#> 2:2    18.00000   18.00379   14.81562 -0.0010
-#> 3:3     2.00000    1.64773    1.55539  0.2825
-#> 4:4     5.00000    1.04545    0.99845  3.9576
-#> 1:0   503.00000  535.05682  227.76750 -2.1241
-#> 2:0   213.00000  243.88636   97.21769 -3.1325
-#> 2:1    99.00000   79.81061   59.01930  2.4978
-#> 3:0    61.00000   74.65909   28.58592 -2.5547
-#> 3:1    28.00000   24.43182   18.99976  0.8186
-#> 3:2    15.00000   11.13636    9.82411  1.2327
-#> 4:0    40.00000   59.72727   22.78583 -4.1327
-#> 4:1    23.00000   19.54545   15.26564  0.8842
-#> 4:2    14.00000    8.90909    7.90051  1.8112
-#> 4:3     5.00000    2.72727    2.58616  1.4133
-#> Jtot 1001.00000 1059.89015  273.78610 -3.5591
 cat("replicates Upton & Fingleton table 3.4 (p. 166)\n")
-#> replicates Upton & Fingleton table 3.4 (p. 166)
 joincount.multi(hopkins4.f, nb2listw(hopkins.bishop.nb, style="B"))
-#>       Joincount   Expected   Variance z-value
-#> 0:0   823.00000  790.76420  144.44877  2.6821
-#> 1:1   101.00000   84.41702   55.98143  2.2164
-#> 2:2    19.00000   17.44117   14.61542  0.4077
-#> 3:3     3.00000    1.59624    1.51444  1.1407
-#> 4:4     3.00000    1.01278    0.97111  2.0166
-#> 1:0   497.00000  518.33629  234.93545 -1.3920
-#> 2:0   216.00000  236.26491  104.42142 -1.9831
-#> 2:1    81.00000   77.31652   58.70829  0.4807
-#> 3:0    58.00000   72.32599   31.49151 -2.5529
-#> 3:1    21.00000   23.66832   18.85316 -0.6145
-#> 3:2    17.00000   10.78835    9.62487  2.0022
-#> 4:0    48.00000   57.86080   25.15973 -1.9659
-#> 4:1    21.00000   18.93466   15.14473  0.5307
-#> 4:2    10.00000    8.63068    7.73708  0.4923
-#> 4:3     4.00000    2.64205    2.51686  0.8560
-#> Jtot  973.00000 1026.76858  284.51030 -3.1877
 cat("replicates Upton & Fingleton table 3.6 (p. 168)\n")
-#> replicates Upton & Fingleton table 3.6 (p. 168)
 joincount.multi(hopkins4.f, nb2listw(hopkins.queen.nb, style="B"))
-#>      Joincount  Expected  Variance z-value
-#> 0:0  1687.0000 1607.0369  303.8034  4.5877
-#> 1:1   195.0000  171.5572  114.2057  2.1936
-#> 2:2    37.0000   35.4450   29.6821  0.2854
-#> 3:3     5.0000    3.2440    3.0687  1.0024
-#> 4:4     8.0000    2.0582    1.9674  4.2361
-#> 1:0  1000.0000 1053.3931  480.6959 -2.4353
-#> 2:0   429.0000  480.1513  215.0360 -3.4882
-#> 2:1   180.0000  157.1271  119.3987  2.0932
-#> 3:0   119.0000  146.9851   65.1029 -3.4684
-#> 3:1    49.0000   48.1001   38.3268  0.1454
-#> 3:2    32.0000   21.9247   19.5237  2.2802
-#> 4:0    88.0000  117.5881   52.0312 -4.1019
-#> 4:1    44.0000   38.4801   30.7868  0.9948
-#> 4:2    24.0000   17.5398   15.6933  1.6308
-#> 4:3     9.0000    5.3693    5.0994  1.6078
-#> Jtot 1974.0000 2086.6587  582.8326 -4.6665
 cat("replicates Upton & Fingleton table 3.7 (p. 169)\n")
-#> replicates Upton & Fingleton table 3.7 (p. 169)
-# }
+} # }
 GDAL37 <- numeric_version(unname(sf::sf_extSoftVersion()["GDAL"]), strict=FALSE)
 (GDAL37 <- ifelse(is.na(GDAL37), FALSE, GDAL37 >= "3.7.0"))
 #> [1] TRUE
 file <- "etc/shapes/GB_2024_southcoast_50m.gpkg.zip"
 zipfile <- system.file(file, package="spdep")
 if (GDAL37) {
-    sc50m <- st_read(zipfile)
+    sc50m <- st_read(zipfile)
 } else {
     td <- tempdir()
     bn <- sub(".zip", "", basename(file), fixed=TRUE)
     target <- unzip(zipfile, files=bn, exdir=td)
-    sc50m <- st_read(target)
+    sc50m <- st_read(target)
 }
 #> Reading layer `GB_2024_southcoast_50m' from data source 
-#>   `/tmp/Rtmp5vVziX/temp_libpath224d25059ed81/spdep/etc/shapes/GB_2024_southcoast_50m.gpkg.zip' 
+#>   `C:\Users\rzomor2\AppData\Local\Temp\RtmpErQTm3\temp_libpath1a5cde63ff3\spdep\etc\shapes\GB_2024_southcoast_50m.gpkg.zip' 
 #>   using driver `GPKG'
 #> Simple feature collection with 119 features and 19 fields
 #> Geometry type: MULTIPOLYGON
@@ -252,19 +186,19 @@ 
Examples#> Projected CRS: OSGB36 / British National Grid
 sc50m$Winner <- factor(sc50m$Winner, levels=c("Con", "Green", "Lab", "LD"))
 plot(sc50m[,"Winner"], pal=c("#2297E6", "#61D04F", "#DF536B", "#F5C710"))
-
+
 nb_sc_50m <- poly2nb(sc50m, row.names=as.character(sc50m$Constituency))
 #> Warning: neighbour object has 2 sub-graphs;
 #> if this sub-graph count seems unexpected, try increasing the snap argument.
 sub2 <- attr(nb_sc_50m, "region.id")[attr(nb_sc_50m, "ncomp")$comp.id == 2L]
 iowe <- match(sub2[1], attr(nb_sc_50m, "region.id"))
-diowe <- c(st_distance(sc50m[iowe,], sc50m))
+diowe <- c(st_distance(sc50m[iowe,], sc50m))
 meet_criterion <- sum(diowe <= units::set_units(5000, "m"))
 cands <- attr(nb_sc_50m, "region.id")[order(diowe)[1:meet_criterion]]
 nb_sc_50m_iowe <- addlinks1(nb_sc_50m, from = cands[1],
  to = cands[3:meet_criterion])
 ioww <- match(sub2[2], attr(nb_sc_50m, "region.id"))
-dioww <- c(st_distance(sc50m[ioww,], sc50m))
+dioww <- c(st_distance(sc50m[ioww,], sc50m))
 meet_criterion <- sum(dioww <= units::set_units(5000, "m"))
 cands <- attr(nb_sc_50m, "region.id")[order(dioww)[1:meet_criterion]]
 nb_sc_50m_iow <- addlinks1(nb_sc_50m_iowe, from = cands[2], to = cands[3:meet_criterion])
@@ -293,7 +227,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.
diff --git a/docs/reference/joincount.test.html b/docs/reference/joincount.test.html index b0657c44..f1a178e9 100644 --- a/docs/reference/joincount.test.html +++ b/docs/reference/joincount.test.html @@ -1,5 +1,5 @@ -BB join count statistic for k-coloured factors — joincount.test • spdepBB join count statistic for k-coloured factors — joincount.test • spdepspdep - 1.3-13 + 1.4-1 @@ -75,7 +75,7 @@

Usage

Arguments

fx
-

a factor of the same length as the neighbours and weights objects in listw

+

a factor of the same length as the neighbours and weights objects in listw; use of an ordered factor is not well understood

listw

a listw object created for example by nb2listw

@@ -337,7 +337,7 @@

Examples#> Same colour statistic Expectation Variance #> 40.500000 23.000000 6.762918 #> -columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE) +columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE) HICRIME <- cut(columbus$CRIME, breaks=c(0,35,80), labels=c("low","high")) (nb <- poly2nb(columbus)) #> Neighbour list object: @@ -371,9 +371,9 @@

Examples#> Same colour statistic Expectation Variance #> 54.00000 27.69388 18.21936 #> -col_geoms <- st_geometry(columbus) -col_geoms[21] <- st_buffer(col_geoms[21], dist=-0.05) -st_geometry(columbus) <- col_geoms +col_geoms <- st_geometry(columbus) +col_geoms[21] <- st_buffer(col_geoms[21], dist=-0.05) +st_geometry(columbus) <- col_geoms (nb <- poly2nb(columbus)) #> Warning: some observations have no neighbours; #> if this seems unexpected, try increasing the snap argument. @@ -424,7 +424,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/knearneigh-1.png b/docs/reference/knearneigh-1.png index 0985372f..4551ae89 100644 Binary files a/docs/reference/knearneigh-1.png and b/docs/reference/knearneigh-1.png differ diff --git a/docs/reference/knearneigh-2.png b/docs/reference/knearneigh-2.png index 9b008868..26fe9ee9 100644 Binary files a/docs/reference/knearneigh-2.png and b/docs/reference/knearneigh-2.png differ diff --git a/docs/reference/knearneigh.html b/docs/reference/knearneigh.html index d8247e98..d3883441 100644 --- a/docs/reference/knearneigh.html +++ b/docs/reference/knearneigh.html @@ -1,5 +1,5 @@ -K nearest neighbours for spatial weights — knearneigh • spdep +K nearest neighbours for spatial weights — knearneigh • spdep Skip to contents @@ -7,7 +7,7 @@ spdep - 1.3-13 + 1.4-1 @@ -96,15 +96,15 @@

Author<

See also

knn, dnearneigh, -knn2nb, kNN

+knn2nb, kNN

Examples

- 
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
-coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE)
+    
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
+coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE)
 col.knn <- knearneigh(coords, k=4)
-plot(st_geometry(columbus), border="grey")
+plot(st_geometry(columbus), border="grey")
 plot(knn2nb(col.knn), coords, add=TRUE)
 title(main="K nearest neighbours, k = 4")
 
@@ -160,13 +160,13 @@ 
Examples#gck4a.nb <- knn2nb(knearneigh(xy1, k=4))
 #summary(gck4a.nb, xy1, scale=0.5)
 
-xy1 <- st_as_sf((as.data.frame(state.center))[m50.48,], coords=1:2,
-  crs=st_crs("OGC:CRS84"))
-old_use_s2 <- sf_use_s2()
-sf_use_s2(TRUE)
+xy1 <- st_as_sf((as.data.frame(state.center))[m50.48,], coords=1:2,
+  crs=st_crs("OGC:CRS84"))
+old_use_s2 <- sf_use_s2()
+sf_use_s2(TRUE)
 system.time(gck4a.nb <- knn2nb(knearneigh(xy1, k=4)))
 #>    user  system elapsed 
-#>   0.023   0.000   0.023 
+#>    0.02    0.00    0.02 
 summary(gck4a.nb, xy1, scale=0.5)
 #> Neighbour list object:
 #> Number of regions: 48 
@@ -182,11 +182,11 @@ 
Examples#> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links
 #> 48 most connected regions:
 #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links
-sf_use_s2(FALSE)
+sf_use_s2(FALSE)
 #> Spherical geometry (s2) switched off
 system.time(gck4a.nb <- knn2nb(knearneigh(xy1, k=4)))
 #>    user  system elapsed 
-#>   0.016   0.000   0.016 
+#>    0.00    0.00    0.01 
 summary(gck4a.nb, xy1, scale=0.5)
 #> Neighbour list object:
 #> Number of regions: 48 
@@ -202,7 +202,7 @@ 
Examples#> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links
 #> 48 most connected regions:
 #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links
-sf_use_s2(old_use_s2)
+sf_use_s2(old_use_s2)
 #> Spherical geometry (s2) switched on
 
 # https://github.com/r-spatial/spdep/issues/38
@@ -214,21 +214,11 @@ 
Examples  out <- knearneigh(x, k=5)
   knn2nb(out)
 }
-#> Neighbour list object:
-#> Number of regions: 50 
-#> Number of nonzero links: 250 
-#> Percentage nonzero weights: 10 
-#> Average number of links: 5 
-#> Non-symmetric neighbours list
 if (run) {
 # fails because dbscan works with > 2 dimensions but does 
 # not work with duplicate points
   try(out <- knearneigh(rbind(x, x[1:10,]), k=5))
 }
-#> Warning: knearneigh: identical points found
-#> Warning: knearneigh: kd_tree not available for identical points
-#> Error in knearneigh(rbind(x, x[1:10, ]), k = 5) : 
-#>   kd_tree required for more than 2 dimensions
diff --git a/docs/reference/knn2nb-1.png b/docs/reference/knn2nb-1.png index 0985372f..4551ae89 100644 Binary files a/docs/reference/knn2nb-1.png and b/docs/reference/knn2nb-1.png differ diff --git a/docs/reference/knn2nb.html b/docs/reference/knn2nb.html index 68ad1020..5c32426f 100644 --- a/docs/reference/knn2nb.html +++ b/docs/reference/knn2nb.html @@ -1,5 +1,5 @@ -Neighbours list from knn object — knn2nb • spdepNeighbours list from knn object — knn2nb • spdepspdep - 1.3-13 + 1.4-1 @@ -84,11 +84,11 @@

See also

Examples

- 
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
-coords <- st_coordinates(st_centroid(columbus))
+    
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
+coords <- st_coordinates(st_centroid(columbus))
 #> Warning: st_centroid assumes attributes are constant over geometries
 col.knn <- knearneigh(coords, k=4)
-plot(st_geometry(columbus), border="grey")
+plot(st_geometry(columbus), border="grey")
 plot(knn2nb(col.knn), coords, add=TRUE)
 title(main="K nearest neighbours, k = 4")
 
@@ -114,7 +114,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.
diff --git a/docs/reference/lag.listw-1.png b/docs/reference/lag.listw-1.png index 1eda7cc4..0926f25e 100644 Binary files a/docs/reference/lag.listw-1.png and b/docs/reference/lag.listw-1.png differ diff --git a/docs/reference/lag.listw-2.png b/docs/reference/lag.listw-2.png index f2ddd93b..3339af8b 100644 Binary files a/docs/reference/lag.listw-2.png and b/docs/reference/lag.listw-2.png differ diff --git a/docs/reference/lag.listw.html b/docs/reference/lag.listw.html index d28a12b5..17a05be8 100644 --- a/docs/reference/lag.listw.html +++ b/docs/reference/lag.listw.html @@ -1,5 +1,5 @@ -Spatial lag of a numeric vector — lag.listw • spdep +Spatial lag of a numeric vector — lag.listw • spdep Skip to contents @@ -7,7 +7,7 @@ spdep - 1.3-13 + 1.4-1 @@ -106,7 +106,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/lee.html b/docs/reference/lee.html index d7e75941..248cdd8c 100644 --- a/docs/reference/lee.html +++ b/docs/reference/lee.html @@ -1,5 +1,5 @@ -Compute Lee's statistic — lee • spdepCompute Lee's statistic — lee • spdepspdep - 1.3-13 + 1.4-1 @@ -134,7 +134,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/lee.mc.html b/docs/reference/lee.mc.html index dbc74ff2..779c8c83 100644 --- a/docs/reference/lee.mc.html +++ b/docs/reference/lee.mc.html @@ -1,5 +1,5 @@ -Permutation test for Lee's L statistic — lee.mc • spdep +Permutation test for Lee's L statistic — lee.mc • spdep Skip to contents @@ -7,7 +7,7 @@ spdep - 1.3-13 + 1.4-1 @@ -170,7 +170,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/lee.test.html b/docs/reference/lee.test.html index 35cbf512..ddeb2b6a 100644 --- a/docs/reference/lee.test.html +++ b/docs/reference/lee.test.html @@ -1,5 +1,5 @@ -Lee's L test for spatial autocorrelation — lee.test • spdep +Lee's L test for spatial autocorrelation — lee.test • spdep Skip to contents @@ -7,7 +7,7 @@ spdep - 1.3-13 + 1.4-1 @@ -231,7 +231,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/licd_multi-1.png b/docs/reference/licd_multi-1.png index 87671502..1eb4b279 100644 Binary files a/docs/reference/licd_multi-1.png and b/docs/reference/licd_multi-1.png differ diff --git a/docs/reference/licd_multi-2.png b/docs/reference/licd_multi-2.png index effb4bc5..f2d015dc 100644 Binary files a/docs/reference/licd_multi-2.png and b/docs/reference/licd_multi-2.png differ diff --git a/docs/reference/licd_multi-3.png b/docs/reference/licd_multi-3.png index 4ae82daf..3096c374 100644 Binary files a/docs/reference/licd_multi-3.png and b/docs/reference/licd_multi-3.png differ diff --git a/docs/reference/licd_multi-4.png b/docs/reference/licd_multi-4.png index d8befe02..f6d23671 100644 Binary files a/docs/reference/licd_multi-4.png and b/docs/reference/licd_multi-4.png differ diff --git a/docs/reference/licd_multi.html b/docs/reference/licd_multi.html index 8ae73724..f26f2616 100644 --- a/docs/reference/licd_multi.html +++ b/docs/reference/licd_multi.html @@ -1,5 +1,5 @@ -Local Indicators for Categorical Data — licd_multi • spdep +Local Indicators for Categorical Data — licd_multi • spdep Skip to contents @@ -7,7 +7,7 @@ spdep - 1.3-13 + 1.4-1 @@ -55,7 +55,7 @@

Usage

Arguments

fx
-

a factor with two or more categories, of the same length as the neighbours and weights objects in listw

+

a factor with two or more categories, of the same length as the neighbours and weights objects in listw; use of an ordered factor is not well understood

listw

a listw object created for example by nb2listw

@@ -128,7 +128,7 @@

See also

Examples

- 
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
+    
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
 HICRIME <- cut(columbus$CRIME, breaks=c(0,35,80), labels=c("low","high"))
 (nb <- poly2nb(columbus))
 #> Neighbour list object:
@@ -164,11 +164,11 @@ 
Examples#>  $ local_comp_sim  : NULL
 #>  $ local_config_sim: NULL
 #>  - attr(*, "timings")=List of 3
-#>   ..$ set_up        : 'proc_time' Named num [1:5] 0 0 0 0 0
+#>   ..$ set_up        : 'proc_time' Named num [1:5] 0 0 0 NA NA
 #>   .. ..- attr(*, "names")= chr [1:5] "user.self" "sys.self" "elapsed" "user.child" ...
-#>   ..$ processing    : 'proc_time' Named num [1:5] 0.104 0 0.106 0 0
+#>   ..$ processing    : 'proc_time' Named num [1:5] 0.01 0 0.08 NA NA
 #>   .. ..- attr(*, "names")= chr [1:5] "user.self" "sys.self" "elapsed" "user.child" ...
-#>   ..$ postprocessing: 'proc_time' Named num [1:5] 0.001 0 0.001 0 0
+#>   ..$ postprocessing: 'proc_time' Named num [1:5] 0 0 0 NA NA
 #>   .. ..- attr(*, "names")= chr [1:5] "user.self" "sys.self" "elapsed" "user.child" ...
 #>  - attr(*, "out")= num [1:49, 1:35] 1 1 1 1 2 1 1 2 1 1 ...
 #>   ..- attr(*, "ncpus")= int 1
@@ -215,15 +215,15 @@ 
Examplesfile <- "etc/shapes/GB_2024_southcoast_50m.gpkg.zip"
 zipfile <- system.file(file, package="spdep")
 if (GDAL37) {
-    sc50m <- st_read(zipfile)
+    sc50m <- st_read(zipfile)
 } else {
     td <- tempdir()
     bn <- sub(".zip", "", basename(file), fixed=TRUE)
     target <- unzip(zipfile, files=bn, exdir=td)
-    sc50m <- st_read(target)
+    sc50m <- st_read(target)
 }
 #> Reading layer `GB_2024_southcoast_50m' from data source 
-#>   `/tmp/Rtmp5vVziX/temp_libpath224d25059ed81/spdep/etc/shapes/GB_2024_southcoast_50m.gpkg.zip' 
+#>   `C:\Users\rzomor2\AppData\Local\Temp\RtmpErQTm3\temp_libpath1a5cde63ff3\spdep\etc\shapes\GB_2024_southcoast_50m.gpkg.zip' 
 #>   using driver `GPKG'
 #> Simple feature collection with 119 features and 19 fields
 #> Geometry type: MULTIPOLYGON
@@ -238,13 +238,13 @@ 
Examples#> if this sub-graph count seems unexpected, try increasing the snap argument.
 sub2 <- attr(nb_sc_50m, "region.id")[attr(nb_sc_50m, "ncomp")$comp.id == 2L]
 iowe <- match(sub2[1], attr(nb_sc_50m, "region.id"))
-diowe <- c(st_distance(sc50m[iowe,], sc50m))
+diowe <- c(st_distance(sc50m[iowe,], sc50m))
 meet_criterion <- sum(diowe <= units::set_units(5000, "m"))
 cands <- attr(nb_sc_50m, "region.id")[order(diowe)[1:meet_criterion]]
 nb_sc_50m_iowe <- addlinks1(nb_sc_50m, from = cands[1],
  to = cands[3:meet_criterion])
 ioww <- match(sub2[2], attr(nb_sc_50m, "region.id"))
-dioww <- c(st_distance(sc50m[ioww,], sc50m))
+dioww <- c(st_distance(sc50m[ioww,], sc50m))
 meet_criterion <- sum(dioww <= units::set_units(5000, "m"))
 cands <- attr(nb_sc_50m, "region.id")[order(dioww)[1:meet_criterion]]
 nb_sc_50m_iow <- addlinks1(nb_sc_50m_iowe, from = cands[2], to = cands[3:meet_criterion])
@@ -270,7 +270,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.
diff --git a/docs/reference/listw2sn.html b/docs/reference/listw2sn.html index 7aa59165..0de55fe5 100644 --- a/docs/reference/listw2sn.html +++ b/docs/reference/listw2sn.html @@ -1,5 +1,5 @@ -Spatial neighbour sparse representation — listw2sn • spdep +#> Classes 'spatial.neighbour' and 'data.frame': 230 obs. of 3 variables: #> $ from : int 1 1 2 2 2 3 3 3 3 4 ... #> $ to : int 2 3 1 3 4 1 2 4 5 2 ... #> $ weights: num 0.5 0.5 0.333 0.333 0.333 ... @@ -133,7 +133,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/lm.RStests.html b/docs/reference/lm.RStests.html index fd73c069..2b3a07fe 100644 --- a/docs/reference/lm.RStests.html +++ b/docs/reference/lm.RStests.html @@ -1,5 +1,5 @@ -Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests • spdepRao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests • spdepspdep - 1.3-13 + 1.4-1 @@ -191,7 +191,7 @@

Examples#> HOVAL -0.2739 0.1032 -2.654 0.0109 * #> INC -1.5973 0.3341 -4.780 1.83e-05 *** #> --- -#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 +#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 #> #> Residual standard error: 11.43 on 46 degrees of freedom #> Multiple R-squared: 0.5524, Adjusted R-squared: 0.5329 @@ -213,21 +213,11 @@

Examples#> adjRSlag 3.720048 1 0.053763 . #> SARMA 9.443178 2 0.008901 ** #> --- -#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 +#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 if (require("spatialreg", quietly=TRUE)) { oldcrime.slx <- lmSLX(CRIME ~ HOVAL + INC, data = COL.OLD, listw=lw) summary(lm.RStests(oldcrime.slx, listw=lw, test=c("adjRSerr", "adjRSlag"))) } -#> Rao's score (a.k.a Lagrange multiplier) diagnostics for spatial -#> dependence -#> data: -#> model: lm(CRIME ~ HOVAL + INC + lag.HOVAL + lag.INC, data = COL.OLD, -#> listw = lw) -#> test weights: lw -#> -#> statistic parameter p.value -#> GNM_adjRSerr 0.10933 1 0.7409 -#> GNM_adjRSlag 0.61580 1 0.4326 run <- require("codingMatrices", quietly=TRUE) if (run) { COL.OLD$fEW <- factor(COL.OLD$EW) @@ -238,46 +228,16 @@

Examplessummary(lm.RStests(lm(f, data=COL.OLD, contrasts=list(fDISCBD="contr.poly", fEW="contr.treatment")), lw, test=c("adjRSerr", "adjRSlag"))) } -#> Rao's score (a.k.a Lagrange multiplier) diagnostics for spatial -#> dependence -#> data: -#> model: lm(formula = f, data = COL.OLD, contrasts = list(fDISCBD = -#> "contr.poly", fEW = "contr.treatment")) -#> test weights: lw -#> -#> statistic parameter p.value -#> adjRSerr 0.98727 1 0.3204 -#> adjRSlag 1.14732 1 0.2841 if (run) { # use codingMatrices::code_diff for ordered factor summary(lm.RStests(lm(f, data=COL.OLD, contrasts=list(fDISCBD="code_diff", fEW="contr.treatment")), lw, test=c("adjRSerr", "adjRSlag"))) } -#> Rao's score (a.k.a Lagrange multiplier) diagnostics for spatial -#> dependence -#> data: -#> model: lm(formula = f, data = COL.OLD, contrasts = list(fDISCBD = -#> "code_diff", fEW = "contr.treatment")) -#> test weights: lw -#> -#> statistic parameter p.value -#> adjRSerr 0.03415 1 0.8534 -#> adjRSlag -0.01572 1 1.0000 if (run) { # use codingMatrices::code_control for both summary(lm.RStests(lm(f, data=COL.OLD, contrasts=list(fDISCBD="code_control", fEW="code_control")), lw, test=c("adjRSerr", "adjRSlag"))) } -#> Rao's score (a.k.a Lagrange multiplier) diagnostics for spatial -#> dependence -#> data: -#> model: lm(formula = f, data = COL.OLD, contrasts = list(fDISCBD = -#> "code_control", fEW = "code_control")) -#> test weights: lw -#> -#> statistic parameter p.value -#> adjRSerr 0.0383759 1 0.8447 -#> adjRSlag -0.0062517 1 1.0000

@@ -93,13 +93,13 @@

See also

Examples

- 
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
+    
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
 col.gal.nb <- read.gal(system.file("weights/columbus.gal", package="spData")[1])
-coords <- st_coordinates(st_centroid(st_geometry(columbus)))
+coords <- st_coordinates(st_centroid(st_geometry(columbus)))
 xx <- poly2nb(as(columbus, "Spatial"))
 dxx <- diffnb(xx, col.gal.nb)
 #> Warning: neighbour object has 46 sub-graphs
-plot(st_geometry(columbus), border="grey")
+plot(st_geometry(columbus), border="grey")
 plot(col.gal.nb, coords, add=TRUE)
 plot(dxx, coords, add=TRUE, col="red")
 title(main=paste("Differences (red) in Columbus GAL weights (black)",
@@ -119,7 +119,7 @@ 
Examples#> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38,
 #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49
 #> 49 disjoint connected subgraphs
-sfc_xx <- poly2nb(st_geometry(columbus))
+sfc_xx <- poly2nb(st_geometry(columbus))
 diffnb(sfc_xx, xx)
 #> Warning: neighbour object has 49 sub-graphs
 #> Neighbour list object:
@@ -135,7 +135,7 @@ 
Examplesxxx <- poly2nb(as(columbus, "Spatial"), queen=FALSE)
 dxxx <- diffnb(xxx, col.gal.nb)
 #> Warning: neighbour object has 34 sub-graphs
-plot(st_geometry(columbus), border = "grey")
+plot(st_geometry(columbus), border = "grey")
 plot(col.gal.nb, coords, add = TRUE)
 plot(dxxx, coords, add = TRUE, col = "red")
 title(main=paste("Differences (red) in Columbus GAL weights (black)",
@@ -147,28 +147,28 @@ 
Examplesfg <- rep("grey", length(cards))
 fg[maxconts] <- "red"
 fg[xx[[maxconts]]] <- "green"
-plot(st_geometry(columbus), col=fg)
+plot(st_geometry(columbus), col=fg)
 title(main="Region with largest number of contiguities", cex.main=0.6)
 
-nc.sids <- st_read(system.file("shapes/sids.gpkg", package="spData")[1], quiet=TRUE)
+nc.sids <- st_read(system.file("shapes/sids.gpkg", package="spData")[1], quiet=TRUE)
 system.time(xxnb <- poly2nb(nc.sids))
 #>    user  system elapsed 
-#>   0.065   0.000   0.066 
+#>    0.02    0.00    0.05 
 system.time(xxnb <- poly2nb(as(nc.sids, "Spatial")))
 #>    user  system elapsed 
-#>   0.085   0.000   0.086 
-plot(st_geometry(nc.sids))
-plot(xxnb, st_coordinates(st_centroid(nc.sids)), add=TRUE, col="blue")
+#>    0.03    0.00    0.06 
+plot(st_geometry(nc.sids))
+plot(xxnb, st_coordinates(st_centroid(nc.sids)), add=TRUE, col="blue")
 #> Warning: st_centroid assumes attributes are constant over geometries
 
-sq <- st_polygon(list(rbind(c(0,0), c(1,0), c(1,1), c(0,1), c(0,0))))
+sq <- st_polygon(list(rbind(c(0,0), c(1,0), c(1,1), c(0,1), c(0,0))))
 sq2 <- sq + c(0,1)
 sq3 <- sq + c(1,0)
 sq4 <- sq + c(1,1)
-gm <- st_sfc(list(sq, sq2, sq3, sq4))
-df <- st_as_sf(data.frame(gm, id=1:4))
-plot(st_geometry(df))
-text(st_coordinates(st_centroid(gm)), as.character(df$id))
+gm <- st_sfc(list(sq, sq2, sq3, sq4))
+df <- st_as_sf(data.frame(gm, id=1:4))
+plot(st_geometry(df))
+text(st_coordinates(st_centroid(gm)), as.character(df$id))
 
 unclass(poly2nb(df, queen = FALSE))
 #> [[1]]
@@ -200,9 +200,9 @@ 
Examples#> attr(,"ncomp")$comp.id
 #> [1] 1 1 1 1
 #> 
-col_geoms <- st_geometry(columbus)
-col_geoms[1] <- st_buffer(col_geoms[1], dist=-0.05)
-st_geometry(columbus) <- col_geoms
+col_geoms <- st_geometry(columbus)
+col_geoms[1] <- st_buffer(col_geoms[1], dist=-0.05)
+st_geometry(columbus) <- col_geoms
 poly2nb(columbus)
 #> Warning: some observations have no neighbours;
 #> if this seems unexpected, try increasing the snap argument.
@@ -227,7 +227,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.
diff --git a/docs/reference/probmap-1.png b/docs/reference/probmap-1.png index c60f0046..f03add9a 100644 Binary files a/docs/reference/probmap-1.png and b/docs/reference/probmap-1.png differ diff --git a/docs/reference/probmap-2.png b/docs/reference/probmap-2.png index 0b1c8718..2ec6b0ce 100644 Binary files a/docs/reference/probmap-2.png and b/docs/reference/probmap-2.png differ diff --git a/docs/reference/probmap-3.png b/docs/reference/probmap-3.png index e1a68453..dac094d7 100644 Binary files a/docs/reference/probmap-3.png and b/docs/reference/probmap-3.png differ diff --git a/docs/reference/probmap.html b/docs/reference/probmap.html index 085f4b57..19fcb25b 100644 --- a/docs/reference/probmap.html +++ b/docs/reference/probmap.html @@ -1,5 +1,5 @@ -Probability mapping for rates — probmap • spdep +Probability mapping for rates — probmap • spdep Skip to contents @@ -7,7 +7,7 @@ spdep - 1.3-13 + 1.4-1 @@ -101,7 +101,7 @@

See also

Examples

- 
auckland <- st_read(system.file("shapes/auckland.gpkg", package="spData")[1], quiet=TRUE)
+    
auckland <- st_read(system.file("shapes/auckland.gpkg", package="spData")[1], quiet=TRUE)
 res <- probmap(auckland$M77_85, 9*auckland$Und5_81)
 rt <- sum(auckland$M77_85)/sum(9*auckland$Und5_81)
 ppois_pmap <- numeric(length(auckland$Und5_81))
@@ -131,7 +131,7 @@ 
Examples
-  
Site built with pkgdown 2.1.3.

+  
Site built with pkgdown 2.1.1.
diff --git a/docs/reference/prunecost.html b/docs/reference/prunecost.html index 82580fc7..53c42835 100644 --- a/docs/reference/prunecost.html +++ b/docs/reference/prunecost.html @@ -1,5 +1,5 @@ -Compute cost of prune each edge — prunecost • spdepCompute cost of prune each edge — prunecost • spdepspdep - 1.3-13 + 1.4-1 @@ -138,7 +138,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/prunemst.html b/docs/reference/prunemst.html index 2e736147..9ae12312 100644 --- a/docs/reference/prunemst.html +++ b/docs/reference/prunemst.html @@ -1,5 +1,5 @@ -Prune a Minimun Spanning Tree — prunemst • spdepPrune a Minimun Spanning Tree — prunemst • spdep Skip to contents @@ -9,7 +9,7 @@ spdep - 1.3-13 + 1.4-1 @@ -127,7 +127,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/read.gal-1.png b/docs/reference/read.gal-1.png index c3d67f16..5943275b 100644 Binary files a/docs/reference/read.gal-1.png and b/docs/reference/read.gal-1.png differ diff --git a/docs/reference/read.gal.html b/docs/reference/read.gal.html index 748b7776..359d13d2 100644 --- a/docs/reference/read.gal.html +++ b/docs/reference/read.gal.html @@ -1,5 +1,5 @@ -Read a GAL lattice file into a neighbours list — read.gal • spdep +Read a GAL lattice file into a neighbours list — read.gal • spdep Skip to contents @@ -7,7 +7,7 @@ spdep - 1.3-13 + 1.4-1 @@ -122,7 +122,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/read.gwt2nb.html b/docs/reference/read.gwt2nb.html index 01220484..606543be 100644 --- a/docs/reference/read.gwt2nb.html +++ b/docs/reference/read.gwt2nb.html @@ -1,5 +1,5 @@ -Read and write spatial neighbour files — read.gwt2nb • spdep +Read and write spatial neighbour files — read.gwt2nb • spdep Skip to contents @@ -7,7 +7,7 @@ spdep - 1.3-13 + 1.4-1 @@ -197,7 +197,9 @@

Examplesnc1 <- read.swmdbf2listw(fn, style="B") nc1 } -#> Reading layer `nc.gpkg' from data source `/home/rsb/lib/r_libs/sf/gpkg/nc.gpkg' using driver `GPKG' +#> Reading layer `nc.gpkg' from data source +#> `C:\Users\rzomor2\AppData\Local\R\win-library\4.4\sf\gpkg\nc.gpkg' +#> using driver `GPKG' #> Simple feature collection with 100 features and 14 fields #> Geometry type: MULTIPOLYGON #> Dimension: XY @@ -265,12 +267,12 @@

Examplesfile <- "etc/shapes/california.gpkg.zip" zipfile <- system.file(file, package="spdep") if (GDAL37) { - cal <- st_read(zipfile) + cal <- st_read(zipfile) } else { td <- tempdir() bn <- sub(".zip", "", basename(file), fixed=TRUE) target <- unzip(zipfile, files=bn, exdir=td) - cal <- st_read(target) + cal <- st_read(target) } fn <- system.file("etc/misc/contiguity_myid.dbf", package="spdep")[1] cal1 <- read.swmdbf2listw(fn, style="B") @@ -278,7 +280,7 @@

Examplesall.equal(cal1, cal1a) } #> Reading layer `california' from data source -#> `/tmp/Rtmp5vVziX/temp_libpath224d25059ed81/spdep/etc/shapes/california.gpkg.zip' +#> `C:\Users\rzomor2\AppData\Local\Temp\RtmpErQTm3\temp_libpath1a5cde63ff3\spdep\etc\shapes\california.gpkg.zip' #> using driver `GPKG' #> Simple feature collection with 58 features and 2 fields #> Geometry type: MULTIPOLYGON @@ -359,7 +361,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/rotation-1.png b/docs/reference/rotation-1.png index eb210d96..cb862424 100644 Binary files a/docs/reference/rotation-1.png and b/docs/reference/rotation-1.png differ diff --git a/docs/reference/rotation-2.png b/docs/reference/rotation-2.png index e4a68a02..719cd9b2 100644 Binary files a/docs/reference/rotation-2.png and b/docs/reference/rotation-2.png differ diff --git a/docs/reference/rotation.html b/docs/reference/rotation.html index cd30b5f4..37c19cd3 100644 --- a/docs/reference/rotation.html +++ b/docs/reference/rotation.html @@ -1,5 +1,5 @@ -Rotate a set of point by a certain angle — Rotation • spdep +Rotate a set of point by a certain angle — Rotation • spdep Skip to contents @@ -7,7 +7,7 @@ spdep - 1.3-13 + 1.4-1 @@ -126,7 +126,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/set.mcOption.html b/docs/reference/set.mcOption.html index 390f21f1..95c5ad0b 100644 --- a/docs/reference/set.mcOption.html +++ b/docs/reference/set.mcOption.html @@ -1,5 +1,5 @@ -Options for parallel support — set.mcOption • spdep +Options for parallel support — set.mcOption • spdep Skip to contents @@ -7,7 +7,7 @@ spdep - 1.3-13 + 1.4-1 @@ -75,7 +75,7 @@

Value

Note

-

An extended example is shown in the documentation of aple.mc, including treatment of seeding of RNG for multicore/cluster.

+

An extended example is shown in the documentation of aple.mc, including treatment of seeding of RNG for multicore/cluster.

Author

@@ -115,7 +115,7 @@

Examples } else { mcOpt <- get.mcOption() print(mcOpt) - print(mclapply(1:get.coresOption(), function(i) exists("moran.mc"), + print(mclapply(1:get.coresOption(), function(i) exists("moran.mc"), mc.cores=get.coresOption())) invisible(set.mcOption(FALSE)) cl <- makeCluster(nc) @@ -133,10 +133,7 @@

Examples } } #> [1] TRUE -#> [1] TRUE -#> [[1]] -#> [1] TRUE -#> +#> [1] FALSE #> [[1]] #> [1] FALSE #> @@ -157,7 +154,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/set.spChkOption.html b/docs/reference/set.spChkOption.html index c2a20a3f..4a17b97e 100644 --- a/docs/reference/set.spChkOption.html +++ b/docs/reference/set.spChkOption.html @@ -1,5 +1,5 @@ -Control checking of spatial object IDs — set.spChkOption • spdep +Control checking of spatial object IDs — set.spChkOption • spdep Skip to contents @@ -7,7 +7,7 @@ spdep - 1.3-13 + 1.4-1 @@ -168,7 +168,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/skater-1.png b/docs/reference/skater-1.png index 848a8178..fbf8a865 100644 Binary files a/docs/reference/skater-1.png and b/docs/reference/skater-1.png differ diff --git a/docs/reference/skater-2.png b/docs/reference/skater-2.png index 7eb51521..aa861e1c 100644 Binary files a/docs/reference/skater-2.png and b/docs/reference/skater-2.png differ diff --git a/docs/reference/skater-3.png b/docs/reference/skater-3.png index 98caa887..a9b11fc6 100644 Binary files a/docs/reference/skater-3.png and b/docs/reference/skater-3.png differ diff --git a/docs/reference/skater-4.png b/docs/reference/skater-4.png index 78911e6f..fb2bebb3 100644 Binary files a/docs/reference/skater-4.png and b/docs/reference/skater-4.png differ diff --git a/docs/reference/skater.html b/docs/reference/skater.html index e68ee912..82e92743 100644 --- a/docs/reference/skater.html +++ b/docs/reference/skater.html @@ -1,5 +1,5 @@ -Spatial 'K'luster Analysis by Tree Edge Removal — skater • spdepSpatial 'K'luster Analysis by Tree Edge Removal — skater • spdepspdep - 1.3-13 + 1.4-1 @@ -170,7 +170,7 @@

Examples bh <- st_read(target) } #> Reading layer `bhicv' from data source -#> `/tmp/Rtmp5vVziX/temp_libpath224d25059ed81/spdep/etc/shapes/bhicv.gpkg.zip' +#> `C:\Users\rzomor2\AppData\Local\Temp\RtmpErQTm3\temp_libpath1a5cde63ff3\spdep\etc\shapes\bhicv.gpkg.zip' #> using driver `GPKG' #> Simple feature collection with 98 features and 8 fields #> Geometry type: POLYGON @@ -342,22 +342,18 @@

Examples#> 1 2 3 4 #> 22 23 33 20 -# \dontrun{ +if (FALSE) { # \dontrun{ data(boston, package="spData") bh.nb <- boston.soi dpad <- data.frame(scale(boston.c[,c(7:10)])) ### calculating costs system.time(lcosts <- nbcosts(bh.nb, dpad)) -#> user system elapsed -#> 0.071 0.000 0.074 ### making listw nb.w <- nb2listw(bh.nb, lcosts, style="B") ### find a minimum spanning tree mst.bh <- mstree(nb.w,5) ### three groups with no restriction system.time(res1 <- spdep::skater(mst.bh[,1:2], dpad, 2)) -#> user system elapsed -#> 1.950 0.105 2.137 library(parallel) nc <- max(2L, detectCores(logical=FALSE), na.rm = TRUE)-1L # set nc to 1L here @@ -371,26 +367,20 @@

Examples} ### calculating costs system.time(plcosts <- nbcosts(bh.nb, dpad)) -#> user system elapsed -#> 0.067 0.000 0.067 all.equal(lcosts, plcosts, check.attributes=FALSE) -#> [1] TRUE ### making listw pnb.w <- nb2listw(bh.nb, plcosts, style="B") ### find a minimum spanning tree pmst.bh <- mstree(pnb.w,5) ### three groups with no restriction system.time(pres1 <- spdep::skater(pmst.bh[,1:2], dpad, 2)) -#> user system elapsed -#> 1.916 0.092 2.019 if(!get.mcOption()) { set.ClusterOption(NULL) stopCluster(cl) } all.equal(res1, pres1, check.attributes=FALSE) -#> [1] TRUE invisible(set.coresOption(coresOpt)) -# } +} # } @@ -403,7 +393,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/sp.correlogram-1.png b/docs/reference/sp.correlogram-1.png index 4fb140a4..fa0259ca 100644 Binary files a/docs/reference/sp.correlogram-1.png and b/docs/reference/sp.correlogram-1.png differ diff --git a/docs/reference/sp.correlogram-2.png b/docs/reference/sp.correlogram-2.png index 1227670c..7cc0ede0 100644 Binary files a/docs/reference/sp.correlogram-2.png and b/docs/reference/sp.correlogram-2.png differ diff --git a/docs/reference/sp.correlogram-3.png b/docs/reference/sp.correlogram-3.png index 7a2e81b9..0f3b23e8 100644 Binary files a/docs/reference/sp.correlogram-3.png and b/docs/reference/sp.correlogram-3.png differ diff --git a/docs/reference/sp.correlogram-4.png b/docs/reference/sp.correlogram-4.png index df35d12b..168ffb5c 100644 Binary files a/docs/reference/sp.correlogram-4.png and b/docs/reference/sp.correlogram-4.png differ diff --git a/docs/reference/sp.correlogram.html b/docs/reference/sp.correlogram.html index e2b24216..4f6b6c69 100644 --- a/docs/reference/sp.correlogram.html +++ b/docs/reference/sp.correlogram.html @@ -1,5 +1,5 @@ -Spatial correlogram — sp.correlogram • spdepSpatial correlogram — sp.correlogram • spdep Skip to contents @@ -9,7 +9,7 @@ spdep - 1.3-13 + 1.4-1 @@ -193,7 +193,7 @@

Examples#> 7 (98) -0.0752243 -0.0103093 0.0022282 -1.3752 0.1690654 #> 8 (98) -0.0261063 -0.0103093 0.0025211 -0.3146 0.7530514 #> --- -#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 +#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 print(Ispc, "bonferroni") #> Spatial correlogram for tr.SIDS74 #> method: Moran's I @@ -207,7 +207,7 @@

Examples#> 7 (98) -0.0752243 -0.0103093 0.0022282 -1.3752 1.000000 #> 8 (98) -0.0261063 -0.0103093 0.0025211 -0.3146 1.000000 #> --- -#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 +#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 plot(Ispc) Cspc <- sp.correlogram(ncCC89_nb, tr.SIDS74, order=8, method="C", @@ -233,7 +233,7 @@

Examples#> 7 (98) 1.0527148 1.0000000 0.0037227 0.8640 0.3875979 #> 8 (98) 1.0067939 1.0000000 0.0036482 0.1125 0.9104415 #> --- -#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 +#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 print(Cspc, "bonferroni") #> Spatial correlogram for tr.SIDS74 #> method: Geary's C @@ -247,7 +247,7 @@

Examples#> 7 (98) 1.0527148 1.0000000 0.0037227 0.8640 1.000000 #> 8 (98) 1.0067939 1.0000000 0.0036482 0.1125 1.000000 #> --- -#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 +#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 plot(Cspc) drop.no.neighs <- !(1:length(ncCC89_nb) %in% which(card(ncCC89_nb) == 0)) @@ -266,7 +266,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/sp.mantel.mc-1.png b/docs/reference/sp.mantel.mc-1.png index c91a9332..22adfade 100644 Binary files a/docs/reference/sp.mantel.mc-1.png and b/docs/reference/sp.mantel.mc-1.png differ diff --git a/docs/reference/sp.mantel.mc.html b/docs/reference/sp.mantel.mc.html index 9777d20c..acc592c1 100644 --- a/docs/reference/sp.mantel.mc.html +++ b/docs/reference/sp.mantel.mc.html @@ -1,5 +1,5 @@ -Mantel-Hubert spatial general cross product statistic — sp.mantel.mc • spdepMantel-Hubert spatial general cross product statistic — sp.mantel.mc • spdepspdep - 1.3-13 + 1.4-1 @@ -233,7 +233,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/spatialdelta.html b/docs/reference/spatialdelta.html index 85cbbebe..ed5016aa 100644 --- a/docs/reference/spatialdelta.html +++ b/docs/reference/spatialdelta.html @@ -1,5 +1,5 @@ -Weighted Multivariate Spatial Autocorrelation Measures — spatialdelta • spdep +Weighted Multivariate Spatial Autocorrelation Measures — spatialdelta • spdep Skip to contents @@ -7,7 +7,7 @@ spdep - 1.3-13 + 1.4-1 @@ -138,7 +138,7 @@

Argumentsiter, tol, tol.margins, print -

arguments passed to Ipfp

+

arguments passed to Ipfp

c

default NULL, a coefficient greater than zero and less than or equal to -1/min(B) where B is the matrix of scalar products associated with the distance matrix; if not given, -1/min(B) is used

@@ -233,7 +233,7 @@

Note

See also

-

Ipfp, distances

+

Ipfp, distances

@@ -341,9 +341,6 @@

Examplesall.equal(unname(moral_gdw$estimate["delta"]), # Eq. 30 p. 588 sum(fG * localdelta(moral_gdw))) } - - -#> [1] TRUE # }

@@ -356,7 +353,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/spdep-defunct.html b/docs/reference/spdep-defunct.html index e0ad3f5e..a50142a9 100644 --- a/docs/reference/spdep-defunct.html +++ b/docs/reference/spdep-defunct.html @@ -1,5 +1,5 @@ -Defunct Functions in Package spdep — spdep-defunct • spdepDefunct Functions in Package spdep — spdep-defunct • spdep Skip to contents @@ -9,7 +9,7 @@ spdep - 1.3-13 + 1.4-1 @@ -191,7 +191,7 @@

See also
-

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/spdep.html b/docs/reference/spdep.html index 1ec2caf5..368aa8a6 100644 --- a/docs/reference/spdep.html +++ b/docs/reference/spdep.html @@ -1,5 +1,5 @@ -Return package version number — spdep • spdep +Return package version number — spdep • spdep Skip to contents @@ -7,7 +7,7 @@ spdep - 1.3-13 + 1.4-1 @@ -75,7 +75,7 @@

Author<
-

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/spweights.constants.html b/docs/reference/spweights.constants.html index 26111e01..0c7e77eb 100644 --- a/docs/reference/spweights.constants.html +++ b/docs/reference/spweights.constants.html @@ -1,5 +1,5 @@ -Provides constants for spatial weights matrices — spweights.constants • spdep +Provides constants for spatial weights matrices — spweights.constants • spdep Skip to contents @@ -7,7 +7,7 @@ spdep - 1.3-13 + 1.4-1 @@ -134,7 +134,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/ssw.html b/docs/reference/ssw.html index 08a1d61f..a37b0dcb 100644 --- a/docs/reference/ssw.html +++ b/docs/reference/ssw.html @@ -1,5 +1,5 @@ -Compute the sum of dissimilarity — ssw • spdepCompute the sum of dissimilarity — ssw • spdep Skip to contents @@ -9,7 +9,7 @@ spdep - 1.3-13 + 1.4-1 @@ -128,7 +128,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/subset.listw.html b/docs/reference/subset.listw.html index b3a0bd71..708c8767 100644 --- a/docs/reference/subset.listw.html +++ b/docs/reference/subset.listw.html @@ -1,5 +1,5 @@ -Subset a spatial weights list — subset.listw • spdep +Subset a spatial weights list — subset.listw • spdep Skip to contents @@ -7,7 +7,7 @@ spdep - 1.3-13 + 1.4-1 @@ -161,7 +161,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/subset.nb-1.png b/docs/reference/subset.nb-1.png index 3b5593f6..be0bbb39 100644 Binary files a/docs/reference/subset.nb-1.png and b/docs/reference/subset.nb-1.png differ diff --git a/docs/reference/subset.nb.html b/docs/reference/subset.nb.html index 95c9a4af..a155d48c 100644 --- a/docs/reference/subset.nb.html +++ b/docs/reference/subset.nb.html @@ -1,5 +1,5 @@ -Subset a neighbours list — subset.nb • spdep +Subset a neighbours list — subset.nb • spdep Skip to contents @@ -7,7 +7,7 @@ spdep - 1.3-13 + 1.4-1 @@ -107,7 +107,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/summary.nb.html b/docs/reference/summary.nb.html index 7d296ef3..604e9e35 100644 --- a/docs/reference/summary.nb.html +++ b/docs/reference/summary.nb.html @@ -1,5 +1,5 @@ -Print and summary function for neighbours and weights lists — summary.nb • spdepPrint and summary function for neighbours and weights lists — summary.nb • spdepspdep - 1.3-13 + 1.4-1 @@ -244,7 +244,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/testnb.html b/docs/reference/testnb.html index 3e36c0fb..eb7edb86 100644 --- a/docs/reference/testnb.html +++ b/docs/reference/testnb.html @@ -1,5 +1,5 @@ -Test a neighbours list for symmetry — is.symmetric.nb • spdepTest a neighbours list for symmetry — is.symmetric.nb • spdepspdep - 1.3-13 + 1.4-1 @@ -126,7 +126,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/tolerance.nb-1.png b/docs/reference/tolerance.nb-1.png index 8f6cc3a9..b5317083 100644 Binary files a/docs/reference/tolerance.nb-1.png and b/docs/reference/tolerance.nb-1.png differ diff --git a/docs/reference/tolerance.nb.html b/docs/reference/tolerance.nb.html index e2765b84..9f2b9bf6 100644 --- a/docs/reference/tolerance.nb.html +++ b/docs/reference/tolerance.nb.html @@ -1,5 +1,5 @@ -Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb • spdep +Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb • spdep Skip to contents @@ -7,7 +7,7 @@ spdep - 1.3-13 + 1.4-1 @@ -136,7 +136,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/tri2nb-1.png b/docs/reference/tri2nb-1.png index e1261eff..3a1373e9 100644 Binary files a/docs/reference/tri2nb-1.png and b/docs/reference/tri2nb-1.png differ diff --git a/docs/reference/tri2nb-2.png b/docs/reference/tri2nb-2.png index 3a6878ca..502b603d 100644 Binary files a/docs/reference/tri2nb-2.png and b/docs/reference/tri2nb-2.png differ diff --git a/docs/reference/tri2nb-3.png b/docs/reference/tri2nb-3.png index a72abd59..913f1073 100644 Binary files a/docs/reference/tri2nb-3.png and b/docs/reference/tri2nb-3.png differ diff --git a/docs/reference/tri2nb.html b/docs/reference/tri2nb.html index e35bce86..59c4e18b 100644 --- a/docs/reference/tri2nb.html +++ b/docs/reference/tri2nb.html @@ -1,5 +1,5 @@ -Neighbours list from tri object — tri2nb • spdepNeighbours list from tri object — tri2nb • spdepspdep - 1.3-13 + 1.4-1 @@ -134,7 +134,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/reference/write.nb.gal.html b/docs/reference/write.nb.gal.html index 10b7eec8..917235bf 100644 --- a/docs/reference/write.nb.gal.html +++ b/docs/reference/write.nb.gal.html @@ -1,5 +1,5 @@ -Write a neighbours list as a GAL lattice file — write.nb.gal • spdep +Write a neighbours list as a GAL lattice file — write.nb.gal • spdep Skip to contents @@ -7,7 +7,7 @@ spdep - 1.3-13 + 1.4-1 @@ -111,7 +111,7 @@

Examples -

Site built with pkgdown 2.1.3.

+

Site built with pkgdown 2.1.1.

diff --git a/docs/search.json b/docs/search.json index 00c6817d..26d1ea0d 100644 --- a/docs/search.json +++ b/docs/search.json @@ -1 +1 @@ -[{"path":"https://r-spatial.github.io/spdep/articles/CO69.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"“The Problem of Spatial Autocorrelation:” forty years on","text":"Cliff Ord (1969), published forty years ago, marked turning point treatment spatial autocorrelation quantitative geography. provided framework needed applied researcher attempt implementation different system, possibly using different programming language. spirit, examine spatial weights represented implementations may reproduced, tabulated results paper may reproduced, may extended cover simulation. One major assertions Cliff Ord (1969) statistic advances measurement spatial autocorrelation respect Moran (1950) Geary (1954) general specification spatial weights used. general form implications preparation weights , calculation measures. look spatial weights first, moving consider measures presented paper subsequent developments. , put together data set matching used Cliff Ord (1969). provide tabulated data counties Irish Republic, omit Dublin analyses. shapefile included package, kindly made available Michael Tiefelsdorf, used starting point: read SpatialPolygonsDataFrame — classes used handling spatial data fully described Roger S. Bivand, Pebesma, Gómez-Rubio (2008). need add data tabulated paper Table 2,1 p. 40, form text file added rainfall values Table 9, p. 49: Since assigned county names feature identifiers reading shapefiles, extra data, combine objects: Finally, need drop Dublin county omitted analyses conducted Cliff Ord (1969): double-check data, let us calculate sample Beta coefficients, using formulae given paper sample moments: differ somewhat ways skewness kurtosis computed modern statistical software, see example Joanes Gill (1998). However, purposes, let us reproduce Table 3, p. 42: Using tabulated value 23.623.6 percentage agricultural holdings 50 1950 Waterford, skewness kurtosis reproduced, comparison irishdata dataset , turns value rather 26.626.6, yields tabulated skewness kurtosis values. going , variables considered presented Table varsvars. Description variables Geary data set.","code":"library(spdep) eire <- as(sf::st_read(system.file(\"shapes/eire.gpkg\", package=\"spData\")[1]), \"Spatial\") row.names(eire) <- as.character(eire$names) #proj4string(eire) <- CRS(\"+proj=utm +zone=30 +ellps=airy +units=km\") class(eire) ## [1] \"SpatialPolygonsDataFrame\" ## attr(,\"package\") ## [1] \"sp\" names(eire) ## [1] \"A\" \"towns\" \"pale\" \"size\" \"ROADACC\" \"OWNCONS\" \"POPCHG\" ## [8] \"RETSALE\" \"INCOME\" \"names\" fn <- system.file(\"etc/misc/geary_eire.txt\", package=\"spdep\")[1] ge <- read.table(fn, header=TRUE) names(ge) ## [1] \"serlet\" \"county\" \"pagval2_10\" \"pagval10_50\" ## [5] \"pagval50p\" \"cowspacre\" \"ocattlepacre\" \"pigspacre\" ## [9] \"sheeppacre\" \"townvillp\" \"carspcap\" \"radiopcap\" ## [13] \"retailpcap\" \"psinglem30_34\" \"rainfall\" row.names(ge) <- as.character(ge$county) all.equal(row.names(ge), row.names(eire)) ## [1] TRUE eire_ge <- cbind(eire, ge) eire_ge1 <- eire_ge[!(row.names(eire_ge) %in% \"Dublin\"),] length(row.names(eire_ge1)) ## [1] 25 skewness <- function(z) {z <- scale(z, scale=FALSE); ((sum(z^3)/length(z))^2)/((sum(z^2)/length(z))^3)} kurtosis <- function(z) {z <- scale(z, scale=FALSE); (sum(z^4)/length(z))/((sum(z^2)/length(z))^2)} print(sapply(as(eire_ge1, \"data.frame\")[13:24], skewness), digits=3) ## pagval2_10 pagval10_50 pagval50p cowspacre ocattlepacre ## 1.675429 1.294978 0.000382 1.682094 0.086267 ## pigspacre sheeppacre townvillp carspcap radiopcap ## 1.138387 1.842362 0.472748 0.011111 0.342805 ## retailpcap psinglem30_34 ## 0.002765 0.068169 print(sapply(as(eire_ge1, \"data.frame\")[13:24], kurtosis), digits=4) ## pagval2_10 pagval10_50 pagval50p cowspacre ocattlepacre ## 3.790 4.331 1.508 4.294 2.985 ## pigspacre sheeppacre townvillp carspcap radiopcap ## 3.754 4.527 2.619 1.865 2.730 ## retailpcap psinglem30_34 ## 2.188 2.034 print(sapply(as(eire_ge1, \"data.frame\")[c(13,16,18,19)], function(x) skewness(log(x))), digits=3) ## pagval2_10 cowspacre pigspacre sheeppacre ## 0.68801 0.17875 0.00767 0.04184 print(sapply(as(eire_ge1, \"data.frame\")[c(13,16,18,19)], function(x) kurtosis(log(x))), digits=4) ## pagval2_10 cowspacre pigspacre sheeppacre ## 2.883 2.799 2.212 2.421"},{"path":"https://r-spatial.github.io/spdep/articles/CO69.html","id":"spatial-weights","dir":"Articles","previous_headings":"","what":"Spatial weights","title":"“The Problem of Spatial Autocorrelation:” forty years on","text":"basis comparison, first read unstandardised weighting matrix given Table A1, p. 54, paper, reading file corrected misprint giving O rather D neighbour V: file, counties represented serial letters, ordering conversion integer index representation required reach representation similar SpatialStats module spatial neighbours: done , can change representation listw object, assigning appropriate style (generalised binary) unstandardised values: Note values S0, S1, S2 correspond closely given page 42 paper, 0.846886720.84688672, 0.018699860.01869986 0.122673190.12267319. discrepancies appear due rounding printed table weights. contiguous neighbours represented object match found using poly2nb. However, see reproduced contiguities smaller link count: missing link Clare Kerry, perhaps Tarbert–Killimer ferry, counties contiguous, Figure plot_nbplot\\_nb shows: County boundaries contiguities attempt also made reproduce generalised weights 25 Irish counties reported Cliff Ord (1969), Dublin omitted. Reproducing inverse distance component dij−1d_{ij}^{-1} generalised weights dij−1βi(j)d_{ij}^{-1} \\beta_{(j)} eased statement Cliff Ord (1973, 55) points chosen represent counties “geographic centres,” different centroids yielded applying chosen computational geometry function. distance metric given, may kilometers miles — tried, results sensitive difference applies equally across weights; miles used . Computing proportion shared distance measure βi(j)\\beta_{(j)} harder, requires availability full topology input polygons. Roger S. Bivand, Pebesma, Gómez-Rubio (2008, 244) show employ vect2neigh function (written Markus Neteler) package using GRASS GIS vector handling create full topology spaghetti vector data extract border segment lengths; similar approach also mentioned using ArcGIS coverages purpose. GRASS used create topology, next proportion shared distance measure calculated. compare, need remove Tarbert–Killimer ferry link manually, view summary original weights, well correlation coefficient reconstructed weights. Naturally, unless boundary coordinates used identical original analysis, presumably measured hand, small differences occur. Even though differences general weights, identical contiguities, small, consequences measure spatial autocorrelation substantial, use fifth variable, cattle per 1000 acres crops pasture (1952), see reconstructed weights seem “reveal” autocorrelation original weights.","code":"fn <- system.file(\"etc/misc/unstand_sn.txt\", package=\"spdep\")[1] unstand <- read.table(fn, header=TRUE) summary(unstand) ## from to weight ## Length:110 Length:110 Min. :0.000600 ## Class :character Class :character 1st Qu.:0.003225 ## Mode :character Mode :character Median :0.007550 ## Mean :0.007705 ## 3rd Qu.:0.010225 ## Max. :0.032400 class(unstand) <- c(\"spatial.neighbour\", class(unstand)) of <- ordered(unstand$from) attr(unstand, \"region.id\") <- levels(of) unstand$from <- as.integer(of) unstand$to <- as.integer(ordered(unstand$to)) attr(unstand, \"n\") <- length(unique(unstand$from)) lw_unstand <- sn2listw(unstand) lw_unstand$style <- \"B\" lw_unstand ## Characteristics of weights list object: ## Neighbour list object: ## Number of regions: 25 ## Number of nonzero links: 110 ## Percentage nonzero weights: 17.6 ## Average number of links: 4.4 ## ## Weights style: B ## Weights constants summary: ## n nn S0 S1 S2 ## B 25 625 0.8476 0.01871808 0.1229232 nb <- poly2nb(eire_ge1) nb ## Neighbour list object: ## Number of regions: 25 ## Number of nonzero links: 108 ## Percentage nonzero weights: 17.28 ## Average number of links: 4.32 xx <- diffnb(nb, lw_unstand$neighbours, legacy=TRUE, verbose=TRUE) ## Neighbour difference for region id: Clare in relation to id: Kerry ## Neighbour difference for region id: Kerry in relation to id: Clare plot(eire_ge1, border=\"grey60\") plot(nb, coordinates(eire_ge1), add=TRUE, pch=\".\", lwd=2) plot(xx, coordinates(eire_ge1), add=TRUE, pch=\".\", lwd=2, col=3) library(terra) v_eire_ge1 <-vect(eire_ge1) SG <- rasterize(v_eire_ge1, rast(nrows=70, ncols=50, extent=ext(v_eire_ge1)), field=\"county\") library(rgrass) grass_home <- \"/home/rsb/topics/grass/g820/grass82\" initGRASS(grass_home, home=tempdir(), SG=SG, override=TRUE) write_VECT(v_eire_ge1, \"eire\", flags=c(\"o\", \"overwrite\")) res <- vect2neigh(\"eire\", ID=\"serlet\") res$length <- res$length*1000 attr(res, \"external\") <- attr(res, \"external\")*1000 attr(res, \"total\") <- attr(res, \"total\")*1000 grass_borders <- sn2listw(res) raw_borders <- grass_borders$weights int_tot <- attr(res, \"total\") - attr(res, \"external\") prop_borders <- lapply(1:length(int_tot), function(i) raw_borders[[i]]/int_tot[i]) dlist <- nbdists(grass_borders$neighbours, coordinates(eire_ge1)) inv_dlist <- lapply(dlist, function(x) 1/(x/1.609344)) combo_km <- lapply(1:length(inv_dlist), function(i) inv_dlist[[i]]*prop_borders[[i]]) combo_km_lw <- nb2listw(grass_borders$neighbours, glist=combo_km, style=\"B\") summary(combo_km_lw) ## Characteristics of weights list object: ## Neighbour list object: ## Number of regions: 25 ## Number of nonzero links: 108 ## Percentage nonzero weights: 17.28 ## Average number of links: 4.32 ## Link number distribution: ## ## 1 2 3 4 5 6 7 8 ## 1 2 5 5 8 1 2 1 ## 1 least connected region: ## E with 1 link ## 1 most connected region: ## V with 8 links ## ## Weights style: B ## Weights constants summary: ## n nn S0 S1.5 S2 ## B 25 625 0.9083144 0.02191845 0.1427746 red_lw_unstand <- lw_unstand Clare <- which(attr(lw_unstand, \"region.id\") == \"C\") Kerry <- which(attr(lw_unstand, \"region.id\") == \"H\") Kerry_in_Clare <- which(lw_unstand$neighbours[[Clare]] == Kerry) Clare_in_Kerry <- which(lw_unstand$neighbours[[Kerry]] == Clare) red_lw_unstand$neighbours[[Clare]] <- red_lw_unstand$neighbours[[Clare]][-Kerry_in_Clare] red_lw_unstand$neighbours[[Kerry]] <- red_lw_unstand$neighbours[[Kerry]][-Clare_in_Kerry] red_lw_unstand$weights[[Clare]] <- red_lw_unstand$weights[[Clare]][-Kerry_in_Clare] red_lw_unstand$weights[[Kerry]] <- red_lw_unstand$weights[[Kerry]][-Clare_in_Kerry] summary(red_lw_unstand) ## Characteristics of weights list object: ## Neighbour list object: ## Number of regions: 25 ## Number of nonzero links: 108 ## Percentage nonzero weights: 17.28 ## Average number of links: 4.32 ## Link number distribution: ## ## 1 2 3 4 5 6 7 8 ## 1 2 5 5 8 1 2 1 ## 1 least connected region: ## E with 1 link ## 1 most connected region: ## V with 8 links ## ## Weights style: B ## Weights constants summary: ## n nn S0 S1 S2 ## B 25 625 0.8437 0.01870287 0.1222501 cor(unlist(red_lw_unstand$weights), unlist(combo_km_lw$weights)) ## [1] 0.969543 flatten <- function(x, digits=3, statistic=\"I\") { res <- c(format(x$estimate, digits=digits), format(x$statistic, digits=digits), format.pval(x$p.value, digits=digits)) res <- matrix(res, ncol=length(res)) colnames(res) <- paste(c(\"\", \"E\", \"V\", \"SD_\", \"P_\"), \"I\", sep=\"\") rownames(res) <- deparse(substitute(x)) res } `reconstructed weights` <- moran.test(eire_ge1$ocattlepacre, combo_km_lw) `original weights` <- moran.test(eire_ge1$ocattlepacre, red_lw_unstand) print(rbind(flatten(`reconstructed weights`), flatten(`original weights`)), quote=FALSE) ## I EI VI SD_I P_I ## reconstructed weights 0.3203 -0.0417 0.0225 2.41 0.00792 ## original weights 0.2779 -0.0417 0.0223 2.14 0.0161"},{"path":"https://r-spatial.github.io/spdep/articles/CO69.html","id":"measures-of-spatial-autocorrelation","dir":"Articles","previous_headings":"","what":"Measures of spatial autocorrelation","title":"“The Problem of Spatial Autocorrelation:” forty years on","text":"targets reproduction Tables 4 5 Cliff Ord (1969, 43–44), first containing standard deviates normality randomisation original Moran measure binary weights, original Geary measure binary weights, proposed measure unstandardised general weights, proposed measure row-standardised general weights. addition, four variables log-transformed basis skewness kurtosis results presented . carry transformation variables, generate additional binary row-standardised general spatial weights objects — note weights constants row-standardised general weights agree given p. 42 paper, allowing small differences due rounding weights values displayed paper (p. 54): standard representation measures : =n∑=1n∑j=1nwij∑=1n∑j=1nwij(xi−x‾)(xj−x‾)∑=1n(xi−x‾)2I = \\frac{n}{\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}} \\frac{\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}(x_i-\\bar{x})(x_j-\\bar{x})}{\\sum_{=1}^{n}(x_i - \\bar{x})^2} Moran’s II — paper termed proposed statistic, Geary’s CC: C=(n−1)2∑=1n∑j=1nwij∑=1n∑j=1nwij(xi−xj)2∑=1n(xi−x‾)2C = \\frac{(n-1)}{2\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}} \\frac{\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}(x_i-x_j)^2}{\\sum_{=1}^{n}(x_i - \\bar{x})^2} xi,=1,…,nx_i, =1, \\ldots, n nn observations numeric variable interest, wijw_{ij} spatial weights. order reproduce standard deviates given paper, sufficient apply moran.test variables three different spatial weights objects, two different values randomisation= argument. addition, geary.test applied single spatial weights objects, two different values randomisation= argument. order conduct 8 different tests 16 variables, use lapply list variables specified order, sapply list output objects name generate table row column order original (save copy six columns comparison bootstrap results ): values standard deviates agree Table 4 original paper, exception proposed statistic standardised weights normality untransformed variables. can see happened substituting weights constants standardised weights unstandardised weights: Next, let us look Table 5 original paper. tabulate values measures , , since expectation constant measure, square root variance measure randomisation — extracting values calculated : values follows, match original exception initial version Moran’s II first two columns. write function implementing equations 3 4: =∑=1n∑j=+1nwij(xi−x‾)(xj−x‾)∑=1n(xi−x‾)2I = \\frac{\\sum_{=1}^{n}\\sum_{j=+1}^{n}w_{ij}(x_i-\\bar{x})(x_j-\\bar{x})}{\\sum_{=1}^{n}(x_i - \\bar{x})^2} crucially inner summation +1…ni+1 \\ldots n, 1…n1 \\ldots n, can reproduce values measure shown original Table 5: variance term given equation 7 original paper case normality, randomisation; reference p. 28 equation 38 p. 26 permit reproduction values second column Table 5. variance equation given equation 1.35 Cliff Ord (1973, 9) either, time possible say tabulated values computed. Note since standard deviances reproduced correctly, can reproduced second column values using measure expectance, just matter establishing formula used, far proved possible.","code":"eire_ge1$ln_pagval2_10 <- log(eire_ge1$pagval2_10) eire_ge1$ln_cowspacre <- log(eire_ge1$cowspacre) eire_ge1$ln_pigspacre <- log(eire_ge1$pigspacre) eire_ge1$ln_sheeppacre <- log(eire_ge1$sheeppacre) vars <- c(\"pagval2_10\", \"ln_pagval2_10\", \"pagval10_50\", \"pagval50p\", \"cowspacre\", \"ln_cowspacre\", \"ocattlepacre\", \"pigspacre\", \"ln_pigspacre\", \"sheeppacre\", \"ln_sheeppacre\", \"townvillp\", \"carspcap\", \"radiopcap\", \"retailpcap\", \"psinglem30_34\") nb_B <- nb2listw(lw_unstand$neighbours, style=\"B\") nb_B ## Characteristics of weights list object: ## Neighbour list object: ## Number of regions: 25 ## Number of nonzero links: 110 ## Percentage nonzero weights: 17.6 ## Average number of links: 4.4 ## ## Weights style: B ## Weights constants summary: ## n nn S0 S1 S2 ## B 25 625 110 220 2176 lw_std <- nb2listw(lw_unstand$neighbours, glist=lw_unstand$weights, style=\"W\") lw_std ## Characteristics of weights list object: ## Neighbour list object: ## Number of regions: 25 ## Number of nonzero links: 110 ## Percentage nonzero weights: 17.6 ## Average number of links: 4.4 ## ## Weights style: W ## Weights constants summary: ## n nn S0 S1 S2 ## W 25 625 25 15.84089 103.6197 system.time({ MoranN <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=nb_B, randomisation=FALSE)) MoranR <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=nb_B, randomisation=TRUE)) GearyN <- lapply(vars, function(x) geary.test(eire_ge1[[x]], listw=nb_B, randomisation=FALSE)) GearyR <- lapply(vars, function(x) geary.test(eire_ge1[[x]], listw=nb_B, randomisation=TRUE)) Prop_unstdN <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=lw_unstand, randomisation=FALSE)) Prop_unstdR <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=lw_unstand, randomisation=TRUE)) Prop_stdN <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=lw_std, randomisation=FALSE)) Prop_stdR <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=lw_std, randomisation=TRUE)) }) ## user system elapsed ## 0.135 0.000 0.137 res <- sapply(c(\"MoranN\", \"MoranR\", \"GearyN\", \"GearyR\", \"Prop_unstdN\", \"Prop_unstdR\", \"Prop_stdN\", \"Prop_stdR\"), function(x) sapply(get(x), \"[[\", \"statistic\")) rownames(res) <- vars ores <- res[,c(1,2,5:8)] print(formatC(res, format=\"f\", digits=4), quote=FALSE) ## MoranN MoranR GearyN GearyR Prop_unstdN Prop_unstdR Prop_stdN Prop_stdR ## pagval2_10 3.7851 3.8779 4.3142 3.9016 3.3307 3.4159 3.9276 4.0292 ## ln_pagval2_10 4.0965 4.1074 4.0841 4.0343 3.5795 3.5894 4.1278 4.1393 ## pagval10_50 1.0899 1.1316 2.7511 2.3760 1.3348 1.3882 1.5127 1.5738 ## pagval50p 5.2011 5.0555 4.0178 4.7194 4.6604 4.5247 4.8823 4.7387 ## cowspacre 5.1969 5.3907 4.3531 3.7709 4.1379 4.2991 4.7274 4.9135 ## ln_cowspacre 5.2420 5.2455 3.9211 3.9085 4.2007 4.2037 4.6532 4.6566 ## ocattlepacre 0.5565 0.5593 -0.1707 -0.1668 2.1366 2.1478 1.9219 1.9320 ## pigspacre 2.4807 2.5393 2.2928 2.0802 2.8312 2.9010 3.1908 3.2703 ## ln_pigspacre 2.3015 2.2724 2.0520 2.1893 2.5171 2.4839 2.8460 2.8081 ## sheeppacre 1.0188 1.0630 0.8689 0.7387 1.7398 1.8187 1.4792 1.5470 ## ln_sheeppacre 1.2930 1.2827 1.5156 1.5767 2.3708 2.3511 2.0374 2.0203 ## townvillp 2.2759 2.2681 2.5475 2.5902 1.2148 1.2104 1.6275 1.6216 ## carspcap 4.4927 4.4015 3.2247 3.5992 3.8897 3.8075 4.1826 4.0934 ## radiopcap 0.3156 0.3153 1.2294 1.2348 0.5915 0.5909 0.7857 0.7849 ## retailpcap 3.4985 3.4524 3.1303 3.3497 2.9291 2.8888 3.0346 2.9926 ## psinglem30_34 2.7349 2.6895 2.3382 2.5519 2.7541 2.7065 2.7078 2.6605 wc_unstd <- spweights.constants(lw_unstand) wrong_N_sqVI <- sqrt((wc_unstd$nn*wc_unstd$S1 - wc_unstd$n*wc_unstd$S2 + 3*wc_unstd$S0*wc_unstd$S0)/((wc_unstd$nn-1)*wc_unstd$S0*wc_unstd$S0)-((-1/(wc_unstd$n-1))^2)) raw_data <- grep(\"^ln_\", vars, invert=TRUE) I <- sapply(Prop_stdN, function(x) x$estimate[1])[raw_data] EI <- sapply(Prop_stdN, function(x) x$estimate[2])[raw_data] res <- (I - EI)/wrong_N_sqVI names(res) <- vars[raw_data] print(formatC(res, format=\"f\", digits=4), quote=FALSE) ## pagval2_10 pagval10_50 pagval50p cowspacre ocattlepacre pigspacre ## 3.8836 1.4957 4.8276 4.6744 1.9003 3.1550 ## sheeppacre townvillp carspcap radiopcap retailpcap psinglem30_34 ## 1.4627 1.6093 4.1357 0.7769 3.0006 2.6774 res <- lapply(c(\"MoranR\", \"GearyR\", \"Prop_unstdR\", \"Prop_stdR\"), function(x) sapply(get(x), function(y) c(y$estimate[1], sqrt(y$estimate[3])))) res <- t(do.call(\"rbind\", res)) colnames(res) <- c(\"I\", \"sigma_I\", \"C\", \"sigma_C\", \"unstd_r\", \"sigma_r\", \"std_r\", \"sigma_r\") rownames(res) <- vars print(formatC(res, format=\"f\", digits=4), quote=FALSE) ## I sigma_I C sigma_C unstd_r sigma_r std_r sigma_r ## pagval2_10 0.4074 0.1158 0.3477 0.1672 0.4559 0.1456 0.5384 0.1440 ## ln_pagval2_10 0.4444 0.1183 0.3825 0.1531 0.4930 0.1490 0.5680 0.1473 ## pagval10_50 0.0877 0.1143 0.5840 0.1751 0.1577 0.1436 0.1818 0.1420 ## pagval50p 0.5754 0.1221 0.3925 0.1287 0.6545 0.1539 0.6795 0.1522 ## cowspacre 0.5749 0.1144 0.3418 0.1745 0.5764 0.1438 0.6566 0.1421 ## ln_cowspacre 0.5803 0.1186 0.4071 0.1517 0.5858 0.1493 0.6456 0.1476 ## ocattlepacre 0.0244 0.1181 1.0258 0.1547 0.2775 0.1486 0.2422 0.1469 ## pigspacre 0.2527 0.1159 0.6533 0.1667 0.3812 0.1458 0.4296 0.1441 ## ln_pigspacre 0.2314 0.1202 0.6897 0.1417 0.3343 0.1514 0.3787 0.1497 ## sheeppacre 0.0792 0.1137 0.8686 0.1778 0.2182 0.1429 0.1768 0.1412 ## ln_sheeppacre 0.1117 0.1196 0.7708 0.1453 0.3125 0.1506 0.2593 0.1489 ## townvillp 0.2284 0.1191 0.6148 0.1487 0.1398 0.1499 0.1987 0.1482 ## carspcap 0.4914 0.1211 0.5124 0.1355 0.5394 0.1526 0.5761 0.1509 ## radiopcap -0.0042 0.1188 0.8141 0.1505 0.0467 0.1495 0.0744 0.1478 ## retailpcap 0.3734 0.1202 0.5267 0.1413 0.3959 0.1515 0.4066 0.1498 ## psinglem30_34 0.2828 0.1207 0.6465 0.1385 0.3697 0.1520 0.3583 0.1503 oMoranf <- function(x, nb) { z <- scale(x, scale=FALSE) n <- length(z) glist <- lapply(1:n, function(i) {ii <- nb[[i]]; ifelse(ii > i, 1, 0)}) lw <- nb2listw(nb, glist=glist, style=\"B\") wz <- lag(lw, z) I <- (sum(z*wz)/sum(z*z)) I } res <- sapply(vars, function(x) oMoranf(eire_ge1[[x]], nb=lw_unstand$neighbours)) print(formatC(res, format=\"f\", digits=4), quote=FALSE) ## pagval2_10 ln_pagval2_10 pagval10_50 pagval50p cowspacre ln_cowspacre ## 0.8964 0.9776 0.1928 1.2660 1.2649 1.2766 ## ocattlepacre pigspacre ln_pigspacre sheeppacre ln_sheeppacre townvillp ## 0.0536 0.5559 0.5091 0.1743 0.2458 0.5024 ## carspcap radiopcap retailpcap psinglem30_34 ## 1.0811 -0.0093 0.8215 0.6222"},{"path":"https://r-spatial.github.io/spdep/articles/CO69.html","id":"simulating-measures-of-spatial-autocorrelation","dir":"Articles","previous_headings":"","what":"Simulating measures of spatial autocorrelation","title":"“The Problem of Spatial Autocorrelation:” forty years on","text":"Cliff Ord (1969) conduct simulation experiments, although sequels , notably Cliff Ord (1973), among many others. Simulation studies necessarily demanding computationally, especially spatially autocorrelated variables created, Cliff Ord (1973, 146–53). book, also report use permutation tests, also known Monte Carlo Hope hypothesis testing procedures (Cliff Ord 1973, 50–52). procedures provided way examine distribution statistic interest exchanging random observed values observations, comparing simulated distribution null hypothesis spatial patterning observed value statistic question. First let us define function MoranI.boot just return value Moran’s II variable var permutation index , function Nsim generate random samples variable interest assuming Normality. make easier process variables turn, encapsulate calls boot wrapper functions f_bperm f_bpara. Running 4999 simulations 16 three different weights specifications parametric permutation bootstrap takes quite lot time. collate results compare analytical standard deviates Normality randomisation, see fact differences large, expressed median absolute difference tables. can also see inferences based one-sided α=0.05\\alpha=0.05 cut-analytical bootstrap approaches. indicates can, general, rely analytical standard deviates, bootstrap methods help assumptions underlying measures met. assumptions affect shape distribution measure tails; one possibility use Saddlepoint approximation find equivalent analytical bootstrap-based standard deviate inference (Tiefelsdorf 2002). Saddlepoint approximation requires eigenvalues weights matrix iterative root-finding global Moran’s II, local Moran’s IiI_i, analytical forms known. Even computational burden, Saddlepoint approximation global Moran’s II runs quite quickly. First need fit null linear models (including intercept) variables, apply lm.morantest.sad fitted model objects: Although analytical standard deviates (Normality) larger reached using Saddlepoint approximation measured median absolute deviation, differences lead different inferences chosen cut-. reflects fact shape distribution sensitive small nn, moderate nn global Moran’s II, effects seen tails. consequences local Moran’s IiI_i much stronger, clique neighbours observation typically small. perhaps interest differences much smaller case general weights unstandardised binary weights. addition choose use exact distribution Moran’s II, described Tiefelsdorf (2000); implementation covered R. S. Bivand, Müller, Reder (2009). global case also needs eigenvalues weights matrix, solution numerical integration function, cases, timings quite acceptable. output comparable Saddlepoint approximation, inferences drawn chosen cut-analytical standard deviates calculated Normality. Li, Calder, Cressie (2007) take challenge Cliff Ord (1969, 31), try give statistic bounded fixed range. APLE measure intended approximate spatial dependence parameter simultaneous autoregressive model better Moran’s II, re-scales measure function eigenvalues spatial weights matrix. APLE requires use row standardised weights. order save time, use two internal functions spatialreg:::preAple spatialreg:::inAple, since definition spatial weights, eigenvalue calculations need made. notation using ::: operator says function named operator found namespace package named operator. APLE values repeat pattern already seen — variables, measured autocorrelation similar irrespective spatial weights definition, others, change definition binary general make difference.","code":"MoranI.boot <- function(var, i, ...) { var <- var[i] return(moran(x=var, ...)$I) } Nsim <- function(d, mle) { n <- length(d) rnorm(n, mle$mean, mle$sd) } f_bperm <- function(x, nsim, listw) { boot(x, statistic=MoranI.boot, R=nsim, sim=\"permutation\", listw=listw, n=length(x), S0=Szero(listw)) } f_bpara <- function(x, nsim, listw) { boot(x, statistic=MoranI.boot, R=nsim, sim=\"parametric\", ran.gen=Nsim, mle=list(mean=mean(x), sd=sd(x)), listw=listw, n=length(x), S0=Szero(listw)) } nsim <- 4999 set.seed(1234) system.time({ MoranNb <- lapply(vars, function(x) f_bpara(x=eire_ge1[[x]], nsim=nsim, listw=nb_B)) MoranRb <- lapply(vars, function(x) f_bperm(x=eire_ge1[[x]], nsim=nsim, listw=nb_B)) Prop_unstdNb <- lapply(vars, function(x) f_bpara(x=eire_ge1[[x]], nsim=nsim, listw=lw_unstand)) Prop_unstdRb <- lapply(vars, function(x) f_bperm(x=eire_ge1[[x]], nsim=nsim, listw=lw_unstand)) Prop_stdNb <- lapply(vars, function(x) f_bpara(x=eire_ge1[[x]], nsim=nsim, listw=lw_std)) Prop_stdRb <- lapply(vars, function(x) f_bperm(x=eire_ge1[[x]], nsim=nsim, listw=lw_std)) }) res <- lapply(c(\"MoranNb\", \"MoranRb\", \"Prop_unstdNb\", \"Prop_unstdRb\", \"Prop_stdNb\", \"Prop_stdRb\"), function(x) sapply(get(x), function(y) (y$t0 - mean(y$t))/sd(y$t))) res <- t(do.call(\"rbind\", res)) colnames(res) <- c(\"MoranNb\", \"MoranRb\", \"Prop_unstdNb\", \"Prop_unstdRb\", \"Prop_stdNb\", \"Prop_stdRb\") rownames(res) <- vars print(formatC(res, format=\"f\", digits=4), quote=FALSE) ## pagval2_10 ln_pagval2_10 pagval10_50 pagval50p cowspacre ln_cowspacre ## 0.8964 0.9776 0.1928 1.2660 1.2649 1.2766 ## ocattlepacre pigspacre ln_pigspacre sheeppacre ln_sheeppacre townvillp ## 0.0536 0.5559 0.5091 0.1743 0.2458 0.5024 ## carspcap radiopcap retailpcap psinglem30_34 ## 1.0811 -0.0093 0.8215 0.6222 oores <- ores - res apply(oores, 2, mad) ## MoranN MoranR Prop_unstdN Prop_unstdR Prop_stdN Prop_stdR ## 1.6470091 1.6241614 0.7681895 0.7170636 1.2615083 1.2723149 alpha_0.05 <- qnorm(0.05, lower.tail=FALSE) all((res >= alpha_0.05) == (ores >= alpha_0.05)) ## [1] FALSE lm_objs <- lapply(vars, function(x) lm(formula(paste(x, \"~1\")), data=eire_ge1)) system.time({ MoranSad <- lapply(lm_objs, function(x) lm.morantest.sad(x, listw=nb_B)) Prop_unstdSad <- lapply(lm_objs, function(x) lm.morantest.sad(x, listw=lw_unstand)) Prop_stdSad <- lapply(lm_objs, function(x) lm.morantest.sad(x, listw=lw_std)) }) ## user system elapsed ## 0.090 0.000 0.091 res <- sapply(c(\"MoranSad\", \"Prop_unstdSad\", \"Prop_stdSad\"), function(x) sapply(get(x), \"[[\", \"statistic\")) rownames(res) <- vars print(formatC(res, format=\"f\", digits=4), quote=FALSE) ## MoranSad Prop_unstdSad Prop_stdSad ## pagval2_10 3.2903 3.1711 3.8283 ## ln_pagval2_10 3.5346 3.3982 4.0441 ## pagval10_50 1.0883 1.3219 1.4791 ## pagval50p 4.4402 4.4258 4.9377 ## cowspacre 4.4366 3.9164 4.7406 ## ln_cowspacre 4.4758 3.9760 4.6493 ## ocattlepacre 0.6030 2.0748 1.8642 ## pigspacre 2.2611 2.7154 3.0775 ## ln_pigspacre 2.1158 2.4271 2.7417 ## sheeppacre 1.0250 1.7040 1.4476 ## ln_sheeppacre 1.2669 2.2921 1.9731 ## townvillp 2.0949 1.2079 1.5872 ## carspcap 3.8500 3.6840 4.1044 ## radiopcap 0.3750 0.6094 0.7906 ## retailpcap 3.0663 2.8049 2.9245 ## psinglem30_34 2.4649 2.6449 2.6089 oores <- res - ores[,c(1,3,5)] apply(oores, 2, mad) ## MoranSad Prop_unstdSad Prop_stdSad ## 0.37142684 0.10779060 0.05650183 all((res >= alpha_0.05) == (ores[,c(1,3,5)] >= alpha_0.05)) ## [1] TRUE system.time({ MoranEx <- lapply(lm_objs, function(x) lm.morantest.exact(x, listw=nb_B)) Prop_unstdEx <- lapply(lm_objs, function(x) lm.morantest.exact(x, listw=lw_unstand)) Prop_stdEx <- lapply(lm_objs, function(x) lm.morantest.exact(x, listw=lw_std)) }) ## user system elapsed ## 0.105 0.000 0.104 res <- sapply(c(\"MoranEx\", \"Prop_unstdEx\", \"Prop_stdEx\"), function(x) sapply(get(x), \"[[\", \"statistic\")) rownames(res) <- vars print(formatC(res, format=\"f\", digits=4), quote=FALSE) ## MoranEx Prop_unstdEx Prop_stdEx ## pagval2_10 3.2895 3.1660 3.8261 ## ln_pagval2_10 3.5384 3.3979 4.0430 ## pagval10_50 1.0798 1.3131 1.4745 ## pagval50p 4.4568 4.4430 4.9446 ## cowspacre 4.4532 3.9268 4.7453 ## ln_cowspacre 4.4928 3.9875 4.6531 ## ocattlepacre 0.5967 2.0611 1.8596 ## pigspacre 2.2486 2.7033 3.0740 ## ln_pigspacre 2.1031 2.4131 2.7380 ## sheeppacre 1.0168 1.6924 1.4430 ## ln_sheeppacre 1.2575 2.2779 1.9685 ## townvillp 2.0822 1.1999 1.5826 ## carspcap 3.8593 3.6899 4.1037 ## radiopcap 0.3696 0.6054 0.7873 ## retailpcap 3.0616 2.7938 2.9210 ## psinglem30_34 2.4533 2.6321 2.6050 oores <- res - ores[,c(1,3,5)] apply(oores, 2, mad) ## MoranEx Prop_unstdEx Prop_stdEx ## 0.37187539 0.09751723 0.05419300 all((res >= alpha_0.05) == (ores[,c(1,3,5)] >= alpha_0.05)) ## [1] TRUE vars_scaled <- lapply(vars, function(x) scale(eire_ge1[[x]], scale=FALSE)) nb_W <- nb2listw(lw_unstand$neighbours, style=\"W\") pre <- spatialreg:::preAple(0, listw=nb_W) MoranAPLE <- sapply(vars_scaled, function(x) spatialreg:::inAple(x, pre)) pre <- spatialreg:::preAple(0, listw=lw_std, override_similarity_check=TRUE) Prop_stdAPLE <- sapply(vars_scaled, function(x) spatialreg:::inAple(x, pre)) res <- cbind(MoranAPLE, Prop_stdAPLE) colnames(res) <- c(\"APLE W\", \"APLE Gstd\") rownames(res) <- vars print(formatC(res, format=\"f\", digits=4), quote=FALSE) ## APLE W APLE Gstd ## pagval2_10 0.7702 0.6628 ## ln_pagval2_10 0.7615 0.6655 ## pagval10_50 0.3954 0.3446 ## pagval50p 0.7519 0.7313 ## cowspacre 0.8329 0.7408 ## ln_cowspacre 0.8148 0.7487 ## ocattlepacre 0.1468 0.4092 ## pigspacre 0.6227 0.6205 ## ln_pigspacre 0.5582 0.5887 ## sheeppacre 0.1594 0.2841 ## ln_sheeppacre 0.2046 0.4550 ## townvillp 0.3442 0.2644 ## carspcap 0.7140 0.6166 ## radiopcap 0.0083 0.1376 ## retailpcap 0.6376 0.5307 ## psinglem30_34 0.4094 0.4889"},{"path":"https://r-spatial.github.io/spdep/articles/CO69.html","id":"odds-and-ends-ldots","dir":"Articles","previous_headings":"","what":"Odds and ends …\\ldots","title":"“The Problem of Spatial Autocorrelation:” forty years on","text":"differences found case variables inference using original binary weights, general weights proposed Cliff Ord (1969) necessarily related weights thenselves. Figures plot_wtsplot\\_wts plot_mapplot\\_map show values weights sparse matrix form, sums weights county sums identical design. case binary weights, matrix entries equal, sums -weight counties many neighbours. General weights -weight counties close , neighbours, share larger boundary proportions (asymmetric relationship). impact using boundary proportions, boundary county exterior subtracted, thus boosting weights edge counties neighbours, even . Standardised general weights -weight -weight counties neighbours, chiefly edges study area. small data set, n=25n=25, possible edge configuration effects relatively strong, may impact inference different ways. issue egde effects really satisfactorily resolved, kept mind analyses data sets size shape.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"creating-neighbours","dir":"Articles","previous_headings":"","what":"Creating Neighbours","title":"Creating Neighbours","text":"vignette formed pp. 239–251 first edition Bivand, R. S., Pebesma, E. Gómez-Rubio V. (2008) Applied Spatial Data Analysis R, Springer-Verlag, New York. retired second edition (2013) accommodate material topics, made available form understanding publishers.","code":""},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"introduction","dir":"Articles","previous_headings":"Creating Neighbours","what":"Introduction","title":"Creating Neighbours","text":"Creating spatial weights necessary step using areal data, perhaps just check remaining spatial patterning residuals. first step define relationships observations given non-zero weight, choose neighbour criterion used; second assign weights identified neighbour links. 281 census tract data set eight central New York State counties featured prominently (Waller Gotway 2004) used many examples, supplemented tract boundaries derived TIGER 1992 distributed SEDAC/CIESIN. boundaries projected geographical coordinates UTM zone~18. file identical boundaries used original source, close may re-distributed, unlike version used book. Starting census tract queen contiguities, touching polygons neighbours, used (Waller Gotway 2004) provided DBF file website, GAL format file created read R. sake simplicity showing create neighbour objects, work subset map consisting census tracts within Syracuse, although principles apply full data set. retrieve part neighbour list Syracuse using subset method.","code":"library(spdep) ## Loading required package: spData ## Loading required package: sf ## Linking to GEOS 3.13.1, GDAL 3.11.0, PROJ 9.6.2; sf_use_s2() is TRUE if (packageVersion(\"spData\") >= \"2.3.2\") { NY8a <- sf::st_read(system.file(\"shapes/NY8_utm18.gpkg\", package=\"spData\")) } else { NY8a <- sf::st_read(system.file(\"shapes/NY8_bna_utm18.gpkg\", package=\"spData\")) sf::st_crs(NY8a) <- \"EPSG:32618\" NY8a$Cases <- NY8a$TRACTCAS } ## Reading layer `NY8_utm18' from data source ## `/home/rsb/lib/r_libs/spData/shapes/NY8_utm18.gpkg' using driver `GPKG' ## Simple feature collection with 281 features and 17 fields ## Geometry type: POLYGON ## Dimension: XY ## Bounding box: xmin: 358241.9 ymin: 4649755 xmax: 480393.1 ymax: 4808545 ## Projected CRS: WGS 84 / UTM zone 18N NY8 <- as(NY8a, \"Spatial\") NY_nb <- read.gal(system.file(\"weights/NY_nb.gal\", package=\"spData\"), region.id=as.character(as.integer(row.names(NY8))-1L)) Syracuse <- NY8[!is.na(NY8$AREANAME) & NY8$AREANAME == \"Syracuse city\",] Sy0_nb <- subset(NY_nb, !is.na(NY8$AREANAME) & NY8$AREANAME == \"Syracuse city\") summary(Sy0_nb) ## Neighbour list object: ## Number of regions: 63 ## Number of nonzero links: 346 ## Percentage nonzero weights: 8.717561 ## Average number of links: 5.492063 ## Link number distribution: ## ## 1 2 3 4 5 6 7 8 9 ## 1 1 5 9 14 17 9 6 1 ## 1 least connected region: ## 164 with 1 link ## 1 most connected region: ## 136 with 9 links"},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"creating-contiguity-neighbours","dir":"Articles","previous_headings":"Creating Neighbours","what":"Creating Contiguity Neighbours","title":"Creating Neighbours","text":"can create copy neighbours object polygon contiguities using poly2nb() function spdep. takes object extending SpatialPolygons class first argument, using heuristics identifies polygons sharing boundary points neighbours. also snap= argument, allow shared boundary points short distance one another. can see, creating contiguity neighbours Syracuse object reproduces neighbours (Waller Gotway 2004). Careful examination next figure shows, however, graph neighbours planar, since neighbour links cross . default, contiguity condition met least one point boundary one polygon within snap distance least one point neighbour. relationship given argument queen=TRUE analogy movements chessboard. three polygons meet single point, meet contiguity condition, giving rise crossed links. queen=FALSE, least two boundary points must within snap distance , conventional name `rook’ relationship. figure shows crossed line differences arise polygons touch single point, compared stricter rook criterion. : Queen-style census tract contiguities, Syracuse; b: Rook-style contiguity differences shown thicker orange lines access GIS GRASS ArcGIS, can export SpatialPolygonsDataFrame object use topology engine GIS find contiguities graph polygon edges - shared edge yield output rook relationship. procedure , however, depend topology set polygons clean, holds subset, full eight-county data set. infrequently, small artefacts, slivers boundary lines intersect diverge distances seen plots, require intervention keep geometries data correctly associated. geometrical artefacts present, topology clean, unambiguous shared polygon boundaries found cases; artefacts typically arise data collected one purpose combined data used another purpose. Topologies usually cleaned GIS snapping' vertices closer threshold distance together, removing artefacts -- example, snapping across river channel correct boundary median line input polygons stop channel banks side. Thepoly2nb()function asnap` argument, may also used input data possess geometrical artefacts. Similar approaches may also used read ArcGIS coverage data tallying left neighbour right neighbour arc indices polygons data set, using either RArcInfo rgdal. Syracuse case, exclaves islands' belonging data set, sharing boundary points within snap distance. number polygons moderate, missing neighbour links may added interactively using theedit()method fornb` objects, displaying polygon background. method may used removing links , although contiguity exists, may considered void, across mountain range.","code":"class(Syracuse) ## [1] \"SpatialPolygonsDataFrame\" ## attr(,\"package\") ## [1] \"sp\" Sy1_nb <- poly2nb(Syracuse) isTRUE(all.equal(Sy0_nb, Sy1_nb, check.attributes=FALSE)) ## [1] TRUE Sy2_nb <- poly2nb(Syracuse, queen=FALSE) isTRUE(all.equal(Sy0_nb, Sy2_nb, check.attributes=FALSE)) ## [1] FALSE oopar <- par(mfrow=c(1,2), mar=c(3,3,1,1)+0.1) plot(Syracuse, border=\"grey60\") plot(Sy0_nb, coordinates(Syracuse), add=TRUE, pch=19, cex=0.6) text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"a)\", cex=0.8) plot(Syracuse, border=\"grey60\") plot(Sy0_nb, coordinates(Syracuse), add=TRUE, pch=19, cex=0.6) plot(diffnb(Sy0_nb, Sy2_nb, verbose=FALSE), coordinates(Syracuse), add=TRUE, pch=\".\", cex=0.6, lwd=2, col=\"orange\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"b)\", cex=0.8) par(oopar) library(rgrass) v <- terra::vect(sf::st_as_sf(Syracuse)) SG <- terra::rast(terra::ext(v), crs=terra::crs(v)) pr <- initGRASS(\"/home/rsb/topics/grass/g840/grass84\", tempdir(), SG=SG, override=TRUE) write_VECT(v, \"SY0\", flags=c(\"o\", \"overwrite\")) contig <- vect2neigh(\"SY0\") Sy3_nb <- sn2listw(contig, style=\"B\")$neighbours isTRUE(all.equal(Sy3_nb, Sy2_nb, check.attributes=FALSE)) ## [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"creating-graph-based-neighbours","dir":"Articles","previous_headings":"Creating Neighbours","what":"Creating Graph-Based Neighbours","title":"Creating Neighbours","text":"Continuing irregularly located areal entities, possible choose point represent polygon-support entities. often polygon centroid, average coordinates dimension, takes proper care weight component triangles polygon area. also possible use points, data available, construct, example population-weighted centroids. representative points available, criteria neighbourhood can extended just contiguity include graph measures, distance thresholds, kk-nearest neighbours. direct graph representation neighbours make Delaunay triangulation points, shown first panel figure. neighbour relationships defined triangulation, extends outwards convex hull points planar. Note graph-based representations construct interpoint relationships based Euclidean distance, option use Great Circle distances geographical coordinates. joins distant points around convex hull, may worthwhile thin triangulation Sphere Influence (SOI) graph, removing links relatively long. Points SOI neighbours circles centred points, radius equal points’ nearest neighbour distances, intersect two places (Avis Horton 1985). Functions graph-based neighbours kindly contributed Nicholas Lewin-Koh. : Delauney triangulation neighbours; b: Sphere influence neighbours (available); c: Gabriel graph neighbours; d: Relative graph neighbours Delaunay triangulation neighbours SOI neighbours symmetric design – ii neighbour jj, jj neighbour ii. Gabriel graph also subgraph Delaunay triangulation, retaining different set neighbours (Matula Sokal 1980). , however, guarantee symmetry; applies Relative graph neighbours (Toussaint 1980). graph2nb() function takes sym argument insert links restore symmetry, graphs longer exactly fulfil neighbour criteria. graph-based neighbour schemes always ensure points least one neighbour. Subgraphs full triangulation may also one graph trimming. functions .symmetric.nb() can used check symmetry, argument force=TRUE symmetry attribute overridden, n.comp.nb() reports number graph components ~components points belong (enforcing symmetry, algorithm assumes graph directed). one graph component, matrix representation spatial weights can become block-diagonal observations appropriately sorted.","code":"coords <- coordinates(Syracuse) IDs <- row.names(as(Syracuse, \"data.frame\")) #FIXME library(tripack) Sy4_nb <- tri2nb(coords, row.names=IDs) if (require(dbscan, quietly=TRUE)) { Sy5_nb <- graph2nb(soi.graph(Sy4_nb, coords), row.names=IDs) } else Sy5_nb <- NULL ## ## Attaching package: 'dbscan' ## The following object is masked from 'package:stats': ## ## as.dendrogram Sy6_nb <- graph2nb(gabrielneigh(coords), row.names=IDs) Sy7_nb <- graph2nb(relativeneigh(coords), row.names=IDs) oopar <- par(mfrow=c(2,2), mar=c(1,1,1,1)+0.1) plot(Syracuse, border=\"grey60\") plot(Sy4_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"a)\", cex=0.8) plot(Syracuse, border=\"grey60\") if (!is.null(Sy5_nb)) { plot(Sy5_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"b)\", cex=0.8) } plot(Syracuse, border=\"grey60\") plot(Sy6_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"c)\", cex=0.8) plot(Syracuse, border=\"grey60\") plot(Sy7_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"d)\", cex=0.8) par(oopar) nb_l <- list(Triangulation=Sy4_nb, Gabriel=Sy6_nb, Relative=Sy7_nb) if (!is.null(Sy5_nb)) nb_l <- c(nb_l, list(SOI=Sy5_nb)) sapply(nb_l, function(x) is.symmetric.nb(x, verbose=FALSE, force=TRUE)) ## Triangulation Gabriel Relative SOI ## TRUE FALSE FALSE TRUE sapply(nb_l, function(x) n.comp.nb(x)$nc) ## Triangulation Gabriel Relative SOI ## 1 1 1 1"},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"distance-based-neighbours","dir":"Articles","previous_headings":"Creating Neighbours","what":"Distance-Based Neighbours","title":"Creating Neighbours","text":"alternative method choose kk nearest points neighbours – adapts across study area, taking account differences densities areal entities. Naturally, overwhelming majority cases, leads asymmetric neighbours, ensure areas kk neighbours. knearneigh() function returns intermediate form converted nb object knn2nb(); knearneigh() can also take longlat= argument handle geographical coordinates. : k=1k=1 neighbours; b: k=2k=2 neighbours; c: k=4k=4 neighbours figure shows neighbour relationships k=1,2,4k= 1, 2, 4, many components k=1k=1. need , kk-nearest neighbour objects can made symmetrical using make.sym.nb() function. k=1k=1 object also useful finding minimum distance areas distance-based neighbour. Using nbdists() function, can calculate list vectors distances corresponding neighbour object, first nearest neighbours. greatest value minimum distance needed make sure areas linked least one neighbour. dnearneigh() function used find neighbours interpoint distance, arguments d1 d2 setting lower upper distance bounds; can also take longlat argument handle geographical coordinates. : Neighbours within 1,158m; b: neighbours within 1,545m; c: neighbours within 2,317m figure shows numbers distance-based neighbours increase moderate increases distance. Moving 0.750.75 times minimum -included distance, -included distance, 1.51.5 times minimum -included distance, numbers links grow rapidly. major problem first nearest neighbour distances study area much larger others, since avoid -neighbour areal entities, distance criterion need set many areas many neighbours. Distance-based neighbours: frequencies numbers neighbours census tract figure shows counts sizes sets neighbours three different distance limits. Syracuse, census tracts similar areas, try use distance-based neighbour criterion eight-county study area, smallest distance securing least one neighbour every areal entity 38km. areal entities approximately regularly spaced, using distance-based neighbours necessarily problem. Provided care taken handle side effects “weighting” areas analysis, using lists neighbours -neighbour areas necessarily problem either, certainly raise questions. Different disciplines handle definition neighbours ways convention; particular, seems ecologists frequently use distance bands. many distance bands used, approach variogram, although underlying understanding spatial autocorrelation seems contagion rather continuous.","code":"Sy8_nb <- knn2nb(knearneigh(coords, k=1), row.names=IDs) ## Warning in knn2nb(knearneigh(coords, k = 1), row.names = IDs): neighbour object ## has 15 sub-graphs Sy9_nb <- knn2nb(knearneigh(coords, k=2), row.names=IDs) Sy10_nb <- knn2nb(knearneigh(coords, k=4), row.names=IDs) nb_l <- list(k1=Sy8_nb, k2=Sy9_nb, k4=Sy10_nb) sapply(nb_l, function(x) is.symmetric.nb(x, verbose=FALSE, force=TRUE)) ## k1 k2 k4 ## FALSE FALSE FALSE sapply(nb_l, function(x) n.comp.nb(x)$nc) ## k1 k2 k4 ## 15 1 1 oopar <- par(mfrow=c(1,3), mar=c(1,1,1,1)+0.1) plot(Syracuse, border=\"grey60\") plot(Sy8_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"a)\", cex=0.8) plot(Syracuse, border=\"grey60\") plot(Sy9_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"b)\", cex=0.8) plot(Syracuse, border=\"grey60\") plot(Sy10_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"c)\", cex=0.8) par(oopar) dsts <- unlist(nbdists(Sy8_nb, coords)) summary(dsts) ## Min. 1st Qu. Median Mean 3rd Qu. Max. ## 395.7 587.3 700.1 760.4 906.1 1544.6 max_1nn <- max(dsts) max_1nn ## [1] 1544.615 Sy11_nb <- dnearneigh(coords, d1=0, d2=0.75*max_1nn, row.names=IDs) ## Warning in dnearneigh(coords, d1 = 0, d2 = 0.75 * max_1nn, row.names = IDs): ## neighbour object has 4 sub-graphs Sy12_nb <- dnearneigh(coords, d1=0, d2=1*max_1nn, row.names=IDs) Sy13_nb <- dnearneigh(coords, d1=0, d2=1.5*max_1nn, row.names=IDs) nb_l <- list(d1=Sy11_nb, d2=Sy12_nb, d3=Sy13_nb) sapply(nb_l, function(x) is.symmetric.nb(x, verbose=FALSE, force=TRUE)) ## d1 d2 d3 ## TRUE TRUE TRUE sapply(nb_l, function(x) n.comp.nb(x)$nc) ## d1 d2 d3 ## 4 1 1 oopar <- par(mfrow=c(1,3), mar=c(1,1,1,1)+0.1) plot(Syracuse, border=\"grey60\") plot(Sy11_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"a)\", cex=0.8) plot(Syracuse, border=\"grey60\") plot(Sy12_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"b)\", cex=0.8) plot(Syracuse, border=\"grey60\") plot(Sy13_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"c)\", cex=0.8) par(oopar) dS <- c(0.75, 1, 1.5)*max_1nn res <- sapply(nb_l, function(x) table(card(x))) mx <- max(card(Sy13_nb)) res1 <- matrix(0, ncol=(mx+1), nrow=3) rownames(res1) <- names(res) colnames(res1) <- as.character(0:mx) res1[1, names(res$d1)] <- res$d1 res1[2, names(res$d2)] <- res$d2 res1[3, names(res$d3)] <- res$d3 library(RColorBrewer) pal <- grey.colors(3, 0.95, 0.55, 2.2) # RSB quietening greys barplot(res1, col=pal, beside=TRUE, legend.text=FALSE, xlab=\"numbers of neighbours\", ylab=\"tracts\") legend(\"topright\", legend=format(dS, digits=1), fill=pal, bty=\"n\", cex=0.8, title=\"max. distance\") dsts0 <- unlist(nbdists(NY_nb, coordinates(NY8))) summary(dsts0) ## Min. 1st Qu. Median Mean 3rd Qu. Max. ## 82.7 1505.0 3378.7 5865.8 8954.3 38438.1"},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"higher-order-neighbours","dir":"Articles","previous_headings":"Creating Neighbours","what":"Higher-Order Neighbours","title":"Creating Neighbours","text":"Distance bands can generated using sequence d1 d2 argument values dnearneigh() function needed construct spatial autocorrelogram understood ecology. conventions, correlograms constructed taking input list neighbours first-order sets, stepping across graph second-, third-, higher-order neighbours based number links traversed, permitting cycles, risk making ii neighbour ii (O’Sullivan Unwin 2003). nblag() function takes existing neighbour list returns list lists, first maxlag= order neighbours. shows wave connectedness graph spreads third order, receding eighth order, dying away ninth order - tracts nine steps graph. distance bands graph step order approaches spreading neighbourhoods can used examine shape relationship intensities space, like variogram, can used attempting look effects scale.","code":"Sy0_nb_lags <- nblag(Sy0_nb, maxlag=9) ## Warning in nblag(Sy0_nb, maxlag = 9): lag 6 neighbour object has 7 sub-graphs ## Warning in nblag(Sy0_nb, maxlag = 9): lag 7 neighbour object has 22 sub-graphs ## Warning in nblag(Sy0_nb, maxlag = 9): lag 8 neighbour object has 52 sub-graphs ## Warning in nblag(Sy0_nb, maxlag = 9): lag 9 neighbour object has 63 sub-graphs names(Sy0_nb_lags) <- c(\"first\", \"second\", \"third\", \"fourth\", \"fifth\", \"sixth\", \"seventh\", \"eighth\", \"ninth\") res <- sapply(Sy0_nb_lags, function(x) table(card(x))) mx <- max(unlist(sapply(Sy0_nb_lags, function(x) card(x)))) nn <- length(Sy0_nb_lags) res1 <- matrix(0, ncol=(mx+1), nrow=nn) rownames(res1) <- names(res) colnames(res1) <- as.character(0:mx) for (i in 1:nn) res1[i, names(res[[i]])] <- res[[i]] res1 ## 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 ## first 0 1 1 5 9 14 17 9 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ## second 0 0 0 0 2 2 0 6 6 11 11 4 3 7 4 6 1 0 0 0 0 0 0 0 0 ## third 0 0 0 0 0 0 0 1 3 5 5 7 14 6 8 3 3 0 1 1 1 3 1 0 1 ## fourth 0 0 0 0 0 0 0 0 1 3 5 7 16 16 5 3 3 2 0 1 1 0 0 0 0 ## fifth 0 0 0 1 1 3 1 1 3 7 13 12 8 9 3 1 0 0 0 0 0 0 0 0 0 ## sixth 6 3 0 2 8 2 5 5 4 8 9 5 5 1 0 0 0 0 0 0 0 0 0 0 0 ## seventh 21 7 4 5 9 7 3 5 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ## eighth 49 6 5 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ## ninth 63 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0"},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"grid-neighbours","dir":"Articles","previous_headings":"Creating Neighbours","what":"Grid Neighbours","title":"Creating Neighbours","text":"data known arranged regular, rectangular grid, cell2nb() function can used construct neighbour lists, including torus. useful simulations, , since areal entities equal numbers neighbours, edges, structure graph neutral can achieved. Neighbours can either type rook queen. regular, rectangular grid complete, can use knowledge cell size stored grid topology create appropriate list neighbours, using tightly bounded distance criterion. Neighbour lists kind commonly found ecological assays, studies species richness national continental scale. also settings, moderately large nn, n=3n=3,103, use sparse, list based representation shows strength. Handling 281×281281 \\times 281 matrix eight-county census tracts feasible, easy 63×6363 \\times 63 matrix Syracuse census tracts, demanding 3,103×3103 \\times 3,103 matrix.","code":"cell2nb(7, 7, type=\"rook\", torus=TRUE) ## Neighbour list object: ## Number of regions: 49 ## Number of nonzero links: 196 ## Percentage nonzero weights: 8.163265 ## Average number of links: 4 cell2nb(7, 7, type=\"rook\", torus=FALSE) ## Neighbour list object: ## Number of regions: 49 ## Number of nonzero links: 168 ## Percentage nonzero weights: 6.997085 ## Average number of links: 3.428571 data(meuse.grid) coordinates(meuse.grid) <- c(\"x\", \"y\") gridded(meuse.grid) <- TRUE dst <- max(slot(slot(meuse.grid, \"grid\"), \"cellsize\")) mg_nb <- dnearneigh(coordinates(meuse.grid), 0, dst) mg_nb ## Neighbour list object: ## Number of regions: 3103 ## Number of nonzero links: 12022 ## Percentage nonzero weights: 0.1248571 ## Average number of links: 3.874315 table(card(mg_nb)) ## ## 1 2 3 4 ## 1 133 121 2848"},{"path":[]},{"path":[]},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"introduction","dir":"Articles","previous_headings":"Creating Neighbours using sf objects","what":"Introduction","title":"Creating Neighbours using sf objects","text":"vignette tracks legacy nb vignette, based part first (2008) edition ASDAR. adds hints code nb vignette use sf vector representation instead sp vector representation create neighbour objects. .","code":""},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"summary","dir":"Articles","previous_headings":"Creating Neighbours using sf objects","what":"Summary","title":"Creating Neighbours using sf objects","text":"summary results : general, need reproduce results using \"Spatial\" objects spdep, coerce sf objects sp objects constructing neighbour objects (particularly polygon centroids used point representation). However, new work, use \"sf\" objects read using sf. spdep 1.1-7, number steps taken choose efficient approaches especially larger data sets, using functions sf approximate nearest neighbour (ANN) implementation dbscan rather RANN.","code":""},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"data-set","dir":"Articles","previous_headings":"Creating Neighbours using sf objects","what":"Data set","title":"Creating Neighbours using sf objects","text":"’ll use whole NY 8 county set boundaries, challenge implementations just Syracuse subset. description input geometries ADSAR : New York leukemia: used documented extensively Waller Gotway (2004) data formerly made available Chap. 9 http://web1.sph.emory.edu/users/lwaller/ch9index.htm; data import process described help file NY_data spData; geometries downloaded CIESIN server formerly sedac.ciesin.columbia.edu/data/set/acrp-boundary-1992/data-download, now possibly earthdata.nasa.gov/data/catalog/sedac-ciesin-sedac-acrp-1992-bf-1.00, file /pub/census/usa/tiger/ny/bna_st/t8_36.zip, extensively edited; zip archive NY_data.zip shapefiles GAL format neighbours list book website. , zipfile now new location requiring login. object listw_NY directly imported nyadjwts.dbf Waller & Gotway (2004) chapter 9 website. version New York 8 counties geometries used ASDAR included shapefile spdep converted original BNA file using external utility program convert MapInfo format converted using GDAL 1.4.1 (OGR BNA driver available; entered OGR 1.5.0, release end 2007), contains invalid geometries. found mid-2007 included villages /excluded -umbilical cords boundary enclosing tract, underlying BNA file first converted MapInfo (holes exist ). use GPKG file created follows (rgdal also used output; GDAL prior GDAL 3.3 built GEOS, BNA vector driver use geometry tests: BNA driver supports reading polygons holes lakes. determines hole lake geometrical analysis (inclusion, non-intersection tests) ignores completely notion polygon winding (whether polygon edges described clockwise counter-clockwise). GDAL must built GEOS enabled make geometry test work.):","code":"library(sf) sf_bna <- st_read(\"t8_36.bna\", stringsAsFactors=FALSE) table(st_is_valid(sf_bna)) sf_bna$AREAKEY <- gsub(\"\\\\.\", \"\", sf_bna$Primary.ID) data(NY_data, package=\"spData\") key <- as.character(nydata$AREAKEY) sf_bna1 <- sf_bna[match(key, sf_bna$AREAKEY), c(\"AREAKEY\")] sf_bna2 <- merge(sf_bna1, nydata, by=\"AREAKEY\") sf_bna2_utm18 <- st_transform(sf_bna2, \"+proj=utm +zone=18 +datum=NAD27\") st_write(sf_bna2_utm18, \"NY8_bna_utm18.gpkg\")"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"nb-and-listw-objects-copied-from-the-nb_igraph-vignette","dir":"Articles","previous_headings":"Creating Neighbours using sf objects","what":"nb and listw objects (copied from the nb_igraph vignette)","title":"Creating Neighbours using sf objects","text":"Since spdep package created, spatial weights objects constructed lists three components attributes, old-style class listw objects. first component listw object nb object, list n integer vectors, least character vector region.id attribute n unique values (like row.names data.frame object); n number spatial entities. Component list contains integer identifiers neighbours sorted vector duplication values 1:n; neighbours, component vector length 1 value 0L. nb object may contain attribute indicating whether symmetric , whether neighbour j implies j neighbour . neighbour definitions symmetric construction, contiguities distance thresholds, others asymmetric, k-nearest neighbours. nb object redundantly stores -j j-links. second component listw object list n numeric vectors, length corresponding non-zero vectors nbobject. give values spatial weights -j neighbour pair. often case neighbours symmetric construction, weights , example weights row-standardised dividing row input weights count neighbours cardinality neighbour set . nb2listwfunction, also possible pass general weights, inverse distances, shares boundary lengths . third component listw object records style weights character code, \"B\" binary weights taking values zero one (one recorded), \"W\" row-standardised weights, . order subset listw objects, knowledge style may necessary.","code":""},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"comparison-of-sp-and-sf-approaches","dir":"Articles","previous_headings":"Creating Neighbours using sf objects","what":"Comparison of sp and sf approaches","title":"Creating Neighbours using sf objects","text":"First housekeeping setup permit vignette built packages missing --date: Let us read GPKG file valid geometries ‘sf’ ‘sp’ objects:","code":"if (!suppressPackageStartupMessages(require(sf, quietly=TRUE))) { message(\"install the sf package\") dothis <- FALSE } if (dothis) sf_extSoftVersion() ## GEOS GDAL proj.4 GDAL_with_GEOS USE_PROJ_H ## \"3.13.1\" \"3.11.0\" \"9.6.2\" \"true\" \"true\" ## PROJ ## \"9.6.2\" NY8_sf <- st_read(system.file(\"shapes/NY8_bna_utm18.gpkg\", package=\"spData\"), quiet=TRUE) table(st_is_valid(NY8_sf)) ## ## TRUE ## 281"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"contiguity-neighbours-for-polygon-support","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Comparison of sp and sf approaches","what":"Contiguity neighbours for polygon support","title":"Creating Neighbours using sf objects","text":"first generate queen contiguity nb object using legacy spdep approach. first either uses pre-computed list vectors probable neighbours finds intersecting bounding boxes internally. points boundaries set polygons making observation checked distance less snap points set polygons making observation included set candidate neighbours. contiguity symmetric, j contiguities tested. queen contiguity found soon one point matches, rook contiguity soon two points match: Using spatial indices check intersection polygons much faster legacy method poly2nb. spdep 1.1-7, use made GEOS sf find candidate neighbours foundInBox=NULL, default value. contiguity symmetric definition, foundInBox= requires intersections higher indices, leading slight overhead remove duplicates, st_intersects() reports j ans j relationships. st_intersects() report whether neighbours queen rook, step needed distinguish two cases. spdep::poly2nb uses two heuristics, first find candidate neighbours intersecting polygons (st_intersects()), second use symmetry relationship halve number remaining tests. means performance linear n, overhead identifying candidates, back-filling symmetric neighbours. , spdep::poly2nb() stops searching queen contiguity soon first neighbour point found within snap distance (identical, tested first); second neighbour point indicates rook contiguities. details alternatives spherical geometries, see section @ref(spher-poly2nb) .","code":"suppressPackageStartupMessages(library(spdep)) reps <- 10 eps <- sqrt(.Machine$double.eps) system.time(for(i in 1:reps) NY8_sf_1_nb <- poly2nb(NY8_sf, queen=TRUE, snap=eps))/reps ## user system elapsed ## 0.1957 0.0078 0.2045 NY8_sf_1_nb ## Neighbour list object: ## Number of regions: 281 ## Number of nonzero links: 1632 ## Percentage nonzero weights: 2.066843 ## Average number of links: 5.807829"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"contiguity-neighbours-from-invalid-polygons","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Comparison of sp and sf approaches","what":"Contiguity neighbours from invalid polygons","title":"Creating Neighbours using sf objects","text":"Next, explore possible source differences neighbour object reproduction, using original version tract boundaries used ASDAR, invalid geometries mentioned earlier (NY8_utm18.gpkg created original ESRI Shapefile used ASDAR): can see number differences neighbour sets derived fully valid geometries older partly invalid set: Using st_make_valid() make geometries valid: also see geometry type geometry column changes: checking \"sfg\" objects, two now objects different topological dimensions. can remedied using st_collection_extract() get polygon objects: However, making geometries valid, change geometries, new sets neighbours still differ made valid geometries ways imposing validity: neighbour sets old boundaries without imposing validity:","code":"if (packageVersion(\"spData\") >= \"2.3.2\") { NY8_sf_old <- sf::st_read(system.file(\"shapes/NY8_utm18.gpkg\", package=\"spData\")) } else { NY8_sf_old <- sf::st_read(system.file(\"shapes/NY8_utm18.shp\", package=\"spData\")) } ## Reading layer `NY8_utm18' from data source ## `/home/rsb/lib/r_libs/spData/shapes/NY8_utm18.gpkg' using driver `GPKG' ## Simple feature collection with 281 features and 17 fields ## Geometry type: POLYGON ## Dimension: XY ## Bounding box: xmin: 358241.9 ymin: 4649755 xmax: 480393.1 ymax: 4808545 ## Projected CRS: WGS 84 / UTM zone 18N table(st_is_valid(NY8_sf_old)) ## ## FALSE TRUE ## 5 276 try(NY8_sf_old_1_nb <- poly2nb(NY8_sf_old), silent = TRUE) all.equal(NY8_sf_old_1_nb, NY8_sf_1_nb, check.attributes=FALSE) ## [1] \"Component 57: Numeric: lengths (4, 5) differ\" ## [2] \"Component 58: Numeric: lengths (5, 6) differ\" ## [3] \"Component 66: Numeric: lengths (7, 11) differ\" ## [4] \"Component 73: Numeric: lengths (4, 5) differ\" ## [5] \"Component 260: Numeric: lengths (8, 9) differ\" NY8_sf_old_val <- st_make_valid(NY8_sf_old, dist=0) table(st_is_valid(NY8_sf_old_val)) ## ## TRUE ## 281 class(st_geometry(NY8_sf_old)) ## [1] \"sfc_POLYGON\" \"sfc\" class(st_geometry(NY8_sf_old_val)) ## [1] \"sfc_GEOMETRY\" \"sfc\" table(sapply(st_geometry(NY8_sf_old_val), function(x) class(x)[[2]])) ## ## MULTIPOLYGON POLYGON ## 3 278 NY8_sf_old_val <- st_collection_extract(NY8_sf_old_val, \"POLYGON\") table(sapply(st_geometry(NY8_sf_old_val), function(x) class(x)[[2]])) ## ## MULTIPOLYGON ## 281 try(NY8_sf_old_1_nb_val <- poly2nb(NY8_sf_old_val), silent = TRUE) all.equal(NY8_sf_old_1_nb_val, NY8_sf_1_nb, check.attributes=FALSE) ## [1] \"Component 57: Numeric: lengths (4, 5) differ\" ## [2] \"Component 58: Numeric: lengths (5, 6) differ\" ## [3] \"Component 66: Numeric: lengths (7, 11) differ\" ## [4] \"Component 73: Numeric: lengths (4, 5) differ\" ## [5] \"Component 260: Numeric: lengths (8, 9) differ\" all.equal(NY8_sf_old_1_nb_val, NY8_sf_old_1_nb, check.attributes=FALSE) ## [1] TRUE"},{"path":[]},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"finding-points-for-polygon-objects","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Planar point-based neighbours","what":"Finding points for polygon objects","title":"Creating Neighbours using sf objects","text":"knearneigh() dnearneigh() require point support, decisions must taken place point areal object. can use st_centroid() get centroids, using of_largest_polygon=TRUE argument make sure centroid largest polygon id observation made one external ring: st_point_on_surface() guarantees point fall surface member polygon: indeed taking centre largest inscribed circle (function returns radius line segment, choose central point, point circle): need check whether coordinates planar :","code":"NY8_ct_sf <- st_centroid(st_geometry(NY8_sf), of_largest_polygon=TRUE) NY8_pos_sf <- st_point_on_surface(st_geometry(NY8_sf)) if (unname(sf_extSoftVersion()[\"GEOS\"] >= \"3.9.0\")) NY8_cic_sf <- st_cast(st_inscribed_circle(st_geometry(NY8_sf), nQuadSegs=0), \"POINT\")[(1:(2*nrow(NY8_sf)) %% 2) != 0] st_is_longlat(NY8_ct_sf) ## [1] FALSE"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"graph-based-neighbours","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Planar point-based neighbours","what":"Graph-based neighbours","title":"Creating Neighbours using sf objects","text":", can check graph-based neighbours (planar coordinates ):","code":"suppressPackageStartupMessages(require(deldir)) NY84_nb <- tri2nb(NY8_ct_sf) if (require(dbscan, quietly=TRUE)) { NY85_nb <- graph2nb(soi.graph(NY84_nb, NY8_ct_sf)) } else NY85_nb <- NULL ## ## Attaching package: 'dbscan' ## The following object is masked from 'package:stats': ## ## as.dendrogram ## Warning in graph2nb(soi.graph(NY84_nb, NY8_ct_sf)): neighbour object has 2 ## sub-graphs NY86_nb <- graph2nb(gabrielneigh(NY8_ct_sf)) NY87_nb <- graph2nb(relativeneigh(NY8_ct_sf))"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"k-nearest-neighbours","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Planar point-based neighbours","what":"K-nearest neighbours","title":"Creating Neighbours using sf objects","text":"K-nearest neighbours use coordinate matrices, can handle Great Circle distances, demonstrated , data set used planar, case dbscan::kNN() 2D 3D building kd-tree used: Legacy code may used omitting kd-tree:","code":"system.time(for (i in 1:reps) suppressWarnings(NY88_nb_sf <- knn2nb(knearneigh(NY8_ct_sf, k=1))))/reps ## user system elapsed ## 0.0277 0.0012 0.0289 system.time(for (i in 1:reps) suppressWarnings(NY89_nb_sf <- knn2nb(knearneigh(NY8_ct_sf, k=1, use_kd_tree=FALSE))))/reps ## user system elapsed ## 0.0280 0.0010 0.0291"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"distance-neighbours","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Planar point-based neighbours","what":"Distance neighbours","title":"Creating Neighbours using sf objects","text":"Distance neighbours need threshold - nbdists shows maximum distance first nearest neighbour: dnearneigh can also handle Great Circle distances, demonstrated , data set used planar: default, function uses dbscan::frNN() build kd-tree 2D 3D used find distance neighbours. small n, argument use_kd_tree=FALSE may speed computation little reverting legacy code building kd-tree first, general differences small user notice:","code":"dsts <- unlist(nbdists(NY88_nb_sf, NY8_ct_sf)) summary(dsts) ## Min. 1st Qu. Median Mean 3rd Qu. Max. ## 82.85 912.85 1801.11 3441.04 4461.26 17033.11 max_1nn <- max(dsts) system.time(for (i in 1:reps) suppressWarnings(NY810_nb <- dnearneigh(NY8_ct_sf, d1=0, d2=0.75*max_1nn)))/reps ## user system elapsed ## 0.0683 0.0003 0.0690 system.time(for (i in 1:reps) suppressWarnings(NY811_nb <- dnearneigh(NY8_ct_sf, d1=0, d2=0.75*max_1nn, use_kd_tree=FALSE)))/reps ## user system elapsed ## 0.0522 0.0007 0.0531"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"spherical-point-based-neighbours","dir":"Articles","previous_headings":"Creating Neighbours using sf objects","what":"Spherical point-based neighbours","title":"Creating Neighbours using sf objects","text":"Spherical point-based neighbours may found using Great Circle distances. used many years, switch sf 1.0-0 use s2 default opened new opportunities spatial indexing sphere may help.","code":"pts_ll <- st_transform(NY8_ct_sf, \"OGC:CRS84\") st_is_longlat(pts_ll) ## [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"k-nearest-neighbours-1","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Spherical point-based neighbours","what":"K-nearest neighbours","title":"Creating Neighbours using sf objects","text":"input geometries geographical coordinates, sf_use_s2() TRUE, knearneigh() use spatially indexed points s2::s2_closest_edges() (see https://github.com/r-spatial/s2/issues/125#issuecomment-860107442) performs well also larger data sets: smaller data set, legacy approach without spatial indexing adequate, slows number observations increases: WGS84 ellipsoid Great Circle distances differ little s2 spherical distances, yielding output diverges two tract centroids:","code":"(old_use_s2 <- sf_use_s2()) ## [1] TRUE sf_use_s2(TRUE) system.time(for (i in 1:reps) pts_ll1_nb <- knn2nb(knearneigh(pts_ll, k=6)))/reps ## user system elapsed ## 0.0428 0.0001 0.0431 sf_use_s2(FALSE) ## Spherical geometry (s2) switched off system.time(for (i in 1:reps) pts_ll2_nb <- knn2nb(knearneigh(pts_ll, k=6)))/reps ## user system elapsed ## 0.0301 0.0000 0.0301 all.equal(pts_ll1_nb, pts_ll2_nb, check.attributes=FALSE) ## [1] \"Component 52: Mean relative difference: 1.466667\" ## [2] \"Component 124: Mean relative difference: 0.0251046\" pts_ll1_nb[[52]] ## [1] 15 38 48 49 50 53 pts_ll2_nb[[52]] ## [1] 37 38 48 49 50 53 pts_ll1_nb[[124]] ## [1] 117 122 123 125 133 134 pts_ll2_nb[[124]] ## [1] 116 117 123 125 133 134 sf_use_s2(old_use_s2) ## Spherical geometry (s2) switched on"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"distance-neighbours-1","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Spherical point-based neighbours","what":"Distance neighbours","title":"Creating Neighbours using sf objects","text":"Distance neighbours problematic. nbdists() works well s2 spherical coordinates, none tried adaptations dnearneigh() work adequately yet. argument use_s2= set TRUE s2 > 1.0-7, using s2::s2_closest_edges() legacy brute-force approach, calculating distances j copying j symmetry. distance metric alway \"km\". permit s2 methods run, without arguments set, s2 > 1.0-7, s2::s2_dwithin_matrix() run: Alternatively, spherical distances can used dwithin=FALSE s2::s2_closest_edges(); although running similar time, s2::s2_closest_edges() depends additional k= argument, , mis-set, may miss valid neighbours: Using s2::s2_closest_edges() respects d1 > 0 without requiring second pass R, faster s2::s2_dwithin_matrix(): Using s2::s2_dwithin_matrix() requires second pass, one lower bound, another upper bound, set difference operation find neighbours distance band: Setting use_s2=FALSE falls back legacy version, uses symmetry reduce time: Minor differences may occur legacy ellipsoid s2 spherical approaches:","code":"max_1nn_ll <- max(unlist(nbdists(knn2nb(knearneigh(pts_ll, k=1)), pts_ll))) ## Warning in knn2nb(knearneigh(pts_ll, k = 1)): neighbour object has 62 ## sub-graphs args(dnearneigh) ## function (x, d1, d2, row.names = NULL, longlat = NULL, bounds = c(\"GE\", ## \"LE\"), use_kd_tree = TRUE, symtest = FALSE, use_s2 = packageVersion(\"s2\") > ## \"1.0.7\", k = 200, dwithin = TRUE) ## NULL if (packageVersion(\"s2\") > \"1.0.7\") { system.time(for (i in 1:(reps/5)) suppressWarnings(pts_ll3_nb <- dnearneigh(pts_ll, d1=0, d2=0.75*max_1nn_ll)))/(reps/5) } ## user system elapsed ## 0.0820 0.0000 0.0825 system.time(for (i in 1:(reps/5)) suppressWarnings(pts_ll5_nb <- dnearneigh(pts_ll, d1=0, d2=0.75*max_1nn_ll, dwithin=FALSE)))/(reps/5) ## user system elapsed ## 0.0700 0.0005 0.0710 if (packageVersion(\"s2\") > \"1.0.7\") all.equal(pts_ll3_nb, pts_ll5_nb, check.attributes=FALSE) ## [1] TRUE if (packageVersion(\"s2\") > \"1.0.7\") { system.time(for (i in 1:(reps/5)) suppressWarnings(pts_ll3a_nb <- dnearneigh(pts_ll, d1=5, d2=0.75*max_1nn_ll, dwithin=FALSE)))/(reps/5) } ## user system elapsed ## 0.0610 0.0000 0.0615 if (packageVersion(\"s2\") > \"1.0.7\") { system.time(for (i in 1:(reps/5)) suppressWarnings(pts_ll5a_nb <- dnearneigh(pts_ll, d1=5, d2=0.75*max_1nn_ll)))/(reps/5) } ## user system elapsed ## 0.1075 0.0000 0.1080 if (packageVersion(\"s2\") > \"1.0.7\") all.equal(pts_ll3a_nb, pts_ll5a_nb, check.attributes=FALSE) ## [1] TRUE system.time(for (i in 1:reps) suppressWarnings(pts_ll6_nb <- dnearneigh(pts_ll, d1=0, d2=0.75*max_1nn_ll, use_s2=FALSE)))/reps ## user system elapsed ## 0.0400 0.0000 0.0402 all.equal(pts_ll5_nb, pts_ll6_nb, check.attributes=FALSE) ## [1] \"Component 20: Numeric: lengths (6, 5) differ\" ## [2] \"Component 28: Numeric: lengths (7, 6) differ\" ## [3] \"Component 112: Numeric: lengths (109, 108) differ\" ## [4] \"Component 116: Numeric: lengths (109, 108) differ\" ## [5] \"Component 122: Numeric: lengths (105, 106) differ\" ## [6] \"Component 123: Numeric: lengths (108, 107) differ\" ## [7] \"Component 130: Numeric: lengths (108, 109) differ\" ## [8] \"Component 134: Numeric: lengths (106, 105) differ\" ## [9] \"Component 158: Numeric: lengths (101, 102) differ\" ## [10] \"Component 165: Numeric: lengths (101, 102) differ\" ## [11] \"Component 168: Numeric: lengths (101, 102) differ\" ## [12] \"Component 179: Numeric: lengths (89, 90) differ\" ## [13] \"Component 180: Numeric: lengths (96, 97) differ\" ## [14] \"Component 188: Numeric: lengths (46, 47) differ\" ## [15] \"Component 189: Numeric: lengths (55, 56) differ\" ## [16] \"Component 196: Numeric: lengths (47, 46) differ\" ## [17] \"Component 210: Numeric: lengths (106, 104) differ\" ## [18] \"Component 226: Numeric: lengths (88, 87) differ\" ## [19] \"Component 229: Numeric: lengths (55, 53) differ\" ## [20] \"Component 235: Numeric: lengths (40, 39) differ\" ## [21] \"Component 237: Numeric: lengths (14, 15) differ\" ## [22] \"Component 245: Numeric: lengths (16, 15) differ\" system.time(for (i in 1:reps) suppressWarnings(pts_ll6a_nb <- dnearneigh(pts_ll, d1=5, d2=0.75*max_1nn_ll, use_s2=FALSE)))/reps ## user system elapsed ## 0.0319 0.0000 0.0319 if (packageVersion(\"s2\") > \"1.0.7\") all.equal(pts_ll5a_nb, pts_ll6a_nb, check.attributes=FALSE) ## [1] \"Component 20: Numeric: lengths (6, 5) differ\" ## [2] \"Component 28: Numeric: lengths (7, 6) differ\" ## [3] \"Component 112: Numeric: lengths (62, 61) differ\" ## [4] \"Component 113: Numeric: lengths (62, 63) differ\" ## [5] \"Component 116: Numeric: lengths (56, 55) differ\" ## [6] \"Component 119: Numeric: lengths (68, 69) differ\" ## [7] \"Component 122: Numeric: lengths (43, 44) differ\" ## [8] \"Component 123: Numeric: lengths (50, 49) differ\" ## [9] \"Component 128: Numeric: lengths (65, 64) differ\" ## [10] \"Component 130: Numeric: lengths (61, 63) differ\" ## [11] \"Component 132: Numeric: lengths (45, 46) differ\" ## [12] \"Component 134: Numeric: lengths (46, 45) differ\" ## [13] \"Component 136: Numeric: lengths (61, 62) differ\" ## [14] \"Component 147: Numeric: lengths (50, 51) differ\" ## [15] \"Component 154: Numeric: lengths (56, 57) differ\" ## [16] \"Component 158: Numeric: lengths (49, 50) differ\" ## [17] \"Component 165: Mean relative difference: 0.02823018\" ## [18] \"Component 168: Numeric: lengths (54, 56) differ\" ## [19] \"Component 179: Numeric: lengths (77, 78) differ\" ## [20] \"Component 180: Numeric: lengths (85, 86) differ\" ## [21] \"Component 188: Numeric: lengths (39, 40) differ\" ## [22] \"Component 189: Numeric: lengths (48, 49) differ\" ## [23] \"Component 196: Numeric: lengths (45, 44) differ\" ## [24] \"Component 210: Numeric: lengths (68, 66) differ\" ## [25] \"Component 226: Numeric: lengths (82, 81) differ\" ## [26] \"Component 229: Numeric: lengths (48, 46) differ\" ## [27] \"Component 235: Numeric: lengths (38, 37) differ\" ## [28] \"Component 237: Numeric: lengths (14, 15) differ\" ## [29] \"Component 245: Numeric: lengths (15, 14) differ\""},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"spher-poly2nb","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Spherical point-based neighbours","what":"Contiguity neighbours for spherical polygon support","title":"Creating Neighbours using sf objects","text":"also turns sf functions used find contiguity neighbours, s2 spatial indexing functionality accessed finding candidate neighbours intersecting geometries. timings little slower st_intersects() hands geometry predicates s2_intersects_matrix(), results , spatial indexing used, scales well larger data sets:","code":"NY8_sf_ll <- st_transform(NY8_sf, \"OGC:CRS84\") st_is_longlat(NY8_sf_ll) ## [1] TRUE sf_use_s2(TRUE) system.time(for (i in 1:reps) NY8_sf_1_nb_ll <- poly2nb(NY8_sf_ll, queen=TRUE, snap=eps))/reps ## user system elapsed ## 0.1759 0.0029 0.1794 all.equal(NY8_sf_1_nb, NY8_sf_1_nb_ll, check.attributes=FALSE) ## [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/articles/sids.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Introduction to the North Carolina SIDS data set (re-revised)","text":"data set presented first Symons, Grimson, Yuan (1983), analysed reference spatial nature data Cressie Read (1985), expanded Cressie Chan (1989), used detail Cressie (1991). 100 counties North Carolina, includes counts numbers live births (also non-white live births) numbers sudden infant deaths, July 1, 1974 June 30, 1978 July 1, 1979 June 30, 1984 periods. Cressie Read (1985), listing county neighbours based shared boundaries (contiguity) given, Cressie Chan (1989), Cressie (1991, 386–89), different listing based criterion distance county seats, cutoff 30 miles. county seat location coordinates given miles local (unknown) coordinate reference system. data also used exemplify range functions spatial statistics module user’s manual (Kaluzny et al. 1996).","code":""},{"path":"https://r-spatial.github.io/spdep/articles/sids.html","id":"getting-the-data-into-r","dir":"Articles","previous_headings":"","what":"Getting the data into R","title":"Introduction to the North Carolina SIDS data set (re-revised)","text":"using spdep spreg packages, version: spdep, version 1.3-13, 2025-06-10, sf package tmap package. data sources referred documented help page nc.sids data set spData. actual data, included shapefile county boundaries North Carolina made available maptools package 1. data known geographical coordinates (longitude-latitude decimal degrees) assumed use NAD27 datum. ESRI Shapefile deprecated, replaced GeoPackage, written reading original files spData 2.3.1: shapefile format presupposed three files extensions .shp, .shx, .dbf, first contains geometry data, second spatial index, third attribute data. required name apart extension, read using sf::st_read() sf object nc; class defined sf. centroids largest polygon county available using st_centroid method sf sfc POINT object, can used place labels extraction coordinate matrix: can examine names columns data frame see contains — fact columns examining , others useful cleaning data set. Let’s check different versions data - sf spData NC SIDS files, GeoDa Center two forms: actual CRS unknown, GeoPackage spData version updated \"EPSG:4267\". Next, geometries ? sf::st_equals returns logical matrix, ’ll check diagonal values TRUE, values TRUE summing recalling n 100: Next, let’s download GeoDa files repeat comparisons: looks though external files assuming WGS84/NAD83 datum, also contain geometries. Now contents files - sids2 also contains rates, file spData contains coordinates given Cressie (1991), parcels contiguous counties p. 554, aggregations used median polishing. spData data set columns reordered surprise: difference NWBIR74: spData follows Cressie (1991) sf Geoda follow Cressie Chan (1989) NWBIR74 Chowan county. now examine data set reproduced Cressie collaborators, included spData (formerly spdep), add neighbour relationships used Cressie Chan (1989) background map graph shown Figure : Printing neighbour object shows neighbour list object, sparse structure — displayed matrix, 3.94% cells filled. Objects class nb contain list long number counties; component list vector index numbers neighbours county question, neighbours county region.id 37001 can retreived matching indices. information can obtained using summary() nb object. Finally, associate vector names neighbour list, row.names argument. names unique, data frame row names. neighbour list object records neighbours order relation list , neighbours list county region.id “37001” seventeenth, nineteenth, thirty-second, forty-first sixty-eighth list. can retreive codes looking region.id attribute. also note neighbour criterion generates two counties neighbours, Dare Hyde, whose county seats 30 miles nearest neighbours. card() function returns cardinality neighbour set. need return methods handling -neighbour objects later . also show new neighbours lists may constructed , compare literature.","code":"library(spdep) nc <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\")[1], quiet=TRUE) #st_crs(nc) <- \"EPSG:4267\" row.names(nc) <- as.character(nc$FIPSNO) sf_use_s2(TRUE) plot(st_geometry(nc), axes=TRUE) text(st_coordinates(st_centroid(st_geometry(nc), of_largest_polygon=TRUE)), label=nc$FIPSNO, cex=0.5) names(nc) ## [1] \"CNTY_ID\" \"AREA\" \"PERIMETER\" \"CNTY_\" \"NAME\" \"FIPS\" ## [7] \"FIPSNO\" \"CRESS_ID\" \"BIR74\" \"SID74\" \"NWBIR74\" \"BIR79\" ## [13] \"SID79\" \"NWBIR79\" \"east\" \"north\" \"x\" \"y\" ## [19] \"lon\" \"lat\" \"L_id\" \"M_id\" \"geom\" summary(nc) ## CNTY_ID AREA PERIMETER CNTY_ ## Min. :1825 Min. :0.0420 Min. :0.999 Min. :1825 ## 1st Qu.:1902 1st Qu.:0.0910 1st Qu.:1.324 1st Qu.:1902 ## Median :1982 Median :0.1205 Median :1.609 Median :1982 ## Mean :1986 Mean :0.1263 Mean :1.673 Mean :1986 ## 3rd Qu.:2067 3rd Qu.:0.1542 3rd Qu.:1.859 3rd Qu.:2067 ## Max. :2241 Max. :0.2410 Max. :3.640 Max. :2241 ## NAME FIPS FIPSNO CRESS_ID ## Length:100 Length:100 Min. :37001 Min. : 1.00 ## Class :character Class :character 1st Qu.:37050 1st Qu.: 25.75 ## Mode :character Mode :character Median :37100 Median : 50.50 ## Mean :37100 Mean : 50.50 ## 3rd Qu.:37150 3rd Qu.: 75.25 ## Max. :37199 Max. :100.00 ## BIR74 SID74 NWBIR74 BIR79 ## Min. : 248 Min. : 0.00 Min. : 1.0 Min. : 319 ## 1st Qu.: 1077 1st Qu.: 2.00 1st Qu.: 190.0 1st Qu.: 1336 ## Median : 2180 Median : 4.00 Median : 697.5 Median : 2636 ## Mean : 3300 Mean : 6.67 Mean :1051.0 Mean : 4224 ## 3rd Qu.: 3936 3rd Qu.: 8.25 3rd Qu.:1168.5 3rd Qu.: 4889 ## Max. :21588 Max. :44.00 Max. :8027.0 Max. :30757 ## SID79 NWBIR79 east north ## Min. : 0.00 Min. : 3.0 Min. : 19.0 Min. : 6.0 ## 1st Qu.: 2.00 1st Qu.: 250.5 1st Qu.:178.8 1st Qu.: 97.0 ## Median : 5.00 Median : 874.5 Median :285.0 Median :125.5 ## Mean : 8.36 Mean : 1352.8 Mean :271.3 Mean :122.1 ## 3rd Qu.:10.25 3rd Qu.: 1406.8 3rd Qu.:361.2 3rd Qu.:151.5 ## Max. :57.00 Max. :11631.0 Max. :482.0 Max. :182.0 ## x y lon lat ## Min. :-328.04 Min. :3757 Min. :-84.08 Min. :33.92 ## 1st Qu.: -60.55 1st Qu.:3920 1st Qu.:-81.20 1st Qu.:35.26 ## Median : 114.38 Median :3963 Median :-79.26 Median :35.68 ## Mean : 91.46 Mean :3953 Mean :-79.51 Mean :35.62 ## 3rd Qu.: 240.03 3rd Qu.:4000 3rd Qu.:-77.87 3rd Qu.:36.05 ## Max. : 439.65 Max. :4060 Max. :-75.67 Max. :36.52 ## L_id M_id geom ## Min. :1.00 Min. :1.00 MULTIPOLYGON :100 ## 1st Qu.:1.00 1st Qu.:2.00 epsg:4267 : 0 ## Median :2.00 Median :3.00 +proj=long...: 0 ## Mean :2.12 Mean :2.67 ## 3rd Qu.:3.00 3rd Qu.:3.25 ## Max. :4.00 Max. :4.00 library(sf) nc_sf <- st_read(system.file(\"shape/nc.shp\", package=\"sf\"), quiet=TRUE) st_crs(nc_sf) ## Coordinate Reference System: ## User input: NAD27 ## wkt: ## GEOGCRS[\"NAD27\", ## DATUM[\"North American Datum 1927\", ## ELLIPSOID[\"Clarke 1866\",6378206.4,294.978698213898, ## LENGTHUNIT[\"metre\",1]]], ## PRIMEM[\"Greenwich\",0, ## ANGLEUNIT[\"degree\",0.0174532925199433]], ## CS[ellipsoidal,2], ## AXIS[\"latitude\",north, ## ORDER[1], ## ANGLEUNIT[\"degree\",0.0174532925199433]], ## AXIS[\"longitude\",east, ## ORDER[2], ## ANGLEUNIT[\"degree\",0.0174532925199433]], ## ID[\"EPSG\",4267]] nc <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\"), quiet=TRUE) st_crs(nc) ## Coordinate Reference System: ## User input: NAD27 ## wkt: ## GEOGCRS[\"NAD27\", ## DATUM[\"North American Datum 1927\", ## ELLIPSOID[\"Clarke 1866\",6378206.4,294.978698213898, ## LENGTHUNIT[\"metre\",1]]], ## PRIMEM[\"Greenwich\",0, ## ANGLEUNIT[\"degree\",0.0174532925199433]], ## CS[ellipsoidal,2], ## AXIS[\"geodetic latitude (Lat)\",north, ## ORDER[1], ## ANGLEUNIT[\"degree\",0.0174532925199433]], ## AXIS[\"geodetic longitude (Lon)\",east, ## ORDER[2], ## ANGLEUNIT[\"degree\",0.0174532925199433]], ## USAGE[ ## SCOPE[\"Geodesy.\"], ## AREA[\"North and central America: Antigua and Barbuda - onshore. Bahamas - onshore plus offshore over internal continental shelf only. Belize - onshore. British Virgin Islands - onshore. Canada onshore - Alberta, British Columbia, Manitoba, New Brunswick, Newfoundland and Labrador, Northwest Territories, Nova Scotia, Nunavut, Ontario, Prince Edward Island, Quebec, Saskatchewan and Yukon - plus offshore east coast. Cuba - onshore and offshore. El Salvador - onshore. Guatemala - onshore. Honduras - onshore. Panama - onshore. Puerto Rico - onshore. Mexico - onshore plus offshore east coast. Nicaragua - onshore. United States (USA) onshore and offshore - Alabama, Alaska, Arizona, Arkansas, California, Colorado, Connecticut, Delaware, Florida, Georgia, Idaho, Illinois, Indiana, Iowa, Kansas, Kentucky, Louisiana, Maine, Maryland, Massachusetts, Michigan, Minnesota, Mississippi, Missouri, Montana, Nebraska, Nevada, New Hampshire, New Jersey, New Mexico, New York, North Carolina, North Dakota, Ohio, Oklahoma, Oregon, Pennsylvania, Rhode Island, South Carolina, South Dakota, Tennessee, Texas, Utah, Vermont, Virginia, Washington, West Virginia, Wisconsin and Wyoming - plus offshore . US Virgin Islands - onshore.\"], ## BBOX[7.15,167.65,83.17,-47.74]], ## ID[\"EPSG\",4267]] suppressWarnings(st_crs(nc_sf) <- st_crs(nc)) xx <- st_equals(nc, nc_sf, sparse=FALSE) all(diag(xx)) && sum(xx) == 100L ## [1] TRUE td <- tempdir() #download.file(\"https://geodacenter.github.io/data-and-lab//data/sids.zip\", file.path(td, \"sids.zip\"), quiet=TRUE) # local copy (2020-10-22) as repository sometimes offline file.copy(system.file(\"etc/misc/sids.zip\", package=\"spdep\"), td) ## [1] TRUE unzip(file.path(td, \"sids.zip\"), c(\"sids/sids.dbf\", \"sids/sids.prj\", \"sids/sids.shp\", \"sids/sids.shx\"), exdir=td) sids_sf <- st_read(file.path(td, \"sids/sids.shp\"), quiet=TRUE) #download.file(\"https://geodacenter.github.io/data-and-lab//data/sids2.zip\", file.path(td, \"sids2.zip\"), quiet=TRUE) file.copy(system.file(\"etc/misc/sids2.zip\", package=\"spdep\"), td) ## [1] TRUE unzip(file.path(td, \"sids2.zip\"), c(\"sids2/sids2.dbf\", \"sids2/sids2.prj\", \"sids2/sids2.shp\", \"sids2/sids2.shx\"), exdir=td) sids2_sf <- st_read(file.path(td, \"sids2/sids2.shp\"), quiet=TRUE) st_crs(sids_sf) ## Coordinate Reference System: ## User input: WGS 84 ## wkt: ## GEOGCRS[\"WGS 84\", ## DATUM[\"World Geodetic System 1984\", ## ELLIPSOID[\"WGS 84\",6378137,298.257223563, ## LENGTHUNIT[\"metre\",1]]], ## PRIMEM[\"Greenwich\",0, ## ANGLEUNIT[\"degree\",0.0174532925199433]], ## CS[ellipsoidal,2], ## AXIS[\"latitude\",north, ## ORDER[1], ## ANGLEUNIT[\"degree\",0.0174532925199433]], ## AXIS[\"longitude\",east, ## ORDER[2], ## ANGLEUNIT[\"degree\",0.0174532925199433]], ## ID[\"EPSG\",4326]] st_crs(sids2_sf) ## Coordinate Reference System: ## User input: WGS 84 ## wkt: ## GEOGCRS[\"WGS 84\", ## DATUM[\"World Geodetic System 1984\", ## ELLIPSOID[\"WGS 84\",6378137,298.257223563, ## LENGTHUNIT[\"metre\",1]]], ## PRIMEM[\"Greenwich\",0, ## ANGLEUNIT[\"degree\",0.0174532925199433]], ## CS[ellipsoidal,2], ## AXIS[\"latitude\",north, ## ORDER[1], ## ANGLEUNIT[\"degree\",0.0174532925199433]], ## AXIS[\"longitude\",east, ## ORDER[2], ## ANGLEUNIT[\"degree\",0.0174532925199433]], ## ID[\"EPSG\",4326]] suppressWarnings(st_crs(sids_sf) <- st_crs(nc_sf)) xx <- st_equals(sids_sf, nc_sf, sparse=FALSE) all(diag(xx)) && sum(xx) == 100L ## [1] FALSE suppressWarnings(st_crs(sids2_sf) <- st_crs(nc_sf)) xx <- st_equals(sids2_sf, nc_sf, sparse=FALSE) all(diag(xx)) && sum(xx) == 100L ## [1] FALSE all.equal(as.data.frame(nc_sf)[,1:14], as.data.frame(sids_sf)[,1:14]) ## [1] \"Names: 12 string mismatches\" ## [2] \"Component 4: Modes: numeric, character\" ## [3] \"Component 4: target is numeric, current is character\" ## [4] \"Component 5: 100 string mismatches\" ## [5] \"Component 6: Modes: character, numeric\" ## [6] \"Component 6: target is character, current is numeric\" ## [7] \"Component 7: Mean relative difference: 0.9986388\" ## [8] \"Component 8: Mean relative difference: 64.33901\" ## [9] \"Component 9: Mean relative difference: 0.9979786\" ## [10] \"Component 10: Mean relative difference: 156.5427\" ## [11] \"Component 11: Mean relative difference: 3.01968\" ## [12] \"Component 12: Mean relative difference: 0.9980208\" ## [13] \"Component 13: Mean relative difference: 160.8194\" ## [14] \"Component 14: Modes: numeric, list\" ## [15] \"Component 14: Attributes: < target is NULL, current is list >\" ## [16] \"Component 14: target is numeric, current is sfc_MULTIPOLYGON\" all.equal(as.data.frame(nc_sf)[,1:14], as.data.frame(sids2_sf)[,1:14]) ## [1] \"Names: 12 string mismatches\" ## [2] \"Component 4: Modes: numeric, character\" ## [3] \"Component 4: target is numeric, current is character\" ## [4] \"Component 5: 100 string mismatches\" ## [5] \"Component 6: Modes: character, numeric\" ## [6] \"Component 6: target is character, current is numeric\" ## [7] \"Component 7: Mean relative difference: 0.9986388\" ## [8] \"Component 8: Mean relative difference: 64.33901\" ## [9] \"Component 9: Mean relative difference: 0.9979786\" ## [10] \"Component 10: Mean relative difference: 156.5427\" ## [11] \"Component 11: Mean relative difference: 3.01968\" ## [12] \"Component 12: Mean relative difference: 0.9980208\" ## [13] \"Component 13: Mean relative difference: 160.8194\" ## [14] \"Component 14: Mean relative difference: 0.9984879\" all.equal(as.data.frame(nc_sf)[,1:14], as.data.frame(nc)[,c(2,3,4,1,5:14)]) ## [1] \"Component \\\"NWBIR74\\\": Mean relative difference: 0.04891304\" which(!(nc_sf$NWBIR74 == nc$NWBIR74)) ## [1] 21 c(nc$NWBIR74[21], nc_sf$NWBIR74[21]) ## [1] 386 368 gal_file <- system.file(\"weights/ncCR85.gal\", package=\"spData\")[1] ncCR85 <- read.gal(gal_file, region.id=nc$FIPSNO) ncCR85 ## Neighbour list object: ## Number of regions: 100 ## Number of nonzero links: 492 ## Percentage nonzero weights: 4.92 ## Average number of links: 4.92 gal_file <- system.file(\"weights/ncCC89.gal\", package=\"spData\")[1] ncCC89 <- read.gal(gal_file, region.id=nc$FIPSNO) ncCC89 ## Neighbour list object: ## Number of regions: 100 ## Number of nonzero links: 394 ## Percentage nonzero weights: 3.94 ## Average number of links: 3.94 ## 2 regions with no links: ## 37055, 37095 ## 3 disjoint connected subgraphs plot(st_geometry(nc), border=\"grey\") plot(ncCC89, st_centroid(st_geometry(nc), of_largest_polygon), add=TRUE, col=\"blue\") r.id <- attr(ncCC89, \"region.id\") ncCC89[[match(\"37001\", r.id)]] ## [1] 11 26 29 30 48 r.id[ncCC89[[match(\"37001\", r.id)]]] ## [1] 37033 37081 37135 37063 37037 as.character(nc$NAME)[card(ncCC89) == 0] ## [1] \"Dare\" \"Hyde\""},{"path":"https://r-spatial.github.io/spdep/articles/sids.html","id":"probability-mapping","dir":"Articles","previous_headings":"Getting the data into R","what":"Probability mapping","title":"Introduction to the North Carolina SIDS data set (re-revised)","text":"Rather review functions measuring modelling spatial dependence spdep package, focus probability mapping disease rates data. Typically, counts incidence disease spatial unit, associated counts populations risk. task try establish whether spatial units seem characterised higher lower counts cases might expected general terms (Bailey Gatrell 1995). early approach Choynowski (1959), described Cressie Read (1985) Bailey Gatrell (1995), assumes, given true rate spatial units small, population risk increases infinity, spatial unit case counts Poisson mean value equal population risk times rate study area whole. Choynowski’s approach folds two tails measured probabilities together, small values, chosen α\\alpha, occur spatial units either unusually high low rates. reason, high low counties plotted separately . Note cut returns factor labeled cut intervals. complicated thematic maps, may helpful use ColorBrewer (https://colorbrewer2.org) colour palettes. use palettes accessed tmap, available R RColorBrewer package. choynowski() function provides probability map values required, probmap() function returns raw (crude) rates, expected counts (assuming constant rate across study area), relative risks, Poisson probability map values calculated using standard cumulative distribution function ppois(). fold tails together, counties lower observed counts expected, based population size, values lower tail, higher observed counts expected values upper tail, can see. Marilia Carvalho (personal communication) Virgilio Gómez Rubio (Gómez-Rubio, Ferrándiz-Ferragud, López-Quílez 2005) pointed unusual shape distribution Poisson probability values (histogram ), repeating doubts probability mapping voiced Cressie (1991, 392): “extreme value …\\ldots may due lack fit Poisson model deviation constant rate assumption”. many high values one expected, suggesting perhaps overdispersion, ratio variance mean larger unity. One ad-hoc way assess impact possible failure assumption counts follow Poisson distribution estimate dispersion fitting generalized linear model observed counts including intercept (null model) offset observed population risk (suggested Marilia Carvalho associates): dispersion equal 2.2786188, much greater unity; calculate corrected probability map values taking standardised residuals model, taking size dispersion account; results shown . Many fewer counties appear now unexpectedly large small numbers cases. ad-hoc adjustment made R provides access wide range model-fitting functions can used help check assumptions. Gómez-Rubio, Ferrándiz-Ferragud, López-Quílez (2005) chose rather construct probability map hypothesis data drawn Negative Binomial distribution. far, none maps presented made use spatial dependence possibly present data. elementary step can taken map Empirical Bayes estimates rates, smoothed relation raw rates. underlying question linked larger variance associated rate estimates counties small populations risk compared counties large populations risk. Empirical Bayes estimates place credence raw rates counties large populations risk, modify much less modify rates small counties. case small populations risk, confidence placed either global rate study area whole, local Empirical Bayes estimates, rates larger moving window including neighbours county estimated. function used spdep EBlocal(), initially contributed Marilia Carvalho. parallels similar function GeoDa, uses Bailey Gatrell (1995) interpretation Marshall (1991), rather GeoDa (Anselin, Syabri, Smirnov 2002). results shown Figure . Like relevant functions spdep,EBlocal() takes zero.policy argument allow missing values passed . case, local estimate available two counties neighbours, marked stars. addition Empirical Bayes smoothing globally, used disease mapping Assuncão Reis correction Moran’s II rates data (shrink towards global rate population risk small, Monte Carlo test), lists local neighbours can used shrink towards local rate.","code":"ch <- choynowski(nc$SID74, nc$BIR74) nc$ch_pmap_low <- ifelse(ch$type, ch$pmap, NA) nc$ch_pmap_high <- ifelse(!ch$type, ch$pmap, NA) prbs <- c(0,.001,.01,.05,.1,1) nc$high = cut(nc$ch_pmap_high, prbs) nc$low = cut(nc$ch_pmap_low,prbs ) is_tmap <- FALSE if (require(tmap, quietly=TRUE)) is_tmap <- TRUE is_tmap ## [1] TRUE library(tmap) tmap4 <- packageVersion(\"tmap\") >= \"3.99\" if (tmap4) { tm_shape(nc) + tm_polygons(fill=c(\"low\", \"high\"), fill.scale = tm_scale(values=\"brewer.set1\"), fill.legend = tm_legend(\"p-values\", frame=FALSE, item.r = 0), fill.free=FALSE, lwd=0.01) + tm_layout(panel.labels=c(\"low\", \"high\")) } else { tm_shape(nc) + tm_fill(c(\"low\", \"high\"), palette=\"Set1\", title=\"p-values\") + tm_facets(free.scales=FALSE) + tm_layout(panel.labels=c(\"low\", \"high\")) } pmap <- probmap(nc$SID74, nc$BIR74) nc$pmap <- pmap$pmap brks <- c(0,0.001,0.01,0.025,0.05,0.95,0.975,0.99,0.999,1) if (tmap4) { tm_shape(nc) + tm_polygons(fill=\"pmap\", fill.scale = tm_scale(values=\"brewer.rd_bu\", midpoint=0.5, breaks=brks), fill.legend = tm_legend(frame=FALSE, item.r = 0, position = tm_pos_out(\"right\", \"center\")), lwd=0.01) + tm_layout(component.autoscale=FALSE) } else { tm_shape(nc) + tm_fill(\"pmap\", breaks=brks, midpoint=0.5, palette=\"RdBu\") + tm_layout(legend.outside=TRUE) } hist(nc$pmap, main=\"\") res <- glm(SID74 ~ offset(log(BIR74)), data=nc, family=\"quasipoisson\") nc$stdres <- rstandard(res) brks <- c(-4, -3, -2, -1.5, -1, -0.5, 0.5, 1, 1.5, 2, 3, 4) if (tmap4) { tm_shape(nc) + tm_polygons(fill=\"stdres\", fill.scale = tm_scale(values=\"brewer.rd_bu\", midpoint=0.5, breaks=brks), fill.legend = tm_legend(frame=FALSE, item.r = 0, position = tm_pos_out(\"right\", \"center\")), lwd=0.01) + tm_layout(component.autoscale=FALSE) } else { tm_shape(nc) + tm_fill(\"stdres\", breaks=brks, midpoint=0, palette=\"RdBu\") + tm_layout(legend.outside=TRUE) } global_rate <- sum(nc$SID74)/sum(nc$BIR74) nc$Expected <- global_rate * nc$BIR74 res <- EBlocal(nc$SID74, nc$Expected, ncCC89, zero.policy=TRUE) nc$EB_loc <- res$est brks <- c(0, 0.25, 0.5, 0.75, 1, 2, 3, 4, 5) nc_miss <- st_centroid(st_geometry(nc[card(ncCC89) == 0,]), of_largest_polygon) if (tmap4) { tm_shape(nc) + tm_polygons(fill=\"stdres\", fill.scale = tm_scale(values=\"brewer.rd_bu\", midpoint=0.5, breaks=brks), fill.legend = tm_legend(frame=FALSE, item.r = 0, position = tm_pos_out(\"right\", \"center\")), lwd=0.01) + tm_layout(component.autoscale=FALSE) + tm_shape(nc_miss) + tm_symbols(shape=8, size=0.5) } else { tm_shape(nc) + tm_fill(\"EB_loc\", breaks=brks, midpoint=1, palette=\"RdBu\") + tm_layout(legend.outside=TRUE) + tm_shape(nc_miss) + tm_symbols(shape=8, size=0.5) } set.seed(1) EBImoran.mc(nc$SID74, nc$BIR74, nb2listw(ncCC89, style=\"B\", zero.policy=TRUE), nsim=999, zero.policy=TRUE) ## ## Monte-Carlo simulation of Empirical Bayes Index (mean subtracted) ## ## data: cases: nc$SID74, risk population: nc$BIR74 ## weights: nb2listw(ncCC89, style = \"B\", zero.policy = TRUE) ## number of simulations + 1: 1000 ## ## statistic = 0.25789, observed rank = 998, p-value = 0.002 ## alternative hypothesis: greater"},{"path":"https://r-spatial.github.io/spdep/articles/sids.html","id":"exploration-and-modelling-of-the-data","dir":"Articles","previous_headings":"","what":"Exploration and modelling of the data","title":"Introduction to the North Carolina SIDS data set (re-revised)","text":"One first steps taken Cressie Read (1985) try bring spatial trends dividing North Carolina 4×44\\times4 rough rectangles. Just see works, let us map rough rectangles proceeding . Cressie constructs transformed SIDS rates variable, 1974–78, analyses (co-workers). can replicate stem--leaf figure p. 396 book, taken Cressie Read (1989):","code":"nc$both <- factor(paste(nc$L_id, nc$M_id, sep=\":\")) nboth <- length(table(unclass(nc$both))) if (tmap4) { tm_shape(nc) + tm_polygons(fill=\"both\", fill.scale=tm_scale(values=\"brewer.set1\"), fill.legend = tm_legend(\"rough\\nrectangles\", frame=FALSE, item.r = 0, position = tm_pos_out(\"right\", \"center\")), lwd=0.01) + tm_layout(component.autoscale=FALSE) } else { tm_shape(nc) + tm_fill(\"both\", palette=\"Set1\", title=\"rough\\nrectangles\") + tm_layout(legend.outside=TRUE) } nc$ft.SID74 <- sqrt(1000)*(sqrt(nc$SID74/nc$BIR74) + sqrt((nc$SID74+1)/nc$BIR74)) stem(round(nc$ft.SID74, 1), scale=2) ## ## The decimal point is at the | ## ## 0 | 9 ## 1 | 111244 ## 1 | 567789999 ## 2 | 0011111222334444 ## 2 | 55555666677778999999999 ## 3 | 000111122333333344444444 ## 3 | 5568999 ## 4 | 013344 ## 4 | 555557 ## 5 | 2 ## 5 | ## 6 | 3"},{"path":"https://r-spatial.github.io/spdep/articles/sids.html","id":"medpol","dir":"Articles","previous_headings":"Exploration and modelling of the data","what":"Median polish smoothing","title":"Introduction to the North Carolina SIDS data set (re-revised)","text":"Cressie (1991, 46–48, 393–400) discusses detail smoothing may used partition variation data smooth rough. order try North Carolina SIDS data set, use coarse gridding four columns four rows given Cressie (1991, 553–54), four grid cells empty; given variables L_id M_id object nc. Next aggregate number live births number SIDS cases 1974–1978 grid cells: Using Freeman-Tukey transformation used county data, coerce data correctly configured matrix, cells empty. medpolish function applied matrix, told remove empty cells; function iterates rows columns matrix using median extract overall effect, row column effects, residuals: Returning factors linking rows columns counties, generating matrices dummy variables using model.matrix, can calculate fitted values Freeman-Tukey adjusted rate county, residuals subtracting fitted value observed rate. Naturally, fitted value counties grid cell: figure shows median polish smoothing results three maps, observed Freeman-Tukey transformed SIDS rates, fitted smoothed values, residuals. addition, plot median polish object also shown, plotting smooth residuals outer product row column effects divided overall effect, indicate lack additivity row column case — relevant analysis tables covariates rather geographical grids.","code":"mBIR74 <- tapply(nc$BIR74, nc$both, sum) mSID74 <- tapply(nc$SID74, nc$both, sum) mFT <- sqrt(1000)*(sqrt(mSID74/mBIR74) + sqrt((mSID74+1)/mBIR74)) # mFT1 <- t(matrix(mFT, 4, 4, byrow=TRUE)) # wrong assignment of 12 elements to a 4x4 matrix detected by CRAN test 2021-05-22 rc <- do.call(\"rbind\", lapply(strsplit(names(mFT), \":\"), as.integer)) mFT1 <- matrix(as.numeric(NA), 4, 4) for (i in 1:nrow(rc)) mFT1[rc[i,1], rc[i,2]] <- mFT[i] med <- medpolish(mFT1, na.rm=TRUE, trace.iter=FALSE) med ## ## Median Polish Results (Dataset: \"mFT1\") ## ## Overall: 2.90965 ## ## Row Effects: ## [1] -0.05686791 -0.37236370 0.05686791 0.79541774 ## ## Column Effects: ## [1] -0.005484562 -0.446250551 0.003656375 0.726443256 ## ## Residuals: ## [,1] [,2] [,3] [,4] ## [1,] NA -0.45800 0.000000 0.37556 ## [2,] -0.092554 0.00000 0.101695 0.00000 ## [3,] 0.092554 0.30464 -0.090726 -0.55364 ## [4,] NA NA 0.000000 NA mL_id <- model.matrix(~ as.factor(nc$L_id) -1) mM_id <- model.matrix(~ as.factor(nc$M_id) -1) nc$pred <- c(med$overall + mL_id %*% med$row + mM_id %*% med$col) nc$mp_resid <- nc$ft.SID74 - nc$pred if (tmap4) { out1 <- tm_shape(nc) + tm_polygons(fill=c(\"ft.SID74\", \"pred\"), fill.scale=tm_scale(values=\"brewer.yl_or_br\"), fill.legend=tm_legend(position=tm_pos_out(\"right\", \"center\"), frame=FALSE, item.r = 0), fill.free=FALSE, lwd=0.01) + tm_layout(panel.labels=c(\"Observed\", \"Median polish prediction\")) out2 <- tm_shape(nc) + tm_polygons(fill=\"mp_resid\", fill.scale=tm_scale(values=\"brewer.rd_yl_gn\", midpoint=0), fill.legend=tm_legend(position=tm_pos_out(\"right\", \"center\"), frame=FALSE, item.r = 0), lwd=0.01) } else { out1 <- tm_shape(nc) + tm_fill(c(\"ft.SID74\", \"pred\")) + tm_facets(free.scales=FALSE) + tm_layout(panel.labels=c(\"Observed\", \"Median polish prediction\")) out2 <- tm_shape(nc) + tm_fill(\"mp_resid\", midpoint=0) + tm_layout(legend.outside=TRUE) } tmap_arrange(out1, out2, ncol=1)"},{"path":[]},{"path":"https://r-spatial.github.io/spdep/articles/subgraphs.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"No-neighbour observation and subgraph handling","text":"spdep package always careful disconnected graphs, especially disconnected observations graph nodes neighbours, incoming outgoing edges. nb neighbour objects, encoded integer vectors length 1 containing integer 0, invalid index [1,N][1, N], NN observation count. Functions taking neighbour objects arguments use zero.policy argument guide handle -neighbour observations. spdep also n.comp.nb find number disjoint connected subgraphs nb object, contributed Nicholas Lewin-Koh 2001 using depth-first search symmetric neighbours, showing addition observations belong subgraph. Obviously, -neighbour observations singleton graph nodes, subgraphs also troubling spatial analysis, connection spatial processes subgraphs. ripples one pond cross separate pond connected. spdep 1.3-1, steps began raise awareness possibility neighbour objects might created disconnected way, mostly warnings, computation subgraph measures default. vignette intended provide background steps.","code":""},{"path":"https://r-spatial.github.io/spdep/articles/subgraphs.html","id":"no-neighbour-observations","dir":"Articles","previous_headings":"","what":"No-neighbour observations","title":"No-neighbour observation and subgraph handling","text":"start, nb objects recorded -neighbour observations integer vector unit length value 0, neighbours recorded ID values 1 N, N observation count. print summary methods always reported presence -neighbour observations, listed IDs (region.id values). nb object contains -neighbour observations, user decide whether drop observations, retained, value give weights. zero.policy argument uses zero value TRUE, FALSE causes nb2listw fail. value zero.policy call functions like nb2listw, subset.listw mat2listw creating listw objects representing sparse spatial weights matrices added created object attribute, used subsequently pass choice functions. example, moran.test takes value attribute default zero.policy argument: observation ii neighbours, weights sum ∑j=1Nwij=0\\sum_{j=1}^N w_{ij} = 0, wij=0,∀jw_{ij} = 0, \\forall j (see discussion Bivand Portnov (2004)). eigenvalue also zero, consequences analytical inference: adjust.n argument measures spatial autocorrelation default TRUE, subtracts count singleton nodes NN attempt acknowledge reduction information available. discussion address problems arising analysing areal/lattice data, neighbours defined polygon features contiguous boundaries. One way -neighbour observations may occur islands. clearly case Freni-Sterrantino, Ventrucci, Rue (2018), Capraia Giglio Isles singleton nodes. take Westminster constituencies Wales used July 2024 UK general election. GDAL least version 3.7.0, driver supports compressed GeoPackage files, must decompressed first. boundaries taken Ordnance Survey Boundary-Line site, https://osdatahub.os.uk/downloads/open/BoundaryLine, choosing 2024 Westminster constituencies, simplified using tolerance 50m reduce object size, merged selected voting outcomes constituencies Great Britain https://electionresults.parliament.uk/countries/1, (https://www.nationalarchives.gov.uk/doc/open-government-licence/version/3/). , subset Wales useful see: two subgraphs singleton Ynys Môn 31 constituencies: left map shows Ynys Môn can shown selecting name, black border, zero cardinality neighbour set, using card, filling polygon. right map shows location island, known English Anglesey, north-west Welsh mainland, neighbour links: maps, can see island close two constituencies across Afon Menai (Menai Strait English), three simplified polygons less 280m apart, measured polygon boundaries: Using snap distance 280m, can join island two obvious proximate neighbours: case, increasing snap default 10mm (close equivalents geometries known metrics; previously sqrt(.Machine$double.eps) 1.4901161^{-8} cases) helps. symmetric links added : always going case, strait narrow. islands much offshore, steps may required, large snap distance draw extra neighbours already connected observations. also possible increasing snap distance may fail link islands considered candidate neighbours, extents (bounding boxes), buffered snap value, intersect. can also use distances pick neighbour candidates meet criterion 280m, taking care lose ordering needed identify correct observations: candidates island , two neighbours across Menai Strait: addlinks1 function can used add links Ynys Môn neighbours, symmetry Ynys Môn. approach means island treated separately (scripted sequence), risk adding spurious neighbours denser parts study area. Since constituency observations areal support, surprising changing support points using kk-nearest neighbours work adequately, distance measurements points representing polygons rather areal unit boundaries: , Clwyd North, east Bangor Aberconwy, given neighbour Ynys Môn Dwyfor Meirionnydd, west Bangor Aberconwy, . addition, two subgraphs, still remain k=6k=6.","code":"library(spdep) ## Loading required package: spData ## Loading required package: sf ## Linking to GEOS 3.13.1, GDAL 3.11.0, PROJ 9.6.2; sf_use_s2() is TRUE args(moran.test) ## function (x, listw, randomisation = TRUE, zero.policy = attr(listw, ## \"zero.policy\"), alternative = \"greater\", rank = FALSE, na.action = na.fail, ## spChk = NULL, adjust.n = TRUE, drop.EI2 = FALSE) ## NULL eigen(0)$values ## [1] 0 GDAL37 <- numeric_version(unname(sf::sf_extSoftVersion()[\"GDAL\"]), strict=FALSE) (GDAL37 <- ifelse(is.na(GDAL37), FALSE, GDAL37 >= \"3.7.0\")) ## [1] TRUE file <- \"etc/shapes/GB_2024_Wales_50m.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) { w50m <- st_read(zipfile) } else { td <- tempdir() bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE) target <- unzip(zipfile, files=bn, exdir=td) w50m <- st_read(target) } ## Reading layer `GB_2024_Wales_50m' from data source ## `/tmp/Rtmp5vVziX/temp_libpath224d25059ed81/spdep/etc/shapes/GB_2024_Wales_50m.gpkg.zip' ## using driver `GPKG' ## Simple feature collection with 32 features and 19 fields ## Geometry type: MULTIPOLYGON ## Dimension: XY ## Bounding box: xmin: 146597.1 ymin: 164536.5 xmax: 355287 ymax: 395993.5 ## Projected CRS: OSGB36 / British National Grid (nb_W_50m <- poly2nb(w50m, row.names=as.character(w50m$Constituency))) ## Warning in poly2nb(w50m, row.names = as.character(w50m$Constituency)): some observations have no neighbours; ## if this seems unexpected, try increasing the snap argument. ## Warning in poly2nb(w50m, row.names = as.character(w50m$Constituency)): neighbour object has 2 sub-graphs; ## if this sub-graph count seems unexpected, try increasing the snap argument. ## Neighbour list object: ## Number of regions: 32 ## Number of nonzero links: 136 ## Percentage nonzero weights: 13.28125 ## Average number of links: 4.25 ## 1 region with no links: ## Ynys Môn ## 2 disjoint connected subgraphs table(table(attr(nb_W_50m, \"ncomp\")$comp.id)) ## ## 1 31 ## 1 1 ynys_mon <- w50m$Constituency == \"Ynys Môn\" pts <- st_point_on_surface(st_geometry(w50m)) opar <- par(mfrow=c(1, 2)) plot(st_geometry(w50m), border=\"grey75\") plot(st_geometry(w50m)[ynys_mon], add=TRUE) plot(st_geometry(w50m)[card(nb_W_50m) == 0L], add=TRUE, border=\"transparent\", col=\"wheat1\") plot(st_geometry(w50m), border=\"grey75\") plot(nb_W_50m, pts, add=TRUE) par(opar) dym <- c(st_distance(w50m[ynys_mon,], w50m)) sort(dym)[1:12] ## Units: [m] ## [1] 0.0000 123.4132 277.5414 16658.7265 37985.7086 54096.7729 ## [7] 58146.4320 65550.2491 67696.3323 93741.9873 113007.3659 137858.1826 (nb_W_50m_snap <- poly2nb(w50m, row.names=as.character(w50m$Constituency), snap=280)) ## Neighbour list object: ## Number of regions: 32 ## Number of nonzero links: 140 ## Percentage nonzero weights: 13.67188 ## Average number of links: 4.375 plot(st_geometry(w50m), border=\"grey75\") plot(nb_W_50m_snap, pts, add=TRUE) attr(nb_W_50m_snap, \"region.id\")[nb_W_50m_snap[[which(ynys_mon)]]] ## [1] \"Bangor Aberconwy\" \"Dwyfor Meirionnydd\" (meet_criterion <- sum(dym <= units::set_units(280, \"m\"))) ## [1] 3 (cands <- attr(nb_W_50m, \"region.id\")[order(dym)[1:meet_criterion]]) ## [1] \"Ynys Môn\" \"Bangor Aberconwy\" \"Dwyfor Meirionnydd\" (nb_W_50m_add <- addlinks1(nb_W_50m, from = cands[1], to = cands[2:meet_criterion])) ## Neighbour list object: ## Number of regions: 32 ## Number of nonzero links: 140 ## Percentage nonzero weights: 13.67188 ## Average number of links: 4.375 all.equal(nb_W_50m_add, nb_W_50m_snap, check.attributes=FALSE) ## [1] TRUE k2 <- knn2nb(knearneigh(pts, k=2), row.names=as.character(w50m$Constituency), sym=TRUE) ## Warning in knn2nb(knearneigh(pts, k = 2), row.names = ## as.character(w50m$Constituency), : neighbour object has 2 sub-graphs attr(k2, \"region.id\")[k2[[which(ynys_mon)]]] ## [1] \"Bangor Aberconwy\" \"Clwyd North\""},{"path":"https://r-spatial.github.io/spdep/articles/subgraphs.html","id":"subgraphs","dir":"Articles","previous_headings":"","what":"Subgraphs","title":"No-neighbour observation and subgraph handling","text":"Subgraphs may found -neighbour observations present, also graph split two blocks observations path observation block another block, across low population density constituencies mid-Wales: can show block structure displaying binary spatial weights matrix: occurs frequently point support, may also occur areal support, Freni-Sterrantino, Ventrucci, Rue (2018) find eight municipalities island Elba. spdep 1.3-6, igraph spatialreg packages available, n.comp.nb uses igraph::components compute graph components, also using depth-first search. original implementation fast, directed (asymmetric) graphs converts first symmetry, igraph::components can handle directed graphs without conversion (see https://github.com/r-spatial/spdep/issues/160 details). Another case demonstrates cyclical subgraphs may appear; taken constituencies 2024 UK general election, subsetted England south London. second subgraph two members, others’ neighbours, known cyclical component. constituencies Isle Wight: consequences eigenvalues spatial weights matrix, pointed Smirnov Anselin (2009) Bivand, Hauke, Kossowski (2013). row-standardised weights, eigenvalues component : “takes ” lower domain boundary, whole data set now : compared lower domain boundary remainder study area: subgraph may added remainder shown : Using 5km cutoff seems prudent, work snap value. Taking Isle Wight East first, four constituencies boundaries within 5km: Obviously contiguous neighbour among zero distance, needs dropped, although addlinks1 drop duplicate: Although constituencies now linked, see whether using 5km criterion brings extra neighbours Isle Wight West: , , need beware sorting order zero self-distance contiguous neighbour distance, now second position: yields links north-west: remains add suitable generalisation addlinks1 handle vector argument argument taking list vectors.","code":"(k6 <- knn2nb(knearneigh(pts, k=6), row.names=as.character(w50m$Constituency), sym=TRUE)) ## Warning in knn2nb(knearneigh(pts, k = 6), row.names = ## as.character(w50m$Constituency), : neighbour object has 2 sub-graphs ## Neighbour list object: ## Number of regions: 32 ## Number of nonzero links: 238 ## Percentage nonzero weights: 23.24219 ## Average number of links: 7.4375 ## 2 disjoint connected subgraphs plot(st_geometry(w50m), border=\"grey75\") plot(k6, pts, add=TRUE) o <- order(attr(k6, \"ncomp\")$comp.id) image(t(nb2mat(k6, style=\"B\")[o, rev(o)]), axes=FALSE, asp=1) (k6a <- knn2nb(knearneigh(pts, k=6), row.names=as.character(w50m$Constituency))) ## Warning in knn2nb(knearneigh(pts, k = 6), row.names = ## as.character(w50m$Constituency)): neighbour object has 2 sub-graphs ## Neighbour list object: ## Number of regions: 32 ## Number of nonzero links: 192 ## Percentage nonzero weights: 18.75 ## Average number of links: 6 ## 2 disjoint connected subgraphs ## Non-symmetric neighbours list file <- \"etc/shapes/GB_2024_southcoast_50m.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) { sc50m <- st_read(zipfile) } else { td <- tempdir() bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE) target <- unzip(zipfile, files=bn, exdir=td) sc50m <- st_read(target) } ## Reading layer `GB_2024_southcoast_50m' from data source ## `/tmp/Rtmp5vVziX/temp_libpath224d25059ed81/spdep/etc/shapes/GB_2024_southcoast_50m.gpkg.zip' ## using driver `GPKG' ## Simple feature collection with 119 features and 19 fields ## Geometry type: MULTIPOLYGON ## Dimension: XY ## Bounding box: xmin: 82643.12 ymin: 5342.9 xmax: 640301.6 ymax: 187226.2 ## Projected CRS: OSGB36 / British National Grid (nb_sc_50m <- poly2nb(sc50m, row.names=as.character(sc50m$Constituency))) ## Warning in poly2nb(sc50m, row.names = as.character(sc50m$Constituency)): neighbour object has 2 sub-graphs; ## if this sub-graph count seems unexpected, try increasing the snap argument. ## Neighbour list object: ## Number of regions: 119 ## Number of nonzero links: 530 ## Percentage nonzero weights: 3.742674 ## Average number of links: 4.453782 ## 2 disjoint connected subgraphs nc <- attr(nb_sc_50m, \"ncomp\")$comp.id table(nc) ## nc ## 1 2 ## 117 2 (sub2 <- attr(nb_sc_50m, \"region.id\")[nc == 2L]) ## [1] \"Isle of Wight East\" \"Isle of Wight West\" pts <- st_point_on_surface(st_geometry(sc50m)) plot(st_geometry(sc50m), border=\"grey75\") plot(st_geometry(sc50m)[nc == 2L], border=\"orange\", lwd=2, add=TRUE) plot(nb_sc_50m, pts, add=TRUE) 1/range(eigen(cbind(c(0, 1), c(1, 0)))$values) ## [1] -1 1 1/range(eigen(nb2mat(subset(nb_sc_50m, nc == 2L), style=\"W\"))$values) ## [1] -1 1 1/range(eigen(nb2mat(nb_sc_50m, style=\"W\"))$values) ## [1] -1 1 1/range(eigen(nb2mat(subset(nb_sc_50m, nc == 1L), style=\"W\"))$values) ## [1] -1.094637 1.000000 iowe <- match(sub2[1], attr(nb_sc_50m, \"region.id\")) diowe <- c(st_distance(sc50m[iowe,], sc50m)) sort(diowe)[1:12] ## Units: [m] ## [1] 0.000 0.000 1886.833 3509.366 6693.575 6943.672 7678.999 ## [8] 8576.454 10579.530 12163.332 16875.920 17161.786 ioww <- match(sub2[2], attr(nb_sc_50m, \"region.id\")) dioww <- c(st_distance(sc50m[ioww,], sc50m)) sort(dioww)[1:12] ## Units: [m] ## [1] 0.000 0.000 1232.724 2541.318 5746.764 5770.602 8902.579 ## [8] 9747.265 10529.540 10909.845 12250.564 12379.871 (meet_criterion <- sum(diowe <= units::set_units(5000, \"m\"))) ## [1] 4 (cands <- attr(nb_sc_50m, \"region.id\")[order(diowe)[1:meet_criterion]]) ## [1] \"Isle of Wight East\" \"Isle of Wight West\" \"Portsmouth South\" ## [4] \"Gosport\" (nb_sc_50m_iowe <- addlinks1(nb_sc_50m, from = cands[1], to = cands[3:meet_criterion])) ## Neighbour list object: ## Number of regions: 119 ## Number of nonzero links: 534 ## Percentage nonzero weights: 3.77092 ## Average number of links: 4.487395 (meet_criterion <- sum(dioww <= units::set_units(5000, \"m\"))) ## [1] 4 (cands <- attr(nb_sc_50m, \"region.id\")[order(dioww)[1:meet_criterion]]) ## [1] \"Isle of Wight East\" \"Isle of Wight West\" \"New Forest West\" ## [4] \"New Forest East\" (nb_sc_50m_iow <- addlinks1(nb_sc_50m_iowe, from = cands[2], to = cands[3:meet_criterion])) ## Neighbour list object: ## Number of regions: 119 ## Number of nonzero links: 538 ## Percentage nonzero weights: 3.799167 ## Average number of links: 4.521008 pts <- st_point_on_surface(st_geometry(sc50m)) plot(st_geometry(sc50m), border=\"grey75\") plot(st_geometry(sc50m)[nc == 2L], border=\"orange\", lwd=2, add=TRUE) plot(nb_sc_50m_iow, pts, add=TRUE)"},{"path":"https://r-spatial.github.io/spdep/articles/subgraphs.html","id":"per-session-control-of-function-behaviour","dir":"Articles","previous_headings":"","what":"Per-session control of function behaviour","title":"No-neighbour observation and subgraph handling","text":"early , default value zero.policy argument many methods functions NULL. value NULL, zero.policy set get.ZeroPolicyOption: loading spdep, internal option set FALSE, functions methods using zero.policy need choose handle islands: case, shown island may reasonably associated proximate constituencies mainland. , however, user wishes override default, set.ZeroPolicyOption may used set different per-session default: listw object created zero.policy set TRUE, choice added output object attribute applied object used (unless specifically overridden). Note also 32 constituencies, observation count reported spweights.constants called print method listw object argument adjust.n TRUE, dropping -neighbour observations observation count. internal options introduced suppress -neighbour subgraph warnings creating nb objects. default values follows: get.NoNeighbourOption controls issuing warnings nb objects created -neighbour observations; get.SubgraphOption works similarly warnings issued one graph component; TRUE default. get.SubgraphCeiling sets integer value graph nodes plus graph edges calculating graph considered costly compute time, default 100,000. corresponds dense neighbour set just 300 nodes (almost 100000 edges) needed use inverse distance weights, just 14,000 nodes average neighbour count 6. print method nb objects reports -neighbour subgraph status anyway, careful users always examine generated objects may prefer supress warnings, warnings seem prudent users may examine objects, generation subsetting larger objects, example creation training test data sets. Welsh constituency boundaries used show behaviour internal options: Turning removes warnings: get.SubgraphOption FALSE, attribute containing output n.comp.nb added: reduction ceiling node count 32 plus edge count 136 also supresses calculation graph components: Restoring remaining default values:","code":"get.ZeroPolicyOption() ## [1] FALSE try(nb2listw(nb_W_50m)) ## Error in nb2listw(nb_W_50m) : ## Empty neighbour sets found (zero.policy: FALSE) set.ZeroPolicyOption(TRUE) get.ZeroPolicyOption() ## [1] TRUE (lw <- nb2listw(nb_W_50m)) ## Characteristics of weights list object: ## Neighbour list object: ## Number of regions: 32 ## Number of nonzero links: 136 ## Percentage nonzero weights: 13.28125 ## Average number of links: 4.25 ## 1 region with no links: ## Ynys Môn ## 2 disjoint connected subgraphs ## ## Weights style: W ## Weights constants summary: ## n nn S0 S1 S2 ## W 31 961 31 15.36355 129.051 attr(lw, \"zero.policy\") ## [1] TRUE set.ZeroPolicyOption(FALSE) get.NoNeighbourOption() ## [1] TRUE get.SubgraphOption() ## [1] TRUE get.SubgraphCeiling() ## [1] 100000 set.NoNeighbourOption(FALSE) (nb_W_50mz <- poly2nb(w50m, row.names=as.character(w50m$Constituency))) ## Warning in poly2nb(w50m, row.names = as.character(w50m$Constituency)): neighbour object has 2 sub-graphs; ## if this sub-graph count seems unexpected, try increasing the snap argument. ## Neighbour list object: ## Number of regions: 32 ## Number of nonzero links: 136 ## Percentage nonzero weights: 13.28125 ## Average number of links: 4.25 ## 1 region with no links: ## Ynys Môn ## 2 disjoint connected subgraphs set.SubgraphOption(FALSE) (nb_W_50my <- poly2nb(w50m, row.names=as.character(w50m$Constituency))) ## Neighbour list object: ## Number of regions: 32 ## Number of nonzero links: 136 ## Percentage nonzero weights: 13.28125 ## Average number of links: 4.25 ## 1 region with no links: ## Ynys Môn str(attr(nb_W_50my, \"ncomp\")) ## NULL set.SubgraphOption(TRUE) set.SubgraphCeiling(100L) (nb_W_50mx <- poly2nb(w50m, row.names=as.character(w50m$Constituency))) ## Neighbour list object: ## Number of regions: 32 ## Number of nonzero links: 136 ## Percentage nonzero weights: 13.28125 ## Average number of links: 4.25 ## 1 region with no links: ## Ynys Môn str(attr(nb_W_50mx, \"ncomp\")) ## NULL set.SubgraphCeiling(100000L) set.NoNeighbourOption(TRUE)"},{"path":"https://r-spatial.github.io/spdep/articles/subgraphs.html","id":"unintentional-disconnected-graphs","dir":"Articles","previous_headings":"","what":"Unintentional disconnected graphs","title":"No-neighbour observation and subgraph handling","text":"Sometimes apparently sensible polygons turn represented way disconnected graphs generated extracting contiguities. One case raised https://github.com/r-spatial/spdep/issues/162, subdivisions Tokyo. original data file tokyomet262.* https://sgsup.asu.edu/sites/g/files/litvpz426/files/SparcFiles/tokyo_0.zip created twenty years ago Tomoki Nakaya Martin Charlton, geometry issues known time. possibility may affect legacy files projection geometries 32-bit platforms, known whether affected file. re-packaged compressed GeoPackage: correcting invalid polygons: applying poly2nb legacy default snap value produced numerous singleton observations well many multiple-observation subgraphs: legacy default snap value coordinates measured metres 15 nanometres, effectively assumed coordinates making polygon boundaries identical: Stepping little 2mm, lack contact ceased problem. basis, default changed spdep 1.3-6 10mm projected polygons, snap value used returned attribute neighbour object: polygons represented geographical (spherical) coordinates, new default spdep 1.3-6 set value mimicking 10mm: default snap value used poly2nb polygons expressed decimal degrees : set based apparent “size” 10mm decimal degrees:","code":"file <- \"etc/shapes/tokyo.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) { tokyo <- st_read(zipfile) } else { td <- tempdir() bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE) target <- unzip(zipfile, files=bn, exdir=td) tokyo <- st_read(target) } ## Reading layer `tokyo' from data source ## `/tmp/Rtmp5vVziX/temp_libpath224d25059ed81/spdep/etc/shapes/tokyo.gpkg.zip' ## using driver `GPKG' ## Simple feature collection with 262 features and 3 fields ## Geometry type: MULTIPOLYGON ## Dimension: XY ## Bounding box: xmin: 266206.6 ymin: -90932.11 xmax: 411400.3 ymax: 37142.75 ## Projected CRS: Tokyo / Japan Plane Rectangular CS VI all(st_is_valid(tokyo)) ## [1] TRUE tokyo <- st_make_valid(tokyo) (nb_t0 <- poly2nb(tokyo, snap=sqrt(.Machine$double.eps))) ## Warning in poly2nb(tokyo, snap = sqrt(.Machine$double.eps)): some observations have no neighbours; ## if this seems unexpected, try increasing the snap argument. ## Warning in poly2nb(tokyo, snap = sqrt(.Machine$double.eps)): neighbour object has 23 sub-graphs; ## if this sub-graph count seems unexpected, try increasing the snap argument. ## Neighbour list object: ## Number of regions: 262 ## Number of nonzero links: 946 ## Percentage nonzero weights: 1.378125 ## Average number of links: 3.610687 ## 10 regions with no links: ## 101, 127, 134, 135, 152, 154, 167, 237, 242, 243 ## 23 disjoint connected subgraphs units::set_units(units::set_units(attr(nb_t0, \"snap\"), \"m\"), \"nm\") ## 14.90116 [nm] (nb_t1 <- poly2nb(tokyo, snap=0.002)) ## Neighbour list object: ## Number of regions: 262 ## Number of nonzero links: 1390 ## Percentage nonzero weights: 2.02494 ## Average number of links: 5.305344 units::set_units(units::set_units(attr(nb_t1, \"snap\"), \"m\"), \"mm\") ## 2 [mm] (nb_t2 <- poly2nb(tokyo)) ## Neighbour list object: ## Number of regions: 262 ## Number of nonzero links: 1390 ## Percentage nonzero weights: 2.02494 ## Average number of links: 5.305344 units::set_units(units::set_units(attr(nb_t2, \"snap\"), \"m\"), \"mm\") ## 10 [mm] (nb_t3 <- poly2nb(st_transform(tokyo, \"OGC:CRS84\"))) ## Neighbour list object: ## Number of regions: 262 ## Number of nonzero links: 1336 ## Percentage nonzero weights: 1.946274 ## Average number of links: 5.099237 attr(nb_t3, \"snap\") ## [1] 9e-08 (180 * 0.01) / (pi * 6378137) ## [1] 8.983153e-08"},{"path":[]},{"path":"https://r-spatial.github.io/spdep/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Roger Bivand. Maintainer, author. Micah Altman. Contributor. Luc Anselin. Contributor. Renato Assunção. Contributor. Anil Bera. Contributor. Olaf Berke. Contributor. F. Guillaume Blanchet. Contributor. Marilia Carvalho. Contributor. Bjarke Christensen. Contributor. Yongwan Chun. Contributor. Carsten Dormann. Contributor. Stéphane Dray. Contributor. Dewey Dunnington. Contributor. Virgilio Gómez-Rubio. Contributor. Malabika Koley. Contributor. Tomasz Kossowski. Contributor. Elias Krainski. Contributor. Pierre Legendre. Contributor. Nicholas Lewin-Koh. Contributor. Angela Li. Contributor. Giovanni Millo. Contributor. Werner Mueller. Contributor. Hisaji Ono. Contributor. Josiah Parry. Contributor. Pedro Peres-Neto. Contributor. Michał Pietrzak. Contributor. Gianfranco Piras. Contributor. Markus Reder. Contributor. Jeff Sauer. Contributor. Michael Tiefelsdorf. Contributor. René Westerholt. Contributor. Justyna Wilk. Contributor. Levi Wolf. Contributor. Danlin Yu. Contributor.","code":""},{"path":"https://r-spatial.github.io/spdep/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Bivand R, Wong D (2018). “Comparing implementations global local indicators spatial association.” TEST, 27(3), 716–748. doi:10.1007/s11749-018-0599-x. Roger Bivand (2022). “R Packages Analyzing Spatial Data: Comparative Case Study Areal Data.” Geographical Analysis, 54(3), 488-518. doi:10.1111/gean.12319. Bivand R, Pebesma E, Gómez-Rubio V (2013). Applied spatial data analysis R, Second edition. Springer, NY. https://asdar-book.org/. Pebesma E, Bivand R (2023). Spatial Data Science Applications R. Chapman & Hall. https://r-spatial.org/book/.","code":"@Article{, author = {Roger Bivand and David W. S. Wong}, title = {Comparing implementations of global and local indicators of spatial association}, journal = {TEST}, year = {2018}, volume = {27}, number = {3}, pages = {716--748}, doi = {10.1007/s11749-018-0599-x}, } @Article{, author = {{Roger Bivand}}, title = {R Packages for Analyzing Spatial Data: A Comparative Case Study with Areal Data}, journal = {Geographical Analysis}, year = {2022}, volume = {54}, number = {3}, pages = {488-518}, doi = {10.1111/gean.12319}, } @Book{, author = {Roger S. Bivand and Edzer Pebesma and Virgilio Gómez-Rubio}, title = {Applied spatial data analysis with {R}, Second edition}, year = {2013}, publisher = {Springer, NY}, url = {https://asdar-book.org/}, } @Book{, author = {Edzer Pebesma and Roger S. Bivand}, title = {Spatial Data Science With Applications in {R}}, year = {2023}, publisher = {Chapman & Hall}, url = {https://r-spatial.org/book/}, }"},{"path":[]},{"path":"https://r-spatial.github.io/spdep/index.html","id":"spatial-dependence-weighting-schemes-and-statistics","dir":"","previous_headings":"","what":"Spatial Dependence: Weighting Schemes and Statistics","title":"Spatial Dependence: Weighting Schemes, Statistics","text":"collection functions create spatial weights matrix objects polygon contiguities, point patterns distance tessellations, summarizing objects, permitting use spatial data analysis, including regional aggregation minimum spanning tree; collection tests spatial autocorrelation, including global Morans Gearys C proposed Cliff Ord (1973, ISBN: 0850860369) (1981, ISBN: 0850860814), Hubert/Mantel general cross product statistic, Empirical Bayes estimates Assunção/Reis (1999) (https://doi.org/10.1002/(SICI)1097-0258(19990830)18:16%3C2147%3A%3AAID-SIM179%3E3.0.CO%3B2-) Index, Getis/Ord G (Getis Ord 1992) (https://doi.org/10.1111/j.1538-4632.1992.tb00261.x) multicoloured join count statistics, APLE (Li et al. ) (https://doi.org/10.1111/j.1538-4632.2007.00708.x), local Morans (Anselin 1995) (https://doi.org/10.1111/j.1538-4632.1995.tb00338.x) Getis/Ord G (Ord Getis 1995) (https://doi.org/10.1111/j.1538-4632.1995.tb00912.x), saddlepoint approximations (Tiefelsdorf 2002) (https://doi.org/10.1111/j.1538-4632.2002.tb01084.x) exact tests global local Morans (Bivand et al. 2009) (https://doi.org/10.1016/j.csda.2008.07.021) LOSH local indicators spatial heteroscedasticity (Ord Getis) (https://doi.org/10.1007/s00168-011-0492-y), extensions Bivand (2022) doi:10.1111/gean.12319. implementation measures described Bivand Wong (2018) (https://doi.org/10.1007/s11749-018-0599-x). Extra measures contributed Josiah Parry. Lagrange multiplier tests spatial dependence linear models provided (Anselin et al. 1996) (https://doi.org/10.1016/0166-0462(95)02111-6), Rao’s score tests hypothesised spatial Durbin models based fitted linear models (Koley Bera 2024) (https://doi.org/10.1080/17421772.2023.2256810). local indicators categorical data (LICD) implementation based Carrer et al. (2021) (https://doi.org/10.1016/j.jas.2020.105306) Bivand et al. (2017) (https://doi.org/10.1016/j.spasta.2017.03.003) added 1.3-7. Multivariate spatialdelta (Bavaud 2024) (https://doi.org/10.1111/gean.12390) added 1.3-13. sfdep (https://cran.r-project.org/package=sfdep) provides piped interface spdep. spdep spatialreg versions >= 1.2-1, model fitting functions previously present package defunct spdep may found spatialreg. Default branch now main Moved R-Forge","code":""},{"path":"https://r-spatial.github.io/spdep/reference/COL.OLD.html","id":null,"dir":"Reference","previous_headings":"","what":"Columbus OH spatial analysis data set - old numbering — oldcol","title":"Columbus OH spatial analysis data set - old numbering — oldcol","text":"COL.OLD data frame 49 rows 22 columns. observations ordered numbered original analyses data set SpaceStat documentation Anselin, L. 1988 Spatial econometrics: methods models, Dordrecht: Kluwer. Unit analysis: 49 neighbourhoods Columbus, OH, 1980 data. addition data set includes COL.nb, neighbours list used Anselin (1988).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/COL.OLD.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Columbus OH spatial analysis data set - old numbering — oldcol","text":"","code":"data(oldcol)"},{"path":"https://r-spatial.github.io/spdep/reference/COL.OLD.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Columbus OH spatial analysis data set - old numbering — oldcol","text":"data frame contains following columns: AREA_PL computed ArcView (agrees areas polygons “columbus” data set PERIMETER computed ArcView COLUMBUS. internal polygon ID (ignore) COLUMBUS.another internal polygon ID (ignore) POLYID yet another polygon ID NEIG neighborhood id value (1-49); conforms id value used Spatial Econometrics book. HOVAL housing value ($1,000) INC household income ($1,000) CRIME residential burglaries vehicle thefts per thousand households neighborhood OPEN open space neighborhood PLUMB percentage housing units without plumbin DISCBD distance CBD X x coordinate (arbitrary digitizing units, polygon coordinates) Y y coordinate (arbitrary digitizing units, polygon coordinates) AREA_SS neighborhood area (computed SpaceStat) NSA north-south dummy (North=1) NSB north-south dummy (North=1) EW east-west dummy (East=1) CP core-periphery dummy (Core=1) THOUS constant=1,000 NEIGNO NEIG+1,000, alternative neighborhood id value PERIM polygon perimeter (computed SpaceStat)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/COL.OLD.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Columbus OH spatial analysis data set - old numbering — oldcol","text":"row names COL.OLD region.id attribute COL.nb set columbus$NEIGNO.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/COL.OLD.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Columbus OH spatial analysis data set - old numbering — oldcol","text":"Anselin, Luc. 1988. Spatial econometrics: methods models. Dordrecht: Kluwer Academic, Table 12.1 p. 189.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/COL.OLD.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Columbus OH spatial analysis data set - old numbering — oldcol","text":"source data files prepared Luc Anselin, Spatial Analysis Laboratory, Department Agricultural Consumer Economics, University Illinois, Urbana-Champaign.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Permutation test for empirical Bayes index — EBImoran.mc","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"empirical Bayes index modification Moran's testing spatial autocorrelation rate, typically number observed cases population risk. index value tested using nsim random permutations index given spatial weighting scheme, establish rank observed statistic relation nsim simulated values.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"","code":"EBImoran.mc(n, x, listw, nsim, zero.policy = attr(listw, \"zero.policy\"), alternative = \"greater\", spChk=NULL, return_boot=FALSE, subtract_mean_in_numerator=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"n numeric vector counts cases length neighbours list listw x numeric vector populations risk length neighbours list listw listw listw object created example nb2listw nsim number permutations zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"two.sided\", \"less\" spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() return_boot return object class boot equivalent permutation bootstrap rather object class htest subtract_mean_in_numerator default TRUE, TRUE subtract mean z numerator EBI equation p. 2157 reference (consulted Renato Assunção 2016-02-19); February 2016 default FALSE agreeing printed paper.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"statistic used (m number observations): $$EBI = \\frac{m}{\\sum_{=1}^{m}\\sum_{j=1}^{m}w_{ij}} \\frac{\\sum_{=1}^{m}\\sum_{j=1}^{m}w_{ij}z_i z_j}{\\sum_{=1}^{m}(z_i - \\bar{z})^2} $$ : $$z_i = \\frac{p_i - b}{\\sqrt{v_i}}$$ : $$p_i = n_i / x_i$$ $$v_i = + (b / x_i)$$ $$b = \\sum_{=1}^{m} n_i / \\sum_{=1}^{m} x_i $$ $$= s^2 - b / (\\sum_{=1}^{m} x_i / m)$$ $$s^2 = \\sum_{=1}^{m} x_i (p_i - b)^2 / \\sum_{=1}^{m} x_i $$","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"list class htest mc.sim containing following components: statistic value observed Moran's . parameter rank observed Moran's . p.value pseudo p-value test. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data, number simulations. res nsim simulated values statistic, final value observed statistic z numerical vector Empirical Bayes indices z ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"Assunção RM, Reis EA 1999 new proposal adjust Moran's population density. Statistics Medicine 18, pp. 2147–2162; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"","code":"nc.sids <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\")[1], quiet=TRUE) rn <- as.character(nc.sids$FIPS) ncCC89_nb <- read.gal(system.file(\"weights/ncCC89.gal\", package=\"spData\")[1], region.id=rn) #> Warning: neighbour object has 3 sub-graphs EBImoran.mc(nc.sids$SID74, nc.sids$BIR74, nb2listw(ncCC89_nb, style=\"B\", zero.policy=TRUE), nsim=999, alternative=\"two.sided\", zero.policy=TRUE) #> The default for subtract_mean_in_numerator set TRUE from February 2016 #> #> \tMonte-Carlo simulation of Empirical Bayes Index (mean subtracted) #> #> data: cases: nc.sids$SID74, risk population: nc.sids$BIR74 #> weights: nb2listw(ncCC89_nb, style = \"B\", zero.policy = TRUE) #> number of simulations + 1: 1000 #> #> statistic = 0.25789, observed rank = 999, p-value = 0.002 #> alternative hypothesis: two.sided #> sids.p <- nc.sids$SID74 / nc.sids$BIR74 moran.mc(sids.p, nb2listw(ncCC89_nb, style=\"B\", zero.policy=TRUE), nsim=999, alternative=\"two.sided\", zero.policy=TRUE) #> #> \tMonte-Carlo simulation of Moran I #> #> data: sids.p #> weights: nb2listw(ncCC89_nb, style = \"B\", zero.policy = TRUE) #> number of simulations + 1: 1000 #> #> statistic = 0.20904, observed rank = 997, p-value = 0.006 #> alternative hypothesis: two.sided #>"},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":null,"dir":"Reference","previous_headings":"","what":"Global Empirical Bayes estimator — EBest","title":"Global Empirical Bayes estimator — EBest","text":"function computes global empirical Bayes estimates rates \"shrunk\" overall mean.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Global Empirical Bayes estimator — EBest","text":"","code":"EBest(n, x, family=\"poisson\")"},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Global Empirical Bayes estimator — EBest","text":"n numeric vector counts cases x numeric vector populations risk family either \"poisson\" rare conditions \"binomial\" non-rare conditions","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Global Empirical Bayes estimator — EBest","text":"Details implementation \"poisson\" family found Marshall, p. 284–5, Bailey Gatrell p. 303–306 exercise 8.2, pp. 328–330. \"binomial\" family, see Martuzzi Elliott (implementation Olaf Berke).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Global Empirical Bayes estimator — EBest","text":"data frame two columns: raw numerical vector raw (crude) rates estmm numerical vector empirical Bayes estimates parameters attribute list components: global method moments phi value m global method moments gamma value","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Global Empirical Bayes estimator — EBest","text":"Marshall R M (1991) Mapping disease mortality rates using Empirical Bayes Estimators, Applied Statistics, 40, 283–294; Bailey T, Gatrell (1995) Interactive Spatial Data Analysis, Harlow: Longman, pp. 303–306, Martuzzi M, Elliott P (1996) Empirical Bayes estimation small area prevalence non-rare conditions, Statistics Medicine 15, 1867–1873.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Global Empirical Bayes estimator — EBest","text":"Roger Bivand Roger.Bivand@nhh.Olaf Berke, Population Medicine, OVC, University Guelph, CANADA","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Global Empirical Bayes estimator — EBest","text":"","code":"auckland <- st_read(system.file(\"shapes/auckland.gpkg\", package=\"spData\")[1], quiet=TRUE) res <- EBest(auckland$M77_85, 9*auckland$Und5_81) attr(res, \"parameters\") #> $a #> [1] 7.284173e-07 #> #> $b #> [1] 0.002633436 #> auckland$estmm000 <- res$estmm*1000 plot(auckland[,\"estmm000\"], breaks=c(0,2,2.5,3,3.5,5), main=\"Infant mortality per 1000 per year\") data(huddersfield, package=\"spData\") res <- EBest(huddersfield$cases, huddersfield$total, family=\"binomial\") round(res[,1:2],4)*100 #> raw estmm #> 1 42.86 34.44 #> 2 28.95 29.56 #> 3 28.31 28.94 #> 4 21.43 28.93 #> 5 33.33 30.72 #> 6 30.86 30.43 #> 7 33.70 31.85 #> 8 45.61 35.93 #> 9 26.67 28.95 #> 10 29.41 29.95 #> 11 27.76 28.36 #> 12 33.75 31.75 #> 13 32.67 31.84 #> 14 22.91 25.36 #> 15 34.21 32.33 #> 16 33.77 31.72 #> 17 29.09 29.69 #> 18 15.87 24.36 #> 19 40.91 32.11 #> 20 40.00 31.01 #> 21 28.79 29.53 #> 22 38.89 31.47 #> 23 28.32 29.10 #> 24 33.33 31.44 #> 25 13.95 22.36 #> 26 33.77 31.72 #> 27 31.58 30.31 #> 28 33.33 30.42 #> 29 26.67 28.26 #> 30 63.64 33.57 #> 31 34.38 32.24 #> 32 20.00 27.62 #> 33 19.15 24.60 #> 34 25.53 28.54 #> 35 24.14 27.79 #> 36 44.00 32.98 #> 37 25.33 27.95 #> 38 18.18 26.96 #> 39 31.78 30.97 #> 40 32.20 30.88 #> 41 26.19 28.23 #> 42 19.05 26.65 #> 43 16.67 26.81 #> 44 20.00 28.66 #> 45 32.99 31.54 #> 46 50.00 31.97 #> 47 37.21 32.30 #> 48 32.79 31.13 #> 49 38.89 31.47 #> 50 25.00 27.26 #> 51 26.03 28.29 #> 52 30.43 30.18 #> 53 19.75 25.28 #> 54 50.00 31.61 #> 55 21.62 27.67 #> 56 22.22 27.88 #> 57 36.36 30.71 #> 58 31.25 30.22 #> 59 0.00 29.73 #> 60 29.41 29.95 #> 61 31.16 30.71 #> 62 33.33 30.58 #> 63 33.87 32.22 #> 64 30.00 30.04 #> 65 30.34 30.19 #> 66 40.74 35.00 #> 67 46.43 38.96 #> 68 34.21 31.91 #> 69 24.26 26.10 #> 70 29.41 29.75 #> 71 47.17 39.13"},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":null,"dir":"Reference","previous_headings":"","what":"Local Empirical Bayes estimator — EBlocal","title":"Local Empirical Bayes estimator — EBlocal","text":"function computes local empirical Bayes estimates rates \"shrunk\" neighbourhood mean neighbourhoods given nb neighbourhood list.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Local Empirical Bayes estimator — EBlocal","text":"","code":"EBlocal(ri, ni, nb, zero.policy = NULL, spChk = NULL, geoda=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Local Empirical Bayes estimator — EBlocal","text":"ri numeric vector counts cases length neighbours list nb; many zero counts, estimates may affected division zero, see https://stat.ethz.ch/pipermail/r-sig-geo/2022-January/028882.html ni numeric vector populations risk length neighbours list nb nb nb object neighbour relationships zero.policy default NULL, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() geoda default=FALSE, following Marshall's algorithm interpreted Bailey Gatrell, pp. 305-307, exercise 8.2, pp. 328-330 definition phi; TRUE definition phi used GeoDa (see discussion OpenSpace mailing list June 2003: http://agec221.agecon.uiuc.edu/pipermail/openspace/2003-June/thread.html)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Local Empirical Bayes estimator — EBlocal","text":"Details implementation found Marshall, p. 286, Bailey Gatrell p. 307 exercise 8.2, pp. 328–330. example results fully correspond sources slightly differing neighbourhoods, generally close. many zero counts, estimates may affected division zero, see https://stat.ethz.ch/pipermail/r-sig-geo/2022-January/028882.html.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Local Empirical Bayes estimator — EBlocal","text":"data frame two columns: raw numerical vector raw (crude) rates est numerical vector local empirical Bayes estimates parameters attribute list components (zero, estimate NaN, https://stat.ethz.ch/pipermail/r-sig-geo/2022-January/028882.html): numerical vector local phi values m numerical vector local gamma values","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Local Empirical Bayes estimator — EBlocal","text":"Marshall R M (1991) Mapping disease mortality rates using Empirical Bayes Estimators, Applied Statistics, 40, 283–294; Bailey T, Gatrell (1995) Interactive Spatial Data Analysis, Harlow: Longman, pp. 303–306.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Local Empirical Bayes estimator — EBlocal","text":"Roger Bivand Roger.Bivand@nhh., based contributions Marilia Carvalho","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Local Empirical Bayes estimator — EBlocal","text":"","code":"auckland <- st_read(system.file(\"shapes/auckland.gpkg\", package=\"spData\")[1], quiet=TRUE) auckland.nb <- poly2nb(auckland) res <- EBlocal(auckland$M77_85, 9*auckland$Und5_81, auckland.nb) auckland$est000 <- res$est*1000 plot(auckland[,\"est000\"], breaks=c(0,2,2.5,3,3.5,8), main=\"Infant mortality per 1000 per year\")"},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":null,"dir":"Reference","previous_headings":"","what":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"function implements chi-square based test statistic local spatial heteroscedasticity (LOSH) proposed Ord & Getis (2012).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"","code":"LOSH.cs(x, listw, zero.policy = attr(listw, \"zero.policy\"), na.action = na.fail, p.adjust.method = \"none\", spChk = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass used, zero substituted NA values calculating spatial lag. (Note na.exclude work properly starting R 1.9.0, na.omit na.exclude assign wrong classes 1.8.*) p.adjust.method character string specifying probability value adjustment multiple tests, default \"none\"; see p.adjustSP. Note number multiple tests region taken number neighbours + 1 region, rather total number regions. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption()","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"test uses = 2 (see LOSH) chi-square based inference applicable exponents. function makes use LOSH calculations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"Hi LOSH statistic E.Hi expectation LOSH Var.Hi variance LOSH Z.Hi approximately chi-square distributed test statistics x_bar_i local spatially weighted mean values ei residuals local spatially weighted mean values Pr() p-values Hi obtained non-central Chi-square distribution \\(2/Var.Hi\\) degrees freedom","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"Ord, J. K., & Getis, . 2012. Local spatial heteroscedasticity (LOSH), Annals Regional Science, 48 (2), 529–539.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"René Westerholt rene.westerholt@tu-dortmund.de","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"","code":"data(boston, package=\"spData\") resLOSH <- LOSH.cs(boston.c$NOX, nb2listw(boston.soi)) hist(resLOSH[,\"Hi\"]) mean(resLOSH[,\"Hi\"]) #> [1] 0.9919329"},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":null,"dir":"Reference","previous_headings":"","what":"Local spatial heteroscedasticity — LOSH","title":"Local spatial heteroscedasticity — LOSH","text":"Local spatial heteroscedasticity calculated location based spatial weights object used. statistic : $$H_i = \\frac{\\sum_j^n w_{ij} \\cdot |e_j|^}{h_1 \\cdot \\sum_j^n w_{ij}}$$ $$e_j = x_j - \\bar{x}_j$$ $$\\bar{x}_j = \\frac{\\sum_k^n w_{jk} \\cdot x_k}{\\sum_k^n w_{jk}}$$ expectation variance given Ord & Getis (2012). exponent allows investigating different types mean dispersal.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Local spatial heteroscedasticity — LOSH","text":"","code":"LOSH(x, listw, a=2, var_hi=TRUE, zero.policy=attr(listw, \"zero.policy\"), na.action=na.fail, spChk=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Local spatial heteroscedasticity — LOSH","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw exponent applied local residuals; default value 2 leads measure heterogeneity spatial variance var_hi default TRUE, moments test statistics calculated location; FALSE, plain LOSH measures, \\(\\bar{x}_i\\) \\(e_i\\) calculated zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass used, zero substituted NA values calculating spatial lag. (Note na.exclude work properly starting R 1.9.0, na.omit na.exclude assign wrong classes 1.8.*) spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption()","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Local spatial heteroscedasticity — LOSH","text":"addition LOSH measure, values returned include local spatially weighted mean values \\(\\bar{x}_i\\) local residuals \\(e_i\\) estimated means. values facilitate interpretation LOSH values. , specified var_hi, statistical moments test statistics proposed Ord & Getis (2012) also calculated returned.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Local spatial heteroscedasticity — LOSH","text":"Hi LOSH statistic E.Hi (optional) expectation LOSH Var.Hi (optional) variance LOSH Z.Hi (optional) approximately Chi-square distributed test statistics x_bar_i local spatially weighted mean values ei residuals local spatially weighted mean values","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Local spatial heteroscedasticity — LOSH","text":"Ord, J. K., & Getis, . 2012. Local spatial heteroscedasticity (LOSH), Annals Regional Science, 48 (2), 529–539.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Local spatial heteroscedasticity — LOSH","text":"René Westerholt rene.westerholt@tu-dortmund.de","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Local spatial heteroscedasticity — LOSH","text":"","code":"data(boston, package=\"spData\") resLOSH <- LOSH(boston.c$NOX, nb2listw(boston.soi)) hist(resLOSH[,\"Hi\"]) mean(resLOSH[,\"Hi\"]) #> [1] 0.9919329"},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"function draws inferences local spatial heteroscedasticity (LOSH) means randomisation-based Monte-Carlo bootstrap proposed Xu et al. (2014).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"","code":"LOSH.mc(x, listw, a = 2, nsim = 99, zero.policy = attr(listw, \"zero.policy\"), na.action = na.fail, spChk = NULL, adjust.n = TRUE, p.adjust.method = \"none\")"},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw exponent applied local residuals; default value 2 leads measure heterogeneity spatial variance nsim number randomisations used bootstrap zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass used, zero substituted NA values calculating spatial lag. (Note na.exclude work properly starting R 1.9.0, na.omit na.exclude assign wrong classes 1.8.*) spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted p.adjust.method character string specifying probability value adjustment multiple tests, default \"none\"; see p.adjustSP. Note number multiple tests region taken number neighbours + 1 region, rather total number regions.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"test calculates LOSH (see LOSH) estimates pseudo p-values conditional bootstrap. Thereby, -th value location held fixed, whereas values permuted nsim times spatial units.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"Hi LOSH statistic E.Hi expectation LOSH Var.Hi variance LOSH Z.Hi approximately chi-square distributed test statistics x_bar_i local spatially weighted mean values ei residuals local spatially weighted mean values Pr() p-values Hi obtained conditional bootstrap distribution","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"Ord, J. K., & Getis, . 2012. Local spatial heteroscedasticity (LOSH), Annals Regional Science, 48 (2), 529–539; Xu, M., Mei, C. L., & Yan, N. 2014. note null distribution local spatial heteroscedasticity (LOSH) statistic. Annals Regional Science, 52 (3), 697–710.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"René Westerholt rene.westerholt@tu-dortmund.de","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"","code":"data(columbus, package=\"spData\") resLOSH_mc <- LOSH.mc(columbus$CRIME, nb2listw(col.gal.nb), 2, 100) summary(resLOSH_mc) #> Hi x_bar_i ei Pr() #> Min. :0.03438 Min. :13.85 Min. :2.982e-02 Min. :0.009901 #> 1st Qu.:0.23838 1st Qu.:24.71 1st Qu.:7.011e+00 1st Qu.:0.079208 #> Median :0.66689 Median :35.90 Median :5.211e+01 Median :0.653465 #> Mean :1.06592 Mean :34.88 Mean :1.519e+02 Mean :0.552233 #> 3rd Qu.:1.59680 3rd Qu.:45.39 3rd Qu.:1.051e+02 3rd Qu.:0.900990 #> Max. :4.68765 Max. :54.91 Max. :2.455e+03 Max. :0.990099 resLOSH_cs <- LOSH.cs(columbus$CRIME, nb2listw(col.gal.nb)) summary(resLOSH_cs) #> Hi E.Hi Var.Hi Z.Hi #> Min. :0.03438 Min. :1 Min. :0.4972 Min. :0.04356 #> 1st Qu.:0.23838 1st Qu.:1 1st Qu.:0.9136 1st Qu.:0.35070 #> Median :0.66689 Median :1 Median :1.4342 Median :1.19176 #> Mean :1.06592 Mean :1 Mean :1.4758 Mean :1.89447 #> 3rd Qu.:1.59680 3rd Qu.:1 3rd Qu.:1.9547 3rd Qu.:2.65120 #> Max. :4.68765 Max. :1 Max. :2.9958 Max. :7.25681 #> x_bar_i ei Pr() #> Min. :13.85 Min. :2.982e-02 Min. :0.0190 #> 1st Qu.:24.71 1st Qu.:7.011e+00 1st Qu.:0.2050 #> Median :35.90 Median :5.211e+01 Median :0.5264 #> Mean :34.88 Mean :1.519e+02 Mean :0.4507 #> 3rd Qu.:45.39 3rd Qu.:1.051e+02 3rd Qu.:0.6529 #> Max. :54.91 Max. :2.455e+03 Max. :0.9540 plot(resLOSH_mc[,\"Pr()\"], resLOSH_cs[,\"Pr()\"])"},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":null,"dir":"Reference","previous_headings":"","what":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"Rao's score adjusted Rao's score tests linear hypotheses applied fitted linear model examine whether either spatially lagged dependent variable lag spatially lagged independent variable(s) WX included model, (SDM). Adjusted tests provided lag WX adapting presence , joint test . joint test equal unadjusted one plus adjusted . addition, draft tests added Koley (2024, section 6) spatial Durbin error models examine whether either spatially lagged error err spatially lagged independent variable(s) WX included model, (SDEM); orthogonality, adjusted tests required. spatial lags categorical variables poorly understood, version 1.3-11 warnings given categorical variables included Durbin term.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"","code":"SD.RStests(model, listw, zero.policy = attr(listw, \"zero.policy\"), test = \"SDM\", Durbin = TRUE) have_factor_preds_mf(mf) warn_factor_preds(x)"},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"model object class lm returned lm listw listw object created example nb2listw, expected row-standardised (W-style) zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA test test=“SDM” computes SDM tests, character vector tests requested chosen SDM_RSlag, SDM_adjRSlag, SDM_RSWX, SDM_adjRSWX, SDM_Joint, test=“SDEM” computes SDEM tests, character vector tests requested chosen SDEM_RSerr, SDEM_RSWX, SDEM_Joint; test=“” computes tests Durbin default TRUE Durbin models including WX; TRUE, full spatial Durbin model; formula object, subset explanatory variables lag mf model.frame object x object created have_factor_preds_mf","code":""},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"list class LMtestlist htest objects, : statistic value Lagrange Multiplier test. parameter number degrees freedom p.value p-value test. method character string giving method used. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"Malabika Koley Anil K. Bera (2024) use, use spatial Durbin model? – question, Spatial Economic Analysis, 19:1, 30-56, doi:10.1080/17421772.2023.2256810 ; Malabika Koley (2024) Specification testing spatial econometric models, Ph.D. dissertation, University Illinois Urbana-Champaign, pp. 78-118, 148-156; https://hdl.handle.net/2142/124329.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"Roger Bivand Roger.Bivand@nhh., Malabika Koley Anil K. Bera","code":""},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"results example agree Table 3, p. 22 Koley Bera (2024).","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"","code":"columbus <- sf::st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1]) #> Reading layer `columbus' from data source #> `/home/rsb/lib/r_libs/spData/shapes/columbus.gpkg' using driver `GPKG' #> Simple feature collection with 49 features and 20 fields #> Geometry type: POLYGON #> Dimension: XY #> Bounding box: xmin: 5.874907 ymin: 10.78863 xmax: 11.28742 ymax: 14.74245 #> Projected CRS: Undefined Cartesian SRS with unknown unit col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) col.listw <- nb2listw(col.gal.nb, style=\"W\") columbus$fEW <- factor(columbus$EW) columbus$fDISCBD <- ordered(cut(columbus$DISCBD, c(0, 1.5, 3, 4.5, 6))) f <- formula(CRIME ~ INC + HOVAL + fDISCBD + fEW) lm_obj <- lm(f, data=columbus) summary(lm.RStests(lm_obj, col.listw, test=\"all\")) #> \tRao's score (a.k.a Lagrange multiplier) diagnostics for spatial #> \tdependence #> data: #> model: lm(formula = f, data = columbus) #> test weights: col.listw #> #> statistic parameter p.value #> RSerr 0.047443 1 0.8276 #> RSlag 0.718623 1 0.3966 #> adjRSerr 0.721842 1 0.3955 #> adjRSlag 1.393021 1 0.2379 #> SARMA 1.440465 2 0.4866 res <- SD.RStests(lm_obj, col.listw, test=\"SDM\") #> Warning: use of spatially lagged factors (categorical variables) #> fDISCBD, fEW #> is not well-understood #> Warning: In addition variable: #> fDISCBD #> is ordered (ordinal) with polynomial contrasts. summary(res) #> \tRao's score test spatial Durbin diagnostics #> data: #> model: lm(formula = f, data = columbus) #> weights: col.listw #> #> statistic parameter p.value #> SDM_RSlag 0.718623 1 0.39660 #> SDM_adjRSlag 0.047443 1 0.82757 #> SDM_RSWX 12.904287 6 0.04458 * #> SDM_adjRSWX 12.233108 6 0.05697 . #> SDM_Joint 12.951730 7 0.07329 . #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 all.equal(unname(res$SDM_Joint$statistic), unname(res$SDM_RSlag$statistic + res$SDM_adjRSWX$statistic)) #> [1] TRUE all.equal(unname(res$SDM_Joint$statistic), unname(res$SDM_adjRSlag$statistic + res$SDM_RSWX$statistic)) #> [1] TRUE res <- SD.RStests(lm_obj, col.listw, test=\"SDEM\") #> Warning: use of spatially lagged factors (categorical variables) #> fDISCBD, fEW #> is not well-understood #> Warning: In addition variable: #> fDISCBD #> is ordered (ordinal) with polynomial contrasts. summary(res) #> \tRao's score test spatial Durbin diagnostics #> data: #> model: lm(formula = f, data = columbus) #> weights: col.listw #> #> statistic parameter p.value #> SDEM_RSerr 0.047443 1 0.82757 #> SDEM_RSWX 12.904287 6 0.04458 * #> SDEM_Joint 12.951730 7 0.07329 . #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 all.equal(unname(res$SDEM_Joint$statistic), unname(res$SDEM_RSerr$statistic + res$SDEM_RSWX$statistic)) #> [1] TRUE summary(SD.RStests(lm_obj, nb2listw(col.gal.nb, style=\"C\"), test=\"all\")) #> Warning: Spatial weights matrix not row standardized #> Warning: use of spatially lagged factors (categorical variables) #> fDISCBD, fEW #> is not well-understood #> Warning: In addition variable: #> fDISCBD #> is ordered (ordinal) with polynomial contrasts. #> \tRao's score test spatial Durbin diagnostics #> data: #> model: lm(formula = f, data = columbus) #> weights: nb2listw(col.gal.nb, style = \"C\") #> #> statistic parameter p.value #> SDM_RSlag 1.3907611 1 0.23828 #> SDM_adjRSlag 0.0030013 1 0.95631 #> SDM_RSWX 12.2469692 7 0.09272 . #> SDM_adjRSWX 10.8592093 7 0.14488 #> SDM_Joint 12.2499705 8 0.14039 #> SDEM_RSerr 0.0030013 1 0.95631 #> SDEM_RSWX 12.2469692 7 0.09272 . #> SDEM_Joint 12.2499705 8 0.14039 #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 summary(SD.RStests(lm_obj, col.listw, test=\"all\", Durbin= ~ INC)) #> \tRao's score test spatial Durbin diagnostics #> data: #> model: lm(formula = f, data = columbus) #> weights: col.listw #> Durbin: ~ INC #> #> statistic parameter p.value #> SDM_RSlag 0.718623 1 0.3966 #> SDM_adjRSlag 0.269636 1 0.6036 #> SDM_RSWX 0.726478 1 0.3940 #> SDM_adjRSWX 0.277492 1 0.5984 #> SDM_Joint 0.996114 2 0.6077 #> SDEM_RSerr 0.047443 1 0.8276 #> SDEM_RSWX 0.726478 1 0.3940 #> SDEM_Joint 0.773922 2 0.6791 lm_obj0 <- lm(I(scale(CRIME)) ~ 0 + I(scale(INC)) + I(scale(HOVAL)), data=columbus) summary(SD.RStests(lm_obj0, col.listw, test=\"all\")) #> \tRao's score test spatial Durbin diagnostics #> data: #> model: lm(formula = I(scale(CRIME)) ~ 0 + I(scale(INC)) + #> I(scale(HOVAL)), data = columbus) #> weights: col.listw #> #> statistic parameter p.value #> SDM_RSlag 7.8250 1 0.005153 ** #> SDM_adjRSlag 4.6111 1 0.031765 * #> SDM_RSWX 6.0609 2 0.048295 * #> SDM_adjRSWX 2.8470 2 0.240873 #> SDM_Joint 10.6720 3 0.013638 * #> SDEM_RSerr 4.6111 1 0.031765 * #> SDEM_RSWX 6.0609 2 0.048295 * #> SDEM_Joint 10.6720 3 0.013638 * #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 columbusNA <- columbus columbusNA$HOVAL[15] <- NA lm_objNA <- lm(CRIME ~ INC + HOVAL, data=columbusNA) summary(SD.RStests(lm_objNA, col.listw, test=\"all\")) #> \tRao's score test spatial Durbin diagnostics #> data: #> model: lm(formula = CRIME ~ INC + HOVAL, data = columbusNA) #> weights: col.listw #> #> statistic parameter p.value #> SDM_RSlag 7.6010 1 0.005834 ** #> SDM_adjRSlag 4.4716 1 0.034463 * #> SDM_RSWX 6.0812 2 0.047807 * #> SDM_adjRSWX 2.9518 2 0.228576 #> SDM_Joint 10.5527 3 0.014407 * #> SDEM_RSerr 4.4716 1 0.034463 * #> SDEM_RSWX 6.0812 2 0.047807 * #> SDEM_Joint 10.5527 3 0.014407 * #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1"},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Aggregate a spatial neighbours object — aggregate.nb","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"method aggregates spatial neighbours object, creating new object listing neighbours aggregates.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"","code":"# S3 method for class 'nb' aggregate(x, IDs, remove.self = TRUE, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"x nb neighbour object IDs character vector IDs grouping members neighbour object remove.self default TRUE: remove self-neighbours resulting aggregation ... unused - arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"nb neighbour object, empty aggregates dropped.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"Method suggested Roberto Patuelli","code":""},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"","code":"data(used.cars, package=\"spData\") data(state) cont_st <- match(attr(usa48.nb, \"region.id\"), state.abb) cents <- as.matrix(as.data.frame(state.center))[cont_st,] opar <- par(mfrow=c(2,1)) plot(usa48.nb, cents, xlim=c(-125, -65), ylim=c(25, 50)) IDs <- as.character(state.division[cont_st]) agg_cents <- aggregate(cents, list(IDs), mean) agg_nb <- aggregate(usa48.nb, IDs) plot(agg_nb, agg_cents[, 2:3], xlim=c(-125, -65), ylim=c(25, 50)) text(agg_cents[, 2:3], agg_cents[, 1], cex=0.6) par(opar)"},{"path":"https://r-spatial.github.io/spdep/reference/airdist.html","id":null,"dir":"Reference","previous_headings":"","what":"Measure distance from plot — airdist","title":"Measure distance from plot — airdist","text":"Measure distance two points plot using locator; function checks par(\"plt\") par(\"usr\") try ensure aspect ratio y/x 1, units measurement x y equivalent.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/airdist.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Measure distance from plot — airdist","text":"","code":"airdist(ann=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/airdist.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Measure distance from plot — airdist","text":"ann annotate plot line measured distance","code":""},{"path":"https://r-spatial.github.io/spdep/reference/airdist.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Measure distance from plot — airdist","text":"list members: dist distance measured coords coordinates distance measured","code":""},{"path":"https://r-spatial.github.io/spdep/reference/airdist.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Measure distance from plot — airdist","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":null,"dir":"Reference","previous_headings":"","what":"Distance-weighted autocovariate — autocov_dist","title":"Distance-weighted autocovariate — autocov_dist","text":"Calculates autocovariate used autonormal, autopoisson autologistic regression. Three distance-weighting schemes available.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Distance-weighted autocovariate — autocov_dist","text":"","code":"autocov_dist(z, xy, nbs = 1, type = \"inverse\", zero.policy = NULL, style = \"B\", longlat=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Distance-weighted autocovariate — autocov_dist","text":"z response variable xy matrix coordinates SpatialPoints, sf sfc points object nbs neighbourhood radius; default 1 type weighting scheme: \"one\" gives equal weight data points neighbourhood; \"inverse\" (default) weights inverse distance; \"inverse.squared\" weights square \"inverse\" zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors style default “B” (changed “W” 2015-01-27); style can take values “W”, “B”, “C”, “U”, “S” longlat TRUE point coordinates longitude-latitude decimal, case distances measured kilometers; xy SpatialPoints object, value taken object ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Distance-weighted autocovariate — autocov_dist","text":"numeric vector autocovariate values","code":""},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Distance-weighted autocovariate — autocov_dist","text":"validity approach strongly hinges correct choice neighbourhood scheme! Using style=\"B\" ensures symmetry neighbourhood matrix (.e. \\(w_{nm} = w_{mn}\\)). Please see Bardos et al. (2015) details.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Distance-weighted autocovariate — autocov_dist","text":"Augustin N.H., Mugglestone M.. Buckland S.T. (1996) autologistic model spatial distribution wildlife. Journal Applied Ecology, 33, 339-347; Gumpertz M.L., Graham J.M. Ristaino J.B. (1997) Autologistic model spatial pattern Phytophthora epidemic bell pepper: effects soil variables disease presence. Journal Agricultural, Biological Environmental Statistics, 2, 131-156; Bardos, D.C., Guillera-Arroita, G. Wintle, B.. (2015) Valid auto-models spatially autocorrelated occupancy abundance data. arXiv, 1501.06529.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Distance-weighted autocovariate — autocov_dist","text":"Carsten F. Dormann Roger Bivand","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Distance-weighted autocovariate — autocov_dist","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) #xy <- cbind(columbus$X, columbus$Y) xy <- st_coordinates(st_centroid(st_geometry(columbus), of_largest_polygon=TRUE)) ac1a <- autocov_dist(columbus$CRIME, xy, nbs=10, style=\"B\", type=\"one\") acinva <- autocov_dist(columbus$CRIME, xy, nbs=10, style=\"B\", type=\"inverse\") acinv2a <- autocov_dist(columbus$CRIME, xy, nbs=10, style=\"B\", type=\"inverse.squared\") plot(ac1a ~ columbus$CRIME, pch=16, ylim=c(0,9000)) points(acinva ~ columbus$CRIME, pch=16, col=\"red\") points(acinv2a ~ columbus$CRIME, pch=16, col=\"blue\") legend(\"topleft\", legend=c(\"one\", \"inverse\", \"inverse.squared\"), col=c(\"black\", \"red\", \"blue\"), bty=\"n\", pch=16) nb <- dnearneigh(xy, 0, 10) lw <- nb2listw(nb, style=\"B\") ac1b <- lag(lw, columbus$CRIME) all.equal(ac1b, ac1a) #> [1] TRUE nbd <- nbdists(nb, xy) gl <- lapply(nbd, function(x) 1/x) lw <- nb2listw(nb, glist=gl, style=\"B\") acinvb <- lag(lw, columbus$CRIME) all.equal(acinvb, acinva) #> [1] TRUE gl2 <- lapply(nbd, function(x) 1/(x^2)) lw <- nb2listw(nb, glist=gl2, style=\"B\") acinv2b <- lag(lw, columbus$CRIME) all.equal(acinv2b, acinv2a) #> [1] TRUE #xy <- SpatialPoints(xy) #acinva <- autocov_dist(columbus$CRIME, xy, nbs=10, style=\"W\", # type=\"inverse\") #nb <- dnearneigh(xy, 0, 10) #nbd <- nbdists(nb, xy) #gl <- lapply(nbd, function(x) 1/x) #lw <- nb2listw(nb, glist=gl) #acinvb <- lag(lw, columbus$CRIME) #all.equal(acinvb, acinva) acinvc <- autocov_dist(columbus$CRIME, st_centroid(st_geometry(columbus), of_largest_polygon=TRUE), nbs=10, style=\"W\", type=\"inverse\") all.equal(acinvc, acinva) #> [1] \"Mean relative difference: 40.63575\""},{"path":"https://r-spatial.github.io/spdep/reference/bhicv.html","id":null,"dir":"Reference","previous_headings":"","what":"Data set with 4 life condition indices of Belo Horizonte region — bhicv","title":"Data set with 4 life condition indices of Belo Horizonte region — bhicv","text":"data collected inthe Atlas condition indices published Joao Pinheiro Foundation UNDP.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/bhicv.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Data set with 4 life condition indices of Belo Horizonte region — bhicv","text":"shape polygon object seven variables: id identificator Name Name city Population population city HLCI Health Life Condition Index ELCI Education Life Condition Index CLCI Children Life Condition Index ELCI Economic Life Condition Index","code":""},{"path":"https://r-spatial.github.io/spdep/reference/bhicv.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Data set with 4 life condition indices of Belo Horizonte region — bhicv","text":"","code":"GDAL37 <- numeric_version(unname(sf::sf_extSoftVersion()[\"GDAL\"]), strict=FALSE) (GDAL37 <- ifelse(is.na(GDAL37), FALSE, GDAL37 >= \"3.7.0\")) #> [1] TRUE file <- \"etc/shapes/bhicv.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) { bh <- st_read(zipfile) } else { td <- tempdir() bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE) target <- unzip(zipfile, files=bn, exdir=td) bh <- st_read(target) } #> Reading layer `bhicv' from data source #> `/tmp/Rtmp5vVziX/temp_libpath224d25059ed81/spdep/etc/shapes/bhicv.gpkg.zip' #> using driver `GPKG' #> Simple feature collection with 98 features and 8 fields #> Geometry type: POLYGON #> Dimension: XY #> Bounding box: xmin: -45.02175 ymin: -20.93007 xmax: -42.50321 ymax: -18.08342 #> Geodetic CRS: Corrego Alegre 1970-72"},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":null,"dir":"Reference","previous_headings":"","what":"Cardinalities for neighbours lists — card","title":"Cardinalities for neighbours lists — card","text":"function tallies numbers neighbours regions neighbours list.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Cardinalities for neighbours lists — card","text":"","code":"card(nb)"},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Cardinalities for neighbours lists — card","text":"nb neighbours list object class nb","code":""},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Cardinalities for neighbours lists — card","text":"integer vector numbers neighbours regions neighbours list.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Cardinalities for neighbours lists — card","text":"“nb” objects stored lists integer vectors, vectors contain either indices range 1:n n length(nb) neighbours region , .integer(0) signal neighbours. function card(nb) used extract numbers neighbours “nb” object.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Cardinalities for neighbours lists — card","text":"Bivand R, Pebesma EJ, Gomez-Rubio V, (2008) Applied Spatial Data Analysis R, Springer, New York, pp. 239-251; Bivand R, Portnov B, (2004) Exploring spatial data analysis techniques using R: case observations neighbours. : Anselin L, Florax R, Rey S, (eds.), Advances Spatial Econometrics, Methodology, Tools Applications. Berlin: Springer-Verlag, pp. 121-142, doi:10.1007/978-3-662-05617-2_6 .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Cardinalities for neighbours lists — card","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Cardinalities for neighbours lists — card","text":"","code":"col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) table(card(col.gal.nb)) #> #> 2 3 4 5 6 7 8 9 10 #> 7 7 13 4 9 6 1 1 1"},{"path":"https://r-spatial.github.io/spdep/reference/cell2nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Generate neighbours list for grid cells — cell2nb","title":"Generate neighbours list for grid cells — cell2nb","text":"function generates list neighbours grid cells. Helper functions used convert vector indices row column grid positions, rook (shared edge) queen (shared edge vertex) neighbour definitions applied type. torus TRUE, grid mapped onto torus, removing edge effects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/cell2nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generate neighbours list for grid cells — cell2nb","text":"","code":"cell2nb(nrow, ncol, type=\"rook\", torus=FALSE, legacy=FALSE, x=NULL) vi2mrc(i, nrow, ncol)"},{"path":"https://r-spatial.github.io/spdep/reference/cell2nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Generate neighbours list for grid cells — cell2nb","text":"nrow number rows grid, may also object inheriting class \"SpatialGrid\" \"GridTopology\" cell2nb ncol number columns grid; nrow x object inheriting class \"SpatialGrid\" \"GridTopology\", may omitted type default rook, may also queen torus default FALSE, TRUE map grid onto torus legacy default FALSE, nrow/ncol reversed, TRUE wrong col/row directions (see https://github.com/r-spatial/spdep/issues/20) x given, object inheriting class \"SpatialGrid\" \"GridTopology\", replaces nrow ncol vector vector indices corresponding rowcol, matrix two columns row, column indices","code":""},{"path":"https://r-spatial.github.io/spdep/reference/cell2nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Generate neighbours list for grid cells — cell2nb","text":"function returns object class nb list integer vectors containing neighbour region number ids. See card details “nb” objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/cell2nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Generate neighbours list for grid cells — cell2nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/cell2nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Generate neighbours list for grid cells — cell2nb","text":"","code":"nb7rt <- cell2nb(7, 7) summary(nb7rt) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 168 #> Percentage nonzero weights: 6.997085 #> Average number of links: 3.428571 #> Link number distribution: #> #> 2 3 4 #> 4 20 25 #> 4 least connected regions: #> 1:1 7:1 1:7 7:7 with 2 links #> 25 most connected regions: #> 2:2 3:2 4:2 5:2 6:2 2:3 3:3 4:3 5:3 6:3 2:4 3:4 4:4 5:4 6:4 2:5 3:5 4:5 5:5 6:5 2:6 3:6 4:6 5:6 6:6 with 4 links xyc <- attr(nb7rt, \"region.id\") xy <- matrix(as.integer(unlist(strsplit(xyc, \":\"))), ncol=2, byrow=TRUE) plot(nb7rt, xy) nb7rt <- cell2nb(7, 7, torus=TRUE) summary(nb7rt) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 196 #> Percentage nonzero weights: 8.163265 #> Average number of links: 4 #> Link number distribution: #> #> 4 #> 49 #> 49 least connected regions: #> 1:1 2:1 3:1 4:1 5:1 6:1 7:1 1:2 2:2 3:2 4:2 5:2 6:2 7:2 1:3 2:3 3:3 4:3 5:3 6:3 7:3 1:4 2:4 3:4 4:4 5:4 6:4 7:4 1:5 2:5 3:5 4:5 5:5 6:5 7:5 1:6 2:6 3:6 4:6 5:6 6:6 7:6 1:7 2:7 3:7 4:7 5:7 6:7 7:7 with 4 links #> 49 most connected regions: #> 1:1 2:1 3:1 4:1 5:1 6:1 7:1 1:2 2:2 3:2 4:2 5:2 6:2 7:2 1:3 2:3 3:3 4:3 5:3 6:3 7:3 1:4 2:4 3:4 4:4 5:4 6:4 7:4 1:5 2:5 3:5 4:5 5:5 6:5 7:5 1:6 2:6 3:6 4:6 5:6 6:6 7:6 1:7 2:7 3:7 4:7 5:7 6:7 7:7 with 4 links run <- FALSE if (require(\"sp\", quietly=TRUE)) run <- TRUE if (run) { # https://github.com/r-spatial/spdep/issues/20 GT <- GridTopology(c(1, 1), c(1, 1), c(10, 50)) SPix <- as(SpatialGrid(GT), \"SpatialPixels\") nb_rook_cont <- poly2nb(as(SPix, \"SpatialPolygons\"), queen=FALSE) nb_rook_dist <- dnearneigh(coordinates(SPix), 0, 1.01) all.equal(nb_rook_cont, nb_rook_dist, check.attributes=FALSE) ## [1] TRUE } #> [1] TRUE if (run) { t.nb <- cell2nb(GT, type='rook', legacy=TRUE) isTRUE(all.equal(nb_rook_cont, t.nb, check.attributes=FALSE)) ## [1] FALSE } #> [1] FALSE if (run) { t.nb <- cell2nb(GT, type='rook') isTRUE(all.equal(nb_rook_cont, t.nb, check.attributes=FALSE)) ## [1] TRUE } #> [1] TRUE if (run) { # https://github.com/r-spatial/spdep/issues/55 # problem reported in issue caused by rep() cycling in unexpected order GT <- GridTopology(c(1, 1), c(1, 1), c(22, 11)) SPix <- as(SpatialGrid(GT), \"SpatialPixels\") nb_rook_cont <- poly2nb(as(SPix, \"SpatialPolygons\"), queen=FALSE) nb_rook_dist <- dnearneigh(coordinates(SPix), 0, 1.01) all.equal(nb_rook_cont, nb_rook_dist, check.attributes=FALSE) } #> [1] TRUE if (run) { t.nb <- cell2nb(GT, type='rook', legacy=TRUE) isTRUE(all.equal(nb_rook_cont, t.nb, check.attributes=FALSE)) ## [1] FALSE } #> [1] FALSE if (run) { t.nb <- cell2nb(GT, type='rook', legacy=FALSE) isTRUE(all.equal(nb_rook_cont, t.nb, check.attributes=FALSE)) ## [1] TRUE } #> [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":null,"dir":"Reference","previous_headings":"","what":"Choynowski probability map values — choynowski","title":"Choynowski probability map values — choynowski","text":"Calculates Choynowski probability map values.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Choynowski probability map values — choynowski","text":"","code":"choynowski(n, x, row.names=NULL, tol = .Machine$double.eps^0.5, legacy=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Choynowski probability map values — choynowski","text":"n numeric vector counts cases x numeric vector populations risk row.names row names passed output data frame tol accumulate values observed counts >= expected value less tol legacy default FALSE using vectorised alternating side ppois version, true use original version written sources iterating tol","code":""},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Choynowski probability map values — choynowski","text":"data frame columns: pmap Poisson probability map values: probablility getting “extreme” count actually observed, one-tailed less expected expected folded together type logical: TRUE observed count less expected","code":""},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Choynowski probability map values — choynowski","text":"Choynowski, M (1959) Maps based probabilities, Journal American Statistical Association, 54, 385–388; Cressie, N, Read, TRC (1985), sudden infant deaths come clusters? Statistics Decisions, Supplement Issue 2, 333–349; Bailey T, Gatrell (1995) Interactive Spatial Data Analysis, Harlow: Longman, pp. 300–303.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Choynowski probability map values — choynowski","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Choynowski probability map values — choynowski","text":"","code":"auckland <- st_read(system.file(\"shapes/auckland.gpkg\", package=\"spData\")[1], quiet=TRUE) auckland.nb <- poly2nb(auckland) res <- choynowski(auckland$M77_85, 9*auckland$Und5_81) resl <- choynowski(auckland$M77_85, 9*auckland$Und5_81, legacy=TRUE) all.equal(res, resl) #> [1] TRUE rt <- sum(auckland$M77_85)/sum(9*auckland$Und5_81) ch_ppois_pmap <- numeric(length(auckland$Und5_81)) side <- c(\"greater\", \"less\") for (i in seq(along=ch_ppois_pmap)) { ch_ppois_pmap[i] <- poisson.test(auckland$M77_85[i], r=rt, T=(9*auckland$Und5_81[i]), alternative=side[(res$type[i]+1)])$p.value } all.equal(ch_ppois_pmap, res$pmap) #> [1] TRUE res1 <- probmap(auckland$M77_85, 9*auckland$Und5_81) table(abs(res$pmap - res1$pmap) < 0.00001, res$type) #> #> FALSE TRUE #> FALSE 74 0 #> TRUE 0 93 lt005 <- (res$pmap < 0.05) & (res$type) ge005 <- (res$pmap < 0.05) & (!res$type) cols <- rep(\"nonsig\", length(lt005)) cols[lt005] <- \"low\" cols[ge005] <- \"high\" auckland$cols <- factor(cols) plot(auckland[,\"cols\"], main=\"Probability map\")"},{"path":"https://r-spatial.github.io/spdep/reference/columbus.html","id":null,"dir":"Reference","previous_headings":"","what":"Columbus OH spatial analysis data set — columbus","title":"Columbus OH spatial analysis data set — columbus","text":"data set now part spData package","code":""},{"path":"https://r-spatial.github.io/spdep/reference/columbus.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Columbus OH spatial analysis data set — columbus","text":"","code":"data(columbus)"},{"path":"https://r-spatial.github.io/spdep/reference/columbus.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Columbus OH spatial analysis data set — columbus","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1])"},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":null,"dir":"Reference","previous_headings":"","what":"Depth First Search on Neighbor Lists — Graph Components","title":"Depth First Search on Neighbor Lists — Graph Components","text":"n.comp.nb() finds number disjoint connected subgraphs graph depicted nb.obj - spatial neighbours list object.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Depth First Search on Neighbor Lists — Graph Components","text":"","code":"n.comp.nb(nb.obj)"},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Depth First Search on Neighbor Lists — Graph Components","text":"nb.obj neighbours list object class nb","code":""},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Depth First Search on Neighbor Lists — Graph Components","text":"attr(nb.obj, \"sym\") FALSE igraph::components available, components directed graph found simple breadth-first search; igraph::components available, object made symmetric (may time-consuming large numbers neighbours) components found depth-first search. attr(nb.obj, \"sym\") TRUE, components directed graph found depth-first search. time complexity algorithms used native code igraph::components linear sum number nodes number edges graph, see https://github.com/r-spatial/spdep/issues/160 details; dense neighbour objects large numbers edges.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Depth First Search on Neighbor Lists — Graph Components","text":"list : nc number disjoint connected subgraphs comp.id vector indices disjoint connected subgraphs nodes nb.obj belong ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Depth First Search on Neighbor Lists — Graph Components","text":"Nicholas Lewin-Koh nikko@hailmail.net","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Depth First Search on Neighbor Lists — Graph Components","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(st_geometry(columbus))) plot(col.gal.nb, coords, col=\"grey\") col2 <- droplinks(col.gal.nb, 21) #> Warning: some observations have no neighbours #> Warning: neighbour object has 3 sub-graphs res <- n.comp.nb(col2) table(res$comp.id) #> #> 1 2 3 #> 42 1 6 plot(col2, coords, add=TRUE) points(coords, col=res$comp.id, pch=16) run <- FALSE if (require(\"igraph\", quietly=TRUE) && require(\"spatialreg\", quietly=TRUE)) run <- TRUE #> #> Attaching package: ‘igraph’ #> The following objects are masked from ‘package:stats’: #> #> decompose, spectrum #> The following object is masked from ‘package:base’: #> #> union #> #> Attaching package: ‘spatialreg’ #> The following objects are masked from ‘package:spdep’: #> #> get.ClusterOption, get.VerboseOption, get.ZeroPolicyOption, #> get.coresOption, get.mcOption, set.ClusterOption, #> set.VerboseOption, set.ZeroPolicyOption, set.coresOption, #> set.mcOption if (run) { B <- as(nb2listw(col2, style=\"B\", zero.policy=TRUE), \"CsparseMatrix\") g1 <- graph_from_adjacency_matrix(B, mode=\"undirected\") c1 <- components(g1) print(c1$no == res$nc) } #> [1] TRUE if (run) { print(all.equal(c1$membership, res$comp.id)) } #> [1] \"names for target but not for current\" if (run) { print(all.equal(c1$csize, c(table(res$comp.id)), check.attributes=FALSE)) } #> [1] TRUE if (run) { W <- as(nb2listw(col2, style=\"W\", zero.policy=TRUE), \"CsparseMatrix\") g1W <- graph_from_adjacency_matrix(W, mode=\"directed\", weighted=\"W\") c1W <- components(g1W, mode=\"weak\") print(all.equal(c1W$membership, res$comp.id, check.attributes=FALSE)) } #> [1] TRUE # \\donttest{ if (run) { data(house, package=\"spData\") house <- sf::st_as_sf(house) k6 <- knn2nb(knearneigh(house, k=6)) is.symmetric.nb(k6) } #> [1] FALSE if (run) { print(k6) } #> Neighbour list object: #> Number of regions: 25357 #> Number of nonzero links: 152142 #> Percentage nonzero weights: 0.02366211 #> Average number of links: 6 #> Non-symmetric neighbours list if (run) { length(k6) + sum(card(k6)) } #> [1] 177499 if (run) { # no pre-computed graph components str(attr(k6, \"ncomp\")) } #> NULL if (run) { # raising the subgraph compute ceiling to above |N|+|E| computes and stores the # object in the neighbour object set.SubgraphCeiling(180000L) k6 <- knn2nb(knearneigh(house, k=6)) str(attr(k6, \"ncomp\")) } #> Warning: neighbour object has 47 sub-graphs #> List of 2 #> $ nc : num 47 #> $ comp.id: num [1:25357] 1 1 1 1 1 1 1 1 1 1 ... if (run) { print(k6) } #> Neighbour list object: #> Number of regions: 25357 #> Number of nonzero links: 152142 #> Percentage nonzero weights: 0.02366211 #> Average number of links: 6 #> 47 disjoint connected subgraphs #> Non-symmetric neighbours list if (run) { system.time(udir <- n.comp.nb(make.sym.nb(k6))) } #> user system elapsed #> 2.303 0.001 2.313 if (run) { system.time(dir <- n.comp.nb(k6)) } #> user system elapsed #> 0.769 0.000 0.771 if (run) { udir$nc } #> [1] 47 if (run) { dir$nc } #> [1] 47 if (run) { all.equal(dir, udir) } #> [1] TRUE # }"},{"path":"https://r-spatial.github.io/spdep/reference/diffnb.html","id":null,"dir":"Reference","previous_headings":"","what":"Differences between neighbours lists — diffnb","title":"Differences between neighbours lists — diffnb","text":"function finds symmetric differences lists neighbours (ordering objects matter), returning nb neighbour list found","code":""},{"path":"https://r-spatial.github.io/spdep/reference/diffnb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Differences between neighbours lists — diffnb","text":"","code":"diffnb(x, y, verbose=NULL, legacy=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/diffnb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Differences between neighbours lists — diffnb","text":"x object class nb y object class nb verbose default NULL, use global option value; report regions ids taken object attribute \"region.id\" differences, ignored legacy= FALSE legacy default TRUE; use legacy code; FALSE use differences sparse matrix representations","code":""},{"path":"https://r-spatial.github.io/spdep/reference/diffnb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Differences between neighbours lists — diffnb","text":"neighbours list class nb","code":""},{"path":"https://r-spatial.github.io/spdep/reference/diffnb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Differences between neighbours lists — diffnb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/diffnb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Differences between neighbours lists — diffnb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE) rn <- row.names(columbus) knn1 <- knearneigh(coords, 1) knn2 <- knearneigh(coords, 2) nb1 <- knn2nb(knn1, row.names=rn) #> Warning: neighbour object has 13 sub-graphs nb2 <- knn2nb(knn2, row.names=rn) diffs <- diffnb(nb2, nb1, legacy=TRUE) #> Warning: neighbour object has 10 sub-graphs diffsl <- diffnb(nb2, nb1, legacy=FALSE) #> Warning: neighbour object has 10 sub-graphs #> Warning: neighbour object has 10 sub-graphs #> Warning: neighbour object has 10 sub-graphs all.equal(diffs, diffsl) #> [1] \"Attributes: < Component “call”: target, current do not match when deparsed >\" # call attribute fifference expected diffsd <- union.nb(setdiff.nb(nb1, nb2), setdiff.nb(nb2, nb1)) #> Warning: neighbour object has 49 sub-graphs #> Warning: neighbour object has 10 sub-graphs #> Warning: neighbour object has 10 sub-graphs all.equal(diffs, diffsd) #> [1] \"Attributes: < Component “call”: target, current do not match when deparsed >\" # call attribute fifference expected opar <- par(no.readonly=TRUE) plot(st_geometry(columbus), border=\"grey\", reset=FALSE, main=\"Plot of first (black) and second (red)\\nnearest neighbours\") plot(nb1, coords, add=TRUE) plot(diffs, coords, add=TRUE, col=\"red\", lty=2) par(opar)"},{"path":"https://r-spatial.github.io/spdep/reference/dnearneigh.html","id":null,"dir":"Reference","previous_headings":"","what":"Neighbourhood contiguity by distance — dnearneigh","title":"Neighbourhood contiguity by distance — dnearneigh","text":"function identifies neighbours region points Euclidean distance metric points lower (greater equal (changed version 1.1-7)) upper (less equal ) bounds, longlat = TRUE, Great Circle distance kilometers. x \"sf\" object use_s2= TRUE, spherical distances km used.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/dnearneigh.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Neighbourhood contiguity by distance — dnearneigh","text":"","code":"dnearneigh(x, d1, d2, row.names = NULL, longlat = NULL, bounds=c(\"GE\", \"LE\"), use_kd_tree=TRUE, symtest=FALSE, use_s2=packageVersion(\"s2\") > \"1.0.7\", k=200, dwithin=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/dnearneigh.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Neighbourhood contiguity by distance — dnearneigh","text":"x matrix point coordinates, object inheriting SpatialPoints \"sf\" \"sfc\" object; \"sf\" \"sfc\" object geometries geographical coordinates (use_s2=FALSE, sf::st_is_longlat(x) == TRUE sf::sf_use_s2() == TRUE), s2 used find neighbours (hope) use spatial indexing https://github.com/r-spatial/s2/issues/125 opposed legacy method uses brute-force (present s2 also uses brute-force) d1 lower distance bound metric points planar coordinates, km geographical coordinates d2 upper distance boundd metric points planar coordinates, km geographical coordinates row.names character vector region ids added neighbours list attribute region.id, default seq(1, nrow(x)) longlat TRUE point coordinates geographical longitude-latitude decimal degrees, case distances measured kilometers; x SpatialPoints object, value taken object , overrides argument NULL bounds character vector length 2, default c(\"GE\", \"LE\"), (GE: greater equal , LE: less equal ) finite closed interval [d1, d2], d1 <= x <= d2. first element may also \"GT\" (GT: greater ), second \"LT\" (LT: less ) finite, open intervals excluding bounds; first bound default changed \"GT\" \"GE\" release 1.1-7. creating multiple distance bands, finite, half-open right-closed intervals may used final interval avoid overlapping bounds: \"GE\", \"LT\", [d1, d2), d1 <= x < d2 use_kd_tree default TRUE, TRUE, use dbscan frNN available (permitting 3D distances). symtest Default FALSE; release 1.1-7, TRUE - run symmetry check output object, costly large numbers points. use_s2 default=packageVersion(\"s2\") > \"1.0.7\", s2 > 1.0-7, distance bound computations use spatial indexing sf::sf_use_s2() TRUE, s2::s2_dwithin_matrix() used distances sphere \"sf\" \"sfc\" objects s2 > 1.0-7. k default 200, number closest points consider searching using s2::s2_closest_edges() dwithin default TRUE, FALSE, use s2::s2_closest_edges(), use_s2=TRUE, sf::st_is_longlat(x) == TRUE sf::sf_use_s2() == TRUE; s2::s2_dwithin_matrix() yields lists neighbours s2::s2_closest_edges() k= set correctly.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/dnearneigh.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Neighbourhood contiguity by distance — dnearneigh","text":"function returns list integer vectors giving region id numbers neighbours satisfying distance criteria. See card details “nb” objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/dnearneigh.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Neighbourhood contiguity by distance — dnearneigh","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/dnearneigh.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Neighbourhood contiguity by distance — dnearneigh","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE) rn <- row.names(columbus) k1 <- knn2nb(knearneigh(coords)) #> Warning: neighbour object has 13 sub-graphs all.linked <- max(unlist(nbdists(k1, coords))) col.nb.0.all <- dnearneigh(coords, 0, all.linked, row.names=rn) #> Warning: neighbour object has 2 sub-graphs summary(col.nb.0.all, coords) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 252 #> Percentage nonzero weights: 10.49563 #> Average number of links: 5.142857 #> 2 disjoint connected subgraphs #> Link number distribution: #> #> 1 2 3 4 5 6 7 8 9 10 11 #> 4 8 6 2 5 8 6 2 6 1 1 #> 4 least connected regions: #> 6 10 21 47 with 1 link #> 1 most connected region: #> 28 with 11 links opar <- par(no.readonly=TRUE) plot(st_geometry(columbus), border=\"grey\", reset=FALSE, main=paste(\"Distance based neighbours 0-\", format(all.linked), sep=\"\")) plot(col.nb.0.all, coords, add=TRUE) par(opar) (sfc_obj <- st_centroid(st_geometry(columbus))) #> Geometry set for 49 features #> Geometry type: POINT #> Dimension: XY #> Bounding box: xmin: 6.221943 ymin: 11.01003 xmax: 10.95359 ymax: 14.36908 #> Projected CRS: Undefined Cartesian SRS with unknown unit #> First 5 geometries: #> POINT (8.827218 14.36908) #> POINT (8.332658 14.03162) #> POINT (9.012265 13.81972) #> POINT (8.460801 13.71696) #> POINT (9.007982 13.29637) col.nb.0.all_sf <- dnearneigh(sfc_obj, 0, all.linked, row.names=rn) #> Warning: neighbour object has 2 sub-graphs all.equal(col.nb.0.all, col.nb.0.all_sf, check.attributes=FALSE) #> [1] TRUE data(state) us48.fipsno <- read.geoda(system.file(\"etc/weights/us48.txt\", package=\"spdep\")[1]) if (as.numeric(paste(version$major, version$minor, sep=\"\")) < 19) { m50.48 <- match(us48.fipsno$\"State.name\", state.name) } else { m50.48 <- match(us48.fipsno$\"State_name\", state.name) } xy <- as.matrix(as.data.frame(state.center))[m50.48,] llk1 <- knn2nb(knearneigh(xy, k=1, longlat=FALSE)) #> Warning: neighbour object has 12 sub-graphs (all.linked <- max(unlist(nbdists(llk1, xy, longlat=FALSE)))) #> [1] 5.161223 ll.nb <- dnearneigh(xy, 0, all.linked, longlat=FALSE) #> Warning: neighbour object has 5 sub-graphs summary(ll.nb, xy, longlat=TRUE, scale=0.5) #> Neighbour list object: #> Number of regions: 48 #> Number of nonzero links: 190 #> Percentage nonzero weights: 8.246528 #> Average number of links: 3.958333 #> 5 disjoint connected subgraphs #> Link number distribution: #> #> 1 2 3 4 5 7 8 9 10 #> 11 9 4 8 4 4 4 3 1 #> 11 least connected regions: #> 2 4 8 10 24 26 29 32 35 41 45 with 1 link #> 1 most connected region: #> 28 with 10 links gck1 <- knn2nb(knearneigh(xy, k=1, longlat=TRUE)) #> Warning: neighbour object has 11 sub-graphs (all.linked <- max(unlist(nbdists(gck1, xy, longlat=TRUE)))) #> [1] 523.5819 gc.nb <- dnearneigh(xy, 0, all.linked, longlat=TRUE) #> Warning: neighbour object has 2 sub-graphs summary(gc.nb, xy, longlat=TRUE, scale=0.5) #> Neighbour list object: #> Number of regions: 48 #> Number of nonzero links: 220 #> Percentage nonzero weights: 9.548611 #> Average number of links: 4.583333 #> 2 disjoint connected subgraphs #> Link number distribution: #> #> 1 2 3 4 5 6 7 8 9 10 #> 5 9 6 8 5 2 3 3 5 2 #> 5 least connected regions: #> 2 4 8 41 45 with 1 link #> 2 most connected regions: #> 7 28 with 10 links plot(ll.nb, xy) plot(diffnb(ll.nb, gc.nb), xy, add=TRUE, col=\"red\", lty=2) #> Warning: neighbour object has 27 sub-graphs title(main=\"Differences Euclidean/Great Circle\") #xy1 <- SpatialPoints((as.data.frame(state.center))[m50.48,], # proj4string=CRS(\"+proj=longlat +ellps=GRS80\")) #gck1a <- knn2nb(knearneigh(xy1, k=1)) #(all.linked <- max(unlist(nbdists(gck1a, xy1)))) #gc.nb <- dnearneigh(xy1, 0, all.linked) #summary(gc.nb, xy1, scale=0.5) xy1 <- st_as_sf((as.data.frame(state.center))[m50.48,], coords=1:2, crs=st_crs(\"OGC:CRS84\")) old_use_s2 <- sf_use_s2() sf_use_s2(TRUE) gck1b <- knn2nb(knearneigh(xy1, k=1)) #> Warning: neighbour object has 11 sub-graphs system.time(o <- nbdists(gck1b, xy1)) #> user system elapsed #> 0.013 0.000 0.012 (all.linked <- max(unlist(o))) #> [1] 522.4464 # use s2 brute-force dwithin_matrix approach for s2 <= 1.0.7 system.time(gc.nb.dwithin <- dnearneigh(xy1, 0, all.linked, use_s2=TRUE, dwithin=TRUE)) #> Warning: neighbour object has 3 sub-graphs #> user system elapsed #> 0.025 0.000 0.025 summary(gc.nb, xy1, scale=0.5) #> Neighbour list object: #> Number of regions: 48 #> Number of nonzero links: 220 #> Percentage nonzero weights: 9.548611 #> Average number of links: 4.583333 #> 2 disjoint connected subgraphs #> Link number distribution: #> #> 1 2 3 4 5 6 7 8 9 10 #> 5 9 6 8 5 2 3 3 5 2 #> 5 least connected regions: #> 2 4 8 41 45 with 1 link #> 2 most connected regions: #> 7 28 with 10 links # use s2 closest_edges approach s2 > 1.0.7 if (packageVersion(\"s2\") > \"1.0.7\") { (system.time(gc.nb.closest <- dnearneigh(xy1, 0, all.linked, dwithin=FALSE))) } #> Warning: neighbour object has 3 sub-graphs #> user system elapsed #> 0.022 0.000 0.022 if (packageVersion(\"s2\") > \"1.0.7\") { system.time(gc.nb.dwithin <- dnearneigh(xy1, 0, all.linked, use_s2=TRUE, dwithin=TRUE)) } #> Warning: neighbour object has 3 sub-graphs #> user system elapsed #> 0.024 0.000 0.024 if (packageVersion(\"s2\") > \"1.0.7\") { summary(gc.nb.dwithin, xy1, scale=0.5) } #> Neighbour list object: #> Number of regions: 48 #> Number of nonzero links: 218 #> Percentage nonzero weights: 9.461806 #> Average number of links: 4.541667 #> 1 region with no links: #> 2 #> 3 disjoint connected subgraphs #> Link number distribution: #> #> 0 1 2 3 4 5 6 7 8 9 10 #> 1 5 8 6 8 5 2 3 3 5 2 #> 5 least connected regions: #> 4 8 29 41 45 with 1 link #> 2 most connected regions: #> 7 28 with 10 links if (packageVersion(\"s2\") > \"1.0.7\") { summary(gc.nb.closest, xy1, scale=0.5) } #> Neighbour list object: #> Number of regions: 48 #> Number of nonzero links: 218 #> Percentage nonzero weights: 9.461806 #> Average number of links: 4.541667 #> 1 region with no links: #> 2 #> 3 disjoint connected subgraphs #> Link number distribution: #> #> 0 1 2 3 4 5 6 7 8 9 10 #> 1 5 8 6 8 5 2 3 3 5 2 #> 5 least connected regions: #> 4 8 29 41 45 with 1 link #> 2 most connected regions: #> 7 28 with 10 links # use legacy symmetric brute-force approach system.time(gc.nb.legacy <- dnearneigh(xy1, 0, all.linked, use_s2=FALSE)) #> Warning: neighbour object has 3 sub-graphs #> user system elapsed #> 0.012 0.000 0.013 summary(gc.nb, xy1, scale=0.5) #> Neighbour list object: #> Number of regions: 48 #> Number of nonzero links: 220 #> Percentage nonzero weights: 9.548611 #> Average number of links: 4.583333 #> 2 disjoint connected subgraphs #> Link number distribution: #> #> 1 2 3 4 5 6 7 8 9 10 #> 5 9 6 8 5 2 3 3 5 2 #> 5 least connected regions: #> 2 4 8 41 45 with 1 link #> 2 most connected regions: #> 7 28 with 10 links if (packageVersion(\"s2\") > \"1.0.7\") all.equal(gc.nb.closest, gc.nb.dwithin, check.attributes=FALSE) #> [1] TRUE # legacy is ellipsoidal, s2 spherical, so minor differences expected if (packageVersion(\"s2\") > \"1.0.7\") all.equal(gc.nb, gc.nb.closest, check.attributes=FALSE) #> [1] \"Component 2: Mean relative difference: 1\" #> [2] \"Component 29: Numeric: lengths (2, 1) differ\" all.equal(gc.nb, gc.nb.dwithin, check.attributes=FALSE) #> [1] \"Component 2: Mean relative difference: 1\" #> [2] \"Component 29: Numeric: lengths (2, 1) differ\" sf_use_s2(old_use_s2) # example of reading points with readr::read_csv() yielding a tibble load(system.file(\"etc/misc/coords.rda\", package=\"spdep\")) class(coords) #> [1] \"spec_tbl_df\" \"tbl_df\" \"tbl\" \"data.frame\" k1 <- knn2nb(knearneigh(coords, k=1)) #> Warning: neighbour object has 29 sub-graphs all.linked <- max(unlist(nbdists(k1, coords))) dnearneigh(coords, 0, all.linked) #> Neighbour list object: #> Number of regions: 100 #> Number of nonzero links: 676 #> Percentage nonzero weights: 6.76 #> Average number of links: 6.76"},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":null,"dir":"Reference","previous_headings":"","what":"Drop and add links in a neighbours list — droplinks","title":"Drop and add links in a neighbours list — droplinks","text":"droplinks drops links just region neighbours list. example corresponds Fingleton's Table 1, (1999) p. 6, lattices 5 19. addlinks1 adds links single region specified regions.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Drop and add links in a neighbours list — droplinks","text":"","code":"droplinks(nb, drop, sym=TRUE) addlinks1(nb, from, to, sym=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Drop and add links in a neighbours list — droplinks","text":"nb neighbours list object class nb drop either logical vector length nb, character vector named regions corresponding nb's region.id attribute, integer vector region numbers sym TRUE removal \"row\" \"column\" links, FALSE \"row\" links; adding links, inserts links region regions single region adding links, either character vector length 1 named region corresponding nb's region.id attribute, integer vector length 1 holding region number regions, either character vector named regions corresponding nb's region.id attribute, integer vector region numbers","code":""},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Drop and add links in a neighbours list — droplinks","text":"function returns object class nb list integer vectors containing neighbour region number ids.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Drop and add links in a neighbours list — droplinks","text":"B. Fingleton (1999) Spurious spatial regression: Monte Carlo results spatial unit root spatial cointegration, Journal Regional Science 39, pp. 1–19.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Drop and add links in a neighbours list — droplinks","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Drop and add links in a neighbours list — droplinks","text":"","code":"# \\donttest{ rho <- c(0.2, 0.5, 0.95, 0.999, 1.0) ns <- c(5, 7, 9, 11, 13, 15, 17, 19) mns <- matrix(0, nrow=length(ns), ncol=length(rho)) rownames(mns) <- ns colnames(mns) <- rho mxs <- matrix(0, nrow=length(ns), ncol=length(rho)) rownames(mxs) <- ns colnames(mxs) <- rho for (i in 1:length(ns)) { nblist <- cell2nb(ns[i], ns[i]) nbdropped <- droplinks(nblist, ((ns[i]*ns[i])+1)/2, sym=FALSE) listw <- nb2listw(nbdropped, style=\"W\", zero.policy=TRUE) wmat <- listw2mat(listw) for (j in 1:length(rho)) { mat <- diag(ns[i]*ns[i]) - rho[j] * wmat res <- diag(solve(t(mat) %*% mat)) mns[i,j] <- mean(res) mxs[i,j] <- max(res) } } #> Warning: some observations have no neighbours #> Warning: some observations have no neighbours #> Warning: some observations have no neighbours #> Warning: some observations have no neighbours #> Warning: some observations have no neighbours #> Warning: some observations have no neighbours #> Warning: some observations have no neighbours #> Warning: some observations have no neighbours print(mns) #> 0.2 0.5 0.95 0.999 1 #> 5 1.038271 1.312627 9.486051 30.81487 32.04915 #> 7 1.036443 1.295621 10.899580 83.25437 92.09812 #> 9 1.035356 1.285145 10.798611 160.90951 195.02166 #> 11 1.034639 1.278279 10.383083 254.83998 347.71145 #> 13 1.034132 1.273442 9.968389 353.66366 555.88699 #> 15 1.033753 1.269852 9.619387 447.19245 824.46560 #> 17 1.033460 1.267082 9.337167 528.49015 1157.77630 #> 19 1.033227 1.264879 9.109487 594.23907 1559.69614 print(mxs) #> 0.2 0.5 0.95 0.999 1 #> 5 1.048834 1.401934 12.00215 39.22742 40.79967 #> 7 1.048834 1.402174 14.66823 106.90031 118.01556 #> 9 1.048834 1.402176 15.49606 207.28928 249.74893 #> 11 1.048834 1.402176 15.75744 329.22973 443.97194 #> 13 1.048834 1.402176 15.83957 458.75739 707.14827 #> 15 1.048834 1.402176 15.86474 583.50722 1044.75562 #> 17 1.048834 1.402176 15.87225 695.10288 1461.57017 #> 19 1.048834 1.402176 15.87445 789.50575 1961.84025 # }"},{"path":"https://r-spatial.github.io/spdep/reference/edit.nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Interactive editing of neighbours lists — edit.nb","title":"Interactive editing of neighbours lists — edit.nb","text":"function provides simple interactive editing neighbours lists allow unneeded links deleted, missing links inserted. uses identify pick endpoints link deleted added, asks confirmation committing. result assigned new object, editing lost - edit. method relies direct contact graphics device. use RStudio.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/edit.nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Interactive editing of neighbours lists — edit.nb","text":"","code":"# S3 method for class 'nb' edit(name, coords, polys=NULL, ..., use_region.id=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/edit.nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Interactive editing of neighbours lists — edit.nb","text":"name object class nb coords matrix region point coordinates; missing polys= inherits SpatialPolygons, label points object used polys polygon boundaries supplied, used background; must inherit SpatialPolygons ... arguments passed methods use_region.id default FALSE, identify use 1-based observation numbers, otherwise use nb region.id attribute values","code":""},{"path":"https://r-spatial.github.io/spdep/reference/edit.nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Interactive editing of neighbours lists — edit.nb","text":"function returns object class nb edited list integer vectors containing neighbour region number ids, added attributes tallying added deleted links.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/edit.nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Interactive editing of neighbours lists — edit.nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/edit.nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Interactive editing of neighbours lists — edit.nb","text":"","code":"# \\dontrun{ columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) class(columbus) #> [1] \"sf\" \"data.frame\" if (FALSE) nnb1 <- edit.nb(col.gal.nb, polys=as(columbus, \"Spatial\")) # }"},{"path":"https://r-spatial.github.io/spdep/reference/eire.html","id":null,"dir":"Reference","previous_headings":"","what":"Eire data sets — eire","title":"Eire data sets — eire","text":"data set now part spData package","code":""},{"path":"https://r-spatial.github.io/spdep/reference/eire.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Eire data sets — eire","text":"","code":"data(eire)"},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute Geary's C — geary","title":"Compute Geary's C — geary","text":"simple function compute Geary's C, called geary.test geary.mc; $$C = \\frac{(n-1)}{2\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}} \\frac{\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}(x_i-x_j)^2}{\\sum_{=1}^{n}(x_i - \\bar{x})^2} $$ geary.intern internal function used vary similarity criterion.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute Geary's C — geary","text":"","code":"geary(x, listw, n, n1, S0, zero.policy=attr(listw, \"zero.policy\"), scale=TRUE) "},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute Geary's C — geary","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw n number zones n1 n - 1 S0 global sum weights zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA scale default TRUE, may FALSE revert changes made accommodate localC November 2021 (see #151)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute Geary's C — geary","text":"list C Geary's C K sample kurtosis x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute Geary's C — geary","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 17.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute Geary's C — geary","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute Geary's C — geary","text":"","code":"data(oldcol) col.W <- nb2listw(COL.nb, style=\"W\") str(geary(COL.OLD$CRIME, col.W, length(COL.nb), length(COL.nb)-1, Szero(col.W))) #> List of 2 #> $ C: num 0.53 #> $ K: num 2.23"},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Permutation test for Geary's C statistic — geary.mc","title":"Permutation test for Geary's C statistic — geary.mc","text":"permutation test Geary's C statistic calculated using nsim random permutations x given spatial weighting scheme, establish rank observed statistic relation nsim simulated values.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Permutation test for Geary's C statistic — geary.mc","text":"","code":"geary.mc(x, listw, nsim, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\", spChk=NULL, adjust.n=TRUE, return_boot=FALSE, na.action=na.fail, scale=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Permutation test for Geary's C statistic — geary.mc","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw nsim number permutations zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"less\"; reversal corresponds geary.test described section output statistic value, based Cliff Ord 1973, p. 21 (changed 2011-04-11, thanks Daniel Garavito). spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted return_boot return object class boot equivalent permutation bootstrap rather object class htest na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass permitted meaningless permutation test. scale default TRUE, may FALSE revert changes made accommodate localC November 2021 (see #151)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Permutation test for Geary's C statistic — geary.mc","text":"list class htest mc.sim containing following components: statistic value observed Geary's C. parameter rank observed Geary's C. p.value pseudo p-value test. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data, number simulations. res nsim simulated values statistic, final value observed statistic","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Permutation test for Geary's C statistic — geary.mc","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 63-5.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Permutation test for Geary's C statistic — geary.mc","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Permutation test for Geary's C statistic — geary.mc","text":"","code":"data(oldcol) set.seed(1) sim1 <- geary.mc(COL.OLD$CRIME, nb2listw(COL.nb, style=\"W\"), nsim=99, alternative=\"less\") sim1 #> #> \tMonte-Carlo simulation of Geary C #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.nb, style = \"W\") #> number of simulations + 1: 100 #> #> statistic = 0.52987, observed rank = 1, p-value = 0.99 #> alternative hypothesis: less #> mean(sim1$res) #> [1] 1.002705 var(sim1$res) #> [1] 0.01043616 summary(sim1$res) #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> 0.5299 0.9362 1.0141 1.0027 1.0673 1.2459 colold.lags <- nblag(COL.nb, 3) sim2 <- geary.mc(COL.OLD$CRIME, nb2listw(colold.lags[[2]], style=\"W\"), nsim=99) sim2 #> #> \tMonte-Carlo simulation of Geary C #> #> data: COL.OLD$CRIME #> weights: nb2listw(colold.lags[[2]], style = \"W\") #> number of simulations + 1: 100 #> #> statistic = 0.81129, observed rank = 1, p-value = 0.01 #> alternative hypothesis: greater #> summary(sim2$res) #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> 0.8113 0.9500 1.0173 1.0147 1.0731 1.1962 sim3 <- geary.mc(COL.OLD$CRIME, nb2listw(colold.lags[[3]], style=\"W\"), nsim=99) sim3 #> #> \tMonte-Carlo simulation of Geary C #> #> data: COL.OLD$CRIME #> weights: nb2listw(colold.lags[[3]], style = \"W\") #> number of simulations + 1: 100 #> #> statistic = 1.1303, observed rank = 89, p-value = 0.89 #> alternative hypothesis: greater #> summary(sim3$res) #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> 0.7903 0.9609 0.9989 1.0148 1.0656 1.2726 crime <- COL.OLD$CRIME is.na(crime) <- sample(1:length(crime), 10) try(geary.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, na.action=na.fail)) #> Error in na.fail.default(x) : missing values in object geary.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE, na.action=na.omit) #> Warning: subsetting caused increase in subgraph count #> #> \tMonte-Carlo simulation of Geary C #> #> data: crime #> weights: nb2listw(COL.nb, style = \"W\") #> omitted: 14, 16, 17, 21, 24, 31, 32, 42, 44, 47 #> number of simulations + 1: 100 #> #> statistic = 0.49368, observed rank = 1, p-value = 0.01 #> alternative hypothesis: greater #> geary.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE, return_boot=TRUE, na.action=na.omit) #> Warning: subsetting caused increase in subgraph count #> NA observations omitted: 14, 16, 17, 21, 24, 31, 32, 42, 44, 47 #> #> DATA PERMUTATION #> #> #> Call: #> boot(data = x, statistic = geary_boot, R = nsim, sim = \"permutation\", #> listw = listw, n = n, n1 = wc$n1, S0 = wc$S0, zero.policy = zero.policy, #> scale = scale, parallel = parallel, ncpus = ncpus, cl = cl) #> #> #> Bootstrap Statistics : #> original bias std. error #> t1* 0.4936767 0.4891213 0.1517218 geary.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE, na.action=na.exclude) #> Warning: subsetting caused increase in subgraph count #> #> \tMonte-Carlo simulation of Geary C #> #> data: crime #> weights: nb2listw(COL.nb, style = \"W\") #> omitted: 14, 16, 17, 21, 24, 31, 32, 42, 44, 47 #> number of simulations + 1: 100 #> #> statistic = 0.49368, observed rank = 1, p-value = 0.01 #> alternative hypothesis: greater #> geary.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE, return_boot=TRUE, na.action=na.exclude) #> Warning: subsetting caused increase in subgraph count #> NA observations omitted: 14, 16, 17, 21, 24, 31, 32, 42, 44, 47 #> #> DATA PERMUTATION #> #> #> Call: #> boot(data = x, statistic = geary_boot, R = nsim, sim = \"permutation\", #> listw = listw, n = n, n1 = wc$n1, S0 = wc$S0, zero.policy = zero.policy, #> scale = scale, parallel = parallel, ncpus = ncpus, cl = cl) #> #> #> Bootstrap Statistics : #> original bias std. error #> t1* 0.4936767 0.4570379 0.1307276 try(geary.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, na.action=na.pass)) #> Error in geary.mc(crime, nb2listw(COL.nb, style = \"W\"), nsim = 99, na.action = na.pass) : #> na.pass not permitted"},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":null,"dir":"Reference","previous_headings":"","what":"Geary's C test for spatial autocorrelation — geary.test","title":"Geary's C test for spatial autocorrelation — geary.test","text":"Geary's test spatial autocorrelation using spatial weights matrix weights list form. assumptions underlying test sensitive form graph neighbour relationships factors, results may checked geary.mc permutations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Geary's C test for spatial autocorrelation — geary.test","text":"","code":"geary.test(x, listw, randomisation=TRUE, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\", spChk=NULL, adjust.n=TRUE, na.action=na.fail, scale=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Geary's C test for spatial autocorrelation — geary.test","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw randomisation variance calculated assumption randomisation, FALSE normality zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"less\" \"two.sided\". spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass permitted. scale default TRUE, may FALSE revert changes made accommodate localC November 2021 (see #151)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Geary's C test for spatial autocorrelation — geary.test","text":"list class htest containing following components: statistic value standard deviate Geary's C, order given Cliff Ord 1973, p. 21, (EC - C) / sqrt(VC), sign reversed respect usual (C - EC) / sqrt(VC); means “greater” alternative Geary C test corresponds “greater” alternative Moran's test. p.value p-value test. estimate value observed Geary's C, expectation variance method assumption. alternative character string describing alternative hypothesis. method character string giving assumption used calculating standard deviate. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Geary's C test for spatial autocorrelation — geary.test","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 21, Cliff, . D., Ord, J. K. 1973 Spatial Autocorrelation, Pion, pp. 15-16, 21; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Geary's C test for spatial autocorrelation — geary.test","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Geary's C test for spatial autocorrelation — geary.test","text":"derivation test (Cliff Ord, 1981, p. 18) assumes weights matrix symmetric. inherently non-symmetric matrices, k-nearest neighbour matrices, listw2U() can used make matrix symmetric. non-symmetric weights matrix cases, variance test statistic may negative (thanks Franz Munoz well documented bug report). Geary's C affected non-symmetric weights normality much Moran's . 0.4-35, sign standard deviate C changed match Cliff Ord (1973, p. 21).","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Geary's C test for spatial autocorrelation — geary.test","text":"","code":"data(oldcol) geary.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"W\")) #> #> \tGeary C test under randomisation #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.nb, style = \"W\") #> #> Geary C statistic standard deviate = 4.7605, p-value = 9.655e-07 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic Expectation Variance #> 0.52986993 1.00000000 0.00975278 #> geary.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"W\"), randomisation=FALSE) #> #> \tGeary C test under normality #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.nb, style = \"W\") #> #> Geary C statistic standard deviate = 4.6388, p-value = 1.752e-06 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic Expectation Variance #> 0.52986993 1.00000000 0.01027137 #> colold.lags <- nblag(COL.nb, 3) geary.test(COL.OLD$CRIME, nb2listw(colold.lags[[2]], style=\"W\")) #> #> \tGeary C test under randomisation #> #> data: COL.OLD$CRIME #> weights: nb2listw(colold.lags[[2]], style = \"W\") #> #> Geary C statistic standard deviate = 2.2896, p-value = 0.01102 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic Expectation Variance #> 0.811285136 1.000000000 0.006793327 #> geary.test(COL.OLD$CRIME, nb2listw(colold.lags[[3]], style=\"W\"), alternative=\"greater\") #> #> \tGeary C test under randomisation #> #> data: COL.OLD$CRIME #> weights: nb2listw(colold.lags[[3]], style = \"W\") #> #> Geary C statistic standard deviate = -1.5667, p-value = 0.9414 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic Expectation Variance #> 1.130277918 1.000000000 0.006914551 #> print(is.symmetric.nb(COL.nb)) #> [1] TRUE coords.OLD <- cbind(COL.OLD$X, COL.OLD$Y) COL.k4.nb <- knn2nb(knearneigh(coords.OLD, 4)) print(is.symmetric.nb(COL.k4.nb)) #> [1] FALSE geary.test(COL.OLD$CRIME, nb2listw(COL.k4.nb, style=\"W\")) #> #> \tGeary C test under randomisation #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.k4.nb, style = \"W\") #> #> Geary C statistic standard deviate = 6.4415, p-value = 5.916e-11 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic Expectation Variance #> 0.399254423 1.000000000 0.008697812 #> geary.test(COL.OLD$CRIME, nb2listw(COL.k4.nb, style=\"W\"), randomisation=FALSE) #> #> \tGeary C test under normality #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.k4.nb, style = \"W\") #> #> Geary C statistic standard deviate = 6.2873, p-value = 1.615e-10 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic Expectation Variance #> 0.399254423 1.000000000 0.009129529 #> cat(\"Note non-symmetric weights matrix - use listw2U()\\n\") #> Note non-symmetric weights matrix - use listw2U() geary.test(COL.OLD$CRIME, listw2U(nb2listw(COL.k4.nb, style=\"W\"))) #> #> \tGeary C test under randomisation #> #> data: COL.OLD$CRIME #> weights: listw2U(nb2listw(COL.k4.nb, style = \"W\")) #> #> Geary C statistic standard deviate = 6.4415, p-value = 5.916e-11 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic Expectation Variance #> 0.399254423 1.000000000 0.008697812 #> geary.test(COL.OLD$CRIME, listw2U(nb2listw(COL.k4.nb, style=\"W\")), randomisation=FALSE) #> #> \tGeary C test under normality #> #> data: COL.OLD$CRIME #> weights: listw2U(nb2listw(COL.k4.nb, style = \"W\")) #> #> Geary C statistic standard deviate = 6.2873, p-value = 1.615e-10 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic Expectation Variance #> 0.399254423 1.000000000 0.009129529 #> crime <- COL.OLD$CRIME is.na(crime) <- sample(1:length(crime), 10) try(geary.test(crime, nb2listw(COL.nb, style=\"W\"), na.action=na.fail)) #> Error in na.fail.default(x) : missing values in object geary.test(crime, nb2listw(COL.nb, style=\"W\"), zero.policy=TRUE, na.action=na.omit) #> #> \tGeary C test under randomisation #> #> data: crime #> weights: nb2listw(COL.nb, style = \"W\") #> omitted: 3, 4, 10, 20, 21, 23, 27, 29, 31, 38 #> #> Geary C statistic standard deviate = 4.2726, p-value = 9.661e-06 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic Expectation Variance #> 0.45199742 1.00000000 0.01645071 #> geary.test(crime, nb2listw(COL.nb, style=\"W\"), zero.policy=TRUE, na.action=na.exclude) #> #> \tGeary C test under randomisation #> #> data: crime #> weights: nb2listw(COL.nb, style = \"W\") #> omitted: 3, 4, 10, 20, 21, 23, 27, 29, 31, 38 #> #> Geary C statistic standard deviate = 4.2726, p-value = 9.661e-06 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic Expectation Variance #> 0.45199742 1.00000000 0.01645071 #> try(geary.test(crime, nb2listw(COL.nb, style=\"W\"), na.action=na.pass)) #> Error in geary.test(crime, nb2listw(COL.nb, style = \"W\"), na.action = na.pass) : #> na.pass not permitted"},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":null,"dir":"Reference","previous_headings":"","what":"Global G test for spatial autocorrelation — globalG.test","title":"Global G test for spatial autocorrelation — globalG.test","text":"global G statistic spatial autocorrelation, complementing local Gi LISA measures: localG.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Global G test for spatial autocorrelation — globalG.test","text":"","code":"globalG.test(x, listw, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\", spChk=NULL, adjust.n=TRUE, B1correct=TRUE, adjust.x=TRUE, Arc_all_x=FALSE, na.action=na.fail)"},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Global G test for spatial autocorrelation — globalG.test","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw; sequence distance bands used, recommended weights style binary (one c(\"B\", \"C\", \"U\")). zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"less\" \"two.sided\". spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted B1correct default TRUE, TRUE, erratum referenced : \"page 195, coefficient W2 B1, (just center page) 6, 3.\" applied; FALSE, 3 used (CrimeStat IV) adjust.x default TRUE, TRUE, x values observations neighbours omitted denominator G Arc_all_x default FALSE, Arc_all_x=TRUE adjust.x=TRUE, use full x vector part denominator term G na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass permitted.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Global G test for spatial autocorrelation — globalG.test","text":"list class htest containing following components: statistic value standard deviate Getis-Ord G. p.value p-value test. estimate value observed statistic, expectation variance. alternative character string describing alternative hypothesis. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Global G test for spatial autocorrelation — globalG.test","text":"Getis. , Ord, J. K. 1992 analysis spatial association use distance statistics, Geographical Analysis, 24, p. 195; see also Getis. , Ord, J. K. 1993 Erratum, Geographical Analysis, 25, p. 276; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Global G test for spatial autocorrelation — globalG.test","text":"Hisaji ONO hi-ono@mn.xdsl.ne.jp Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Global G test for spatial autocorrelation — globalG.test","text":"","code":"nc.sids <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\")[1], quiet=TRUE) sidsrate79 <- (1000*nc.sids$SID79)/nc.sids$BIR79 dists <- c(10, 20, 30, 33, 40, 50, 60, 70, 80, 90, 100) ndists <- length(dists) ZG <- vector(mode=\"list\", length=ndists) names(ZG) <- as.character(dists) milesxy <- cbind(nc.sids$east, nc.sids$north) for (i in 1:ndists) { thisnb <- dnearneigh(milesxy, 0, dists[i]) thislw <- nb2listw(thisnb, style=\"B\", zero.policy=TRUE) ZG[[i]] <- globalG.test(sidsrate79, thislw, zero.policy=TRUE) } #> Warning: neighbour object has 98 sub-graphs #> Warning: neighbour object has 37 sub-graphs #> Warning: neighbour object has 3 sub-graphs t(sapply(ZG, function(x) c(x$estimate[1], x$statistic, p.value=unname(x$p.value)))) #> Global G statistic standard deviate p.value #> 10 0.33548581 0.04859237 0.4806221 #> 20 0.02024945 -0.73262399 0.7681061 #> 30 0.04032434 -0.75011405 0.7734070 #> 33 0.05312271 0.40157023 0.3440002 #> 40 0.07400279 -0.04345713 0.5173314 #> 50 0.11471743 0.58686472 0.2786473 #> 60 0.15457553 -0.35823892 0.6399177 #> 70 0.19839023 -0.27864299 0.6097406 #> 80 0.24606972 -0.18791364 0.5745278 #> 90 0.30073463 0.11457610 0.4543906 #> 100 0.34879996 0.31591356 0.3760341 for (i in 1:ndists) { thisnb <- dnearneigh(milesxy, 0, dists[i]) thislw <- nb2listw(thisnb, style=\"B\", zero.policy=TRUE) ZG[[i]] <- globalG.test(sidsrate79, thislw, zero.policy=TRUE, alternative=\"two.sided\") } #> Warning: neighbour object has 98 sub-graphs #> Warning: neighbour object has 37 sub-graphs #> Warning: neighbour object has 3 sub-graphs t(sapply(ZG, function(x) c(x$estimate[1], x$statistic, p.value=unname(x$p.value)))) #> Global G statistic standard deviate p.value #> 10 0.33548581 0.04859237 0.9612441 #> 20 0.02024945 -0.73262399 0.4637878 #> 30 0.04032434 -0.75011405 0.4531860 #> 33 0.05312271 0.40157023 0.6880003 #> 40 0.07400279 -0.04345713 0.9653371 #> 50 0.11471743 0.58686472 0.5572946 #> 60 0.15457553 -0.35823892 0.7201645 #> 70 0.19839023 -0.27864299 0.7805188 #> 80 0.24606972 -0.18791364 0.8509443 #> 90 0.30073463 0.11457610 0.9087811 #> 100 0.34879996 0.31591356 0.7520681 data(oldcol) crime <- COL.OLD$CRIME is.na(crime) <- sample(1:length(crime), 10) res <- try(globalG.test(crime, nb2listw(COL.nb, style=\"B\"), na.action=na.fail)) #> Error in na.fail.default(x) : missing values in object globalG.test(crime, nb2listw(COL.nb, style=\"B\"), zero.policy=TRUE, na.action=na.omit) #> Warning: subsetting caused increase in subgraph count #> #> \tGetis-Ord global G statistic #> #> data: crime #> weights: nb2listw(COL.nb, style = \"B\") #> omitted: 2, 3, 5, 6, 7, 10, 13, 30, 39, 49 #> n reduced by no-neighbour observations #> #> standard deviate = 3.8084, p-value = 6.993e-05 #> alternative hypothesis: greater #> sample estimates: #> Global G statistic Expectation Variance #> 1.441233e-01 1.123755e-01 6.949287e-05 #> globalG.test(crime, nb2listw(COL.nb, style=\"B\"), zero.policy=TRUE, na.action=na.exclude) #> Warning: subsetting caused increase in subgraph count #> #> \tGetis-Ord global G statistic #> #> data: crime #> weights: nb2listw(COL.nb, style = \"B\") #> omitted: 2, 3, 5, 6, 7, 10, 13, 30, 39, 49 #> n reduced by no-neighbour observations #> #> standard deviate = 3.8084, p-value = 6.993e-05 #> alternative hypothesis: greater #> sample estimates: #> Global G statistic Expectation Variance #> 1.441233e-01 1.123755e-01 6.949287e-05 #> try(globalG.test(crime, nb2listw(COL.nb, style=\"B\"), na.action=na.pass)) #> Error in globalG.test(crime, nb2listw(COL.nb, style = \"B\"), na.action = na.pass) : #> na.pass not permitted"},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":null,"dir":"Reference","previous_headings":"","what":"Graph based spatial weights — graphneigh","title":"Graph based spatial weights — graphneigh","text":"Functions return graph object containing list vertex coordinates indices defining edges. /functions assume coordinates exactly regularly spaced. helper function graph2nb converts graph object neighbour list. plot functions plot graph objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Graph based spatial weights — graphneigh","text":"","code":"gabrielneigh(coords, nnmult=3) relativeneigh(coords, nnmult=3) soi.graph(tri.nb, coords, quadsegs=10) graph2nb(gob, row.names=NULL,sym=FALSE) # S3 method for class 'Gabriel' plot(x, show.points=FALSE, add=FALSE, linecol=par(col), ...) # S3 method for class 'relative' plot(x, show.points=FALSE, add=FALSE, linecol=par(col),...)"},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Graph based spatial weights — graphneigh","text":"coords matrix region point coordinates SpatialPoints object sfc points object nnmult scaling factor memory allocation, default 3; higher values required, function exit error; example thanks Dan Putler tri.nb neighbor list created tri2nb quadsegs number line segments making quarter circle buffer, see nQuadSegs argument geos_unary gob graph object created graph funtions row.names character vector region ids added neighbours list attribute region.id, default seq(1, nrow(x)) sym logical argument indicating whether neighbors symetric (->j j->) x object plotted show.points (logical) add points plot add (logical) add existing plot linecol edge plotting colour ... graphical parameters par(..)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Graph based spatial weights — graphneigh","text":"graph functions produce graphs 2d point set subgraphs Delaunay triangulation. relative neighbor graph defined relation, x y neighbors $$d(x,y) \\le min(max(d(x,z),d(y,z))| z \\S)$$ d() distance, S set points z arbitrary point S. Gabriel graph subgraph delaunay triangulation relative neighbor graph sub-graph. relative neighbor graph defined relation x y Gabriel neighbors $$d(x,y) \\le min((d(x,z)^2 + d(y,z)^2)^{1/2} |z \\S)$$ x,y,z S . sphere influence graph defined finite point set S, let \\(r_x\\) distance point x nearest neighbor S, \\(C_x\\) circle centered x. x y SOI neigbors iff \\(C_x\\) \\(C_y\\) intersect least 2 places. 2016-05-31, Computational Geometry C code replaced calls functions dbscan sf; large quadsegs= argument, behaviour function , otherwise buffer intersections closely approximate original function. See card details “nb” objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Graph based spatial weights — graphneigh","text":"list class Graph following elements np number input points array origin ids array destination ids nedges number edges graph x input x coordinates y input y coordinates helper functions return nb object list integer vectors containing neighbour region number ids.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Graph based spatial weights — graphneigh","text":"Matula, D. W. Sokal R. R. 1980, Properties Gabriel graphs relevant geographic variation research clustering points plane, Geographic Analysis, 12(3), pp. 205-222. Toussaint, G. T. 1980, relative neighborhood graph finite planar set, Pattern Recognition, 12(4), pp. 261-268. Kirkpatrick, D. G. Radke, J. D. 1985, framework computational morphology. Computational Geometry, Ed. G. T. Toussaint, North Holland.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Graph based spatial weights — graphneigh","text":"Nicholas Lewin-Koh nikko@hailmail.net","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Graph based spatial weights — graphneigh","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) sf_obj <- st_centroid(st_geometry(columbus), of_largest_polygon) sp_obj <- as(sf_obj, \"Spatial\") coords <- st_coordinates(sf_obj) suppressMessages(col.tri.nb <- tri2nb(coords)) col.gab.nb <- graph2nb(gabrielneigh(coords), sym=TRUE) col.rel.nb <- graph2nb(relativeneigh(coords), sym=TRUE) par(mfrow=c(2,2)) plot(st_geometry(columbus), border=\"grey\") plot(col.tri.nb,coords,add=TRUE) title(main=\"Delaunay Triangulation\", cex.main=0.6) plot(st_geometry(columbus), border=\"grey\") plot(col.gab.nb, coords, add=TRUE) title(main=\"Gabriel Graph\", cex.main=0.6) plot(st_geometry(columbus), border=\"grey\") plot(col.rel.nb, coords, add=TRUE) title(main=\"Relative Neighbor Graph\", cex.main=0.6) plot(st_geometry(columbus), border=\"grey\") if (require(\"dbscan\", quietly=TRUE)) { col.soi.nb <- graph2nb(soi.graph(col.tri.nb,coords), sym=TRUE) plot(col.soi.nb, coords, add=TRUE) title(main=\"Sphere of Influence Graph\", cex.main=0.6) } #> #> Attaching package: ‘dbscan’ #> The following object is masked from ‘package:stats’: #> #> as.dendrogram par(mfrow=c(1,1)) col.tri.nb_sf <- tri2nb(sf_obj) all.equal(col.tri.nb, col.tri.nb_sf, check.attributes=FALSE) #> [1] TRUE col.tri.nb_sp <- tri2nb(sp_obj) all.equal(col.tri.nb, col.tri.nb_sp, check.attributes=FALSE) #> [1] TRUE if (require(\"dbscan\", quietly=TRUE)) { col.soi.nb_sf <- graph2nb(soi.graph(col.tri.nb, sf_obj), sym=TRUE) all.equal(col.soi.nb, col.soi.nb_sf, check.attributes=FALSE) col.soi.nb_sp <- graph2nb(soi.graph(col.tri.nb, sp_obj), sym=TRUE) all.equal(col.soi.nb, col.soi.nb_sp, check.attributes=FALSE) } #> [1] TRUE col.gab.nb_sp <- graph2nb(gabrielneigh(sp_obj), sym=TRUE) all.equal(col.gab.nb, col.gab.nb_sp, check.attributes=FALSE) #> [1] TRUE col.gab.nb_sf <- graph2nb(gabrielneigh(sf_obj), sym=TRUE) all.equal(col.gab.nb, col.gab.nb_sf, check.attributes=FALSE) #> [1] TRUE col.rel.nb_sp <- graph2nb(relativeneigh(sp_obj), sym=TRUE) all.equal(col.rel.nb, col.rel.nb_sp, check.attributes=FALSE) #> [1] TRUE col.rel.nb_sf <- graph2nb(relativeneigh(sf_obj), sym=TRUE) all.equal(col.rel.nb, col.rel.nb_sf, check.attributes=FALSE) #> [1] TRUE dx <- rep(0.25*0:4,5) dy <- c(rep(0,5),rep(0.25,5),rep(0.5,5), rep(0.75,5),rep(1,5)) m <- cbind(c(dx, dx, 3+dx, 3+dx), c(dy, 3+dy, dy, 3+dy)) cat(try(res <- gabrielneigh(m), silent=TRUE), \"\\n\") #> Error in gabrielneigh(m) : number of neighbours overrun - increase nnmult #> res <- gabrielneigh(m, nnmult=4) summary(graph2nb(res)) #> Neighbour list object: #> Number of regions: 100 #> Number of nonzero links: 342 #> Percentage nonzero weights: 3.42 #> Average number of links: 3.42 #> 1 region with no links: #> 100 #> Non-symmetric neighbours list #> Link number distribution: #> #> 0 1 2 3 4 5 #> 1 8 10 18 55 8 #> 8 least connected regions: #> 46 47 48 49 96 97 98 99 with 1 link #> 8 most connected regions: #> 10 15 20 25 30 35 40 45 with 5 links grd <- as.matrix(expand.grid(x=1:5, y=1:5)) #gridded data r2 <- gabrielneigh(grd) set.seed(1) grd1 <- as.matrix(expand.grid(x=1:5, y=1:5)) + matrix(runif(50, .0001, .0006), nrow=25) r3 <- gabrielneigh(grd1) opar <- par(mfrow=c(1,2)) plot(r2, show=TRUE, linecol=2) plot(r3, show=TRUE, linecol=2) par(opar) # example of reading points with readr::read_csv() yielding a tibble load(system.file(\"etc/misc/coords.rda\", package=\"spdep\")) class(coords) #> [1] \"spec_tbl_df\" \"tbl_df\" \"tbl\" \"data.frame\" graph2nb(gabrielneigh(coords)) #> Neighbour list object: #> Number of regions: 100 #> Number of nonzero links: 179 #> Percentage nonzero weights: 1.79 #> Average number of links: 1.79 #> 23 regions with no links: #> 22, 39, 43, 53, 58, 61, 66, 70, 71, 73, 76, 78, 81, 88, 90, 93, 94, 95, #> 96, 97, 98, 99, 100 #> Non-symmetric neighbours list graph2nb(relativeneigh(coords)) #> Neighbour list object: #> Number of regions: 100 #> Number of nonzero links: 117 #> Percentage nonzero weights: 1.17 #> Average number of links: 1.17 #> 31 regions with no links: #> 22, 29, 33, 39, 41, 42, 43, 44, 53, 58, 61, 64, 65, 66, 70, 71, 73, 75, #> 76, 78, 81, 88, 90, 93, 94, 95, 96, 97, 98, 99, 100 #> Non-symmetric neighbours list"},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Construct neighbours for a GridTopology — grid2nb","title":"Construct neighbours for a GridTopology — grid2nb","text":"function builds neighbours list grid topology. works k-dimentional grid topology, k>=1.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Construct neighbours for a GridTopology — grid2nb","text":"","code":"grid2nb(grid, d = grid@cells.dim, queen = TRUE, nb = TRUE, self = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Construct neighbours for a GridTopology — grid2nb","text":"grid object class GridTopology. One can avoid supply just suplying dimentions d argument. d scalar (one dimentional grid) length k vector specyfying number grid cells direction k dimentions. queen Logical. Default TRUE. inform queen neighbourhood structure considered. FALSE, hyper-cube common face considered neighbour. TRUE, single shared coordinate meets contiguity condition. nb Default TRUE. TRUE, return result neighbours list class nb. FALSE, result matrix 3^k columns self = TRUE 3^k-1 self = FALSE. Zeros used hyper-cubes boundaries. self Default FALSE, indicate hyper-cube neighbour considered neighbour.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Construct neighbours for a GridTopology — grid2nb","text":"Either matrix, “nb” FALSE neighbours list class nb. See card details “nb” objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Construct neighbours for a GridTopology — grid2nb","text":"applies k-dimentional grid topology.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Construct neighbours for a GridTopology — grid2nb","text":"Elias T Krainski eliaskrainski@gmail.com","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Construct neighbours for a GridTopology — grid2nb","text":"","code":"nb <- grid2nb(d = c(5L, 5L, 5L)) nb #> Neighbour list object: #> Number of regions: 125 #> Number of nonzero links: 2072 #> Percentage nonzero weights: 13.2608 #> Average number of links: 16.576 summary(nb) #> Neighbour list object: #> Number of regions: 125 #> Number of nonzero links: 2072 #> Percentage nonzero weights: 13.2608 #> Average number of links: 16.576 #> Link number distribution: #> #> 7 11 17 26 #> 8 36 54 27 #> 8 least connected regions: #> 1 5 21 25 101 105 121 125 with 7 links #> 27 most connected regions: #> 32 33 34 37 38 39 42 43 44 57 58 59 62 63 64 67 68 69 82 83 84 87 88 89 92 93 94 with 26 links if (require(\"sp\", quietly=TRUE)) { gt <- GridTopology(c(.125,.1), c(.25,.2), c(4L, 5L)) nb1 <- grid2nb(gt, queen = FALSE) nb2 <- grid2nb(gt) sg <- SpatialGrid(gt) plot(sg, lwd=3) plot(nb1, coordinates(sg), add=TRUE, lty=2, col=2, lwd=2) plot(nb2, coordinates(sg), add=TRUE, lty=3, col=4) str(grid2nb(d=5)) } #> List of 5 #> $ : int 2 #> $ : int [1:2] 1 3 #> $ : int [1:2] 2 4 #> $ : int [1:2] 3 5 #> $ : int 4 #> - attr(*, \"class\")= chr \"nb\""},{"path":"https://r-spatial.github.io/spdep/reference/hotspotmap.html","id":null,"dir":"Reference","previous_headings":"","what":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","title":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","text":"Used return factor showing -called cluster classification local indicators spatial association local Moran's , local Geary's C (multivariate variant) local Getis-Ord G. factor vector can added spatial object mapping. obj class licd, list six factors measures local composition (analytical permutation), local configuration (analytical permutation), combined measures, interaction composition configuration, simplified recoding .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/hotspotmap.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","text":"","code":"hotspot(obj, ...) # Default S3 method hotspot(obj, ...) # S3 method for class 'localmoran' hotspot(obj, Prname, cutoff=0.005, quadrant.type=\"mean\", p.adjust=\"fdr\", droplevels=TRUE, ...) # S3 method for class 'summary.localmoransad' hotspot(obj, Prname, cutoff=0.005, quadrant.type=\"mean\", p.adjust=\"fdr\", droplevels=TRUE, ...) # S3 method for class 'data.frame.localmoranex' hotspot(obj, Prname, cutoff=0.005, quadrant.type=\"mean\", p.adjust=\"fdr\", droplevels=TRUE, ...) # S3 method for class 'localG' hotspot(obj, Prname, cutoff=0.005, p.adjust=\"fdr\", droplevels=TRUE, ...) # S3 method for class 'localC' hotspot(obj, Prname, cutoff=0.005, p.adjust=\"fdr\", droplevels=TRUE, ...) # S3 method for class 'licd' hotspot(obj, type = \"both\", cutoff = 0.05, p.adjust = \"none\", droplevels = TRUE, control = list(), ...)"},{"path":"https://r-spatial.github.io/spdep/reference/hotspotmap.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","text":"obj object class localmoran, localC localG Prname character string, name column containing probability values classified cluster type found “interesting” cutoff Default 0.005, probability value cutoff larger observation found “interesting” p.adjust Default \"fdr\", p.adjust() method used, one c(\"holm\", \"hochberg\", \"hommel\", \"bonferroni\", \"BH\", \"\", \"fdr\", \"none\") droplevels Default TRUE, empty levels input cluster factor dropped quadrant.type Default \"mean\", \"localmoran\" objects , can c(\"mean\", \"median\", \"pysal\") partition Moran scatterplot; \"mean\" partitions means variable spatial lag, \"median\" medians variable spatial lag, \"pysal\" zero centred variable spatial lag type obj class licd, default , may also comp local composition config local configuration control obj class licd, default binomial_sidak 2, binomial_overlap TRUE, jcm_sidak 3. binomial_overlap may set FALSE avoid Binomial probability values summing unity - tests Boots (2003, p. 141) overlap (>= <=), Šidák exponents may set 1 prevent -observation correction 2 Binomial 3 Normal probability values per observation ... arguments passed methods.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/hotspotmap.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","text":"factor showing -called cluster classification local indicators spatial association. obj class licd, list six factors measures local composition (analytical permutation), local configuration (analytical permutation), combined measures, interaction composition configuration, simplified recoding .","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/hotspotmap.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","text":"Roger Bivand","code":""},{"path":"https://r-spatial.github.io/spdep/reference/hotspotmap.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","text":"","code":"orig <- spData::africa.rook.nb listw <- nb2listw(orig) x <- spData::afcon$totcon set.seed(1) C <- localC_perm(x, listw) Ch <- hotspot(C, Prname=\"Pr(z != E(Ci)) Sim\", cutoff=0.05, p.adjust=\"none\") table(addNA(Ch)) #> #> High-High Low-Low #> 4 1 37 set.seed(1) I <- localmoran_perm(x, listw) Ih <- hotspot(I, Prname=\"Pr(z != E(Ii)) Sim\", cutoff=0.05, p.adjust=\"none\") table(addNA(Ih)) #> #> High-High #> 6 36 Is <- summary(localmoran.sad(lm(x ~ 1), nb=orig)) Ish <- hotspot(Is, Prname=\"Pr. (Sad)\", cutoff=0.05, p.adjust=\"none\") table(addNA(Ish)) #> #> High-High #> 5 37 Ie <- as.data.frame(localmoran.exact(lm(x ~ 1), nb=orig)) Ieh <- hotspot(Ie, Prname=\"Pr. (exact)\", cutoff=0.05, p.adjust=\"none\") table(addNA(Ieh)) #> #> High-High #> 5 37 set.seed(1) G <- localG_perm(x, listw) Gh <- hotspot(G, Prname=\"Pr(z != E(Gi)) Sim\", cutoff=0.05, p.adjust=\"none\") table(addNA(Gh)) #> #> High #> 6 36"},{"path":"https://r-spatial.github.io/spdep/reference/include.self.html","id":null,"dir":"Reference","previous_headings":"","what":"Include self in neighbours list — include.self","title":"Include self in neighbours list — include.self","text":"function includes region list neighbours, sets attribute \"self.included\" TRUE; remove.self reverts effects include.self.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/include.self.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Include self in neighbours list — include.self","text":"","code":"include.self(nb) remove.self(nb)"},{"path":"https://r-spatial.github.io/spdep/reference/include.self.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Include self in neighbours list — include.self","text":"nb input neighbours list class nb","code":""},{"path":"https://r-spatial.github.io/spdep/reference/include.self.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Include self in neighbours list — include.self","text":"function returns object class nb list integer vectors containing neighbour region number ids; attribute \"self.included\" set TRUE.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/include.self.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Include self in neighbours list — include.self","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/include.self.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Include self in neighbours list — include.self","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries summary(col.gal.nb, coords) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> Link number distribution: #> #> 2 3 4 5 6 7 8 9 10 #> 7 7 13 4 9 6 1 1 1 #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links summary(include.self(col.gal.nb), coords) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 279 #> Percentage nonzero weights: 11.62016 #> Average number of links: 5.693878 #> Link number distribution: #> #> 3 4 5 6 7 8 9 10 11 #> 7 7 13 4 9 6 1 1 1 #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 3 links #> 1 most connected region: #> 20 with 11 links summary(remove.self(include.self(col.gal.nb)), coords) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> Link number distribution: #> #> 2 3 4 5 6 7 8 9 10 #> 7 7 13 4 9 6 1 1 1 #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links"},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Permutation test for same colour join count statistics — joincount.mc","title":"Permutation test for same colour join count statistics — joincount.mc","text":"permutation test colour join count statistics calculated using nsim random permutations fx given spatial weighting scheme, establish ranks observed statistics (colour) relation nsim simulated values.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Permutation test for same colour join count statistics — joincount.mc","text":"","code":"joincount.mc(fx, listw, nsim, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\", spChk=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Permutation test for same colour join count statistics — joincount.mc","text":"fx factor length neighbours weights objects listw listw listw object created example nb2listw nsim number permutations zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"two.sided\", \"less\". spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption()","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Permutation test for same colour join count statistics — joincount.mc","text":"list class jclist lists class htest mc.sim k colours containing following components: statistic value observed statistic. parameter rank observed statistic. method character string giving method used. data.name character string giving name(s) data. p.value pseudo p-value test. alternative character string describing alternative hypothesis. estimate mean variance simulated distribution. res nsim simulated values statistic, final element observed statistic","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Permutation test for same colour join count statistics — joincount.mc","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 63-5.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Permutation test for same colour join count statistics — joincount.mc","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Permutation test for same colour join count statistics — joincount.mc","text":"","code":"data(oldcol) HICRIME <- cut(COL.OLD$CRIME, breaks=c(0,35,80), labels=c(\"low\",\"high\")) names(HICRIME) <- rownames(COL.OLD) joincount.mc(HICRIME, nb2listw(COL.nb, style=\"B\"), nsim=99, alternative=\"two.sided\") #> #> \tMonte-Carlo simulation of join-count statistic #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"B\") #> number of simulations + 1: 100 #> #> Join-count statistic for low = 34, rank of observed statistic = 88.5, #> p-value = 0.23 #> alternative hypothesis: two.sided #> sample estimates: #> mean of simulation variance of simulation #> 28.96970 18.19295 #> #> #> \tMonte-Carlo simulation of join-count statistic #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"B\") #> number of simulations + 1: 100 #> #> Join-count statistic for high = 54, rank of observed statistic = 100, #> p-value < 2.2e-16 #> alternative hypothesis: two.sided #> sample estimates: #> mean of simulation variance of simulation #> 26.83838 20.13688 #> joincount.test(HICRIME, nb2listw(COL.nb, style=\"B\"), alternative=\"two.sided\") #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"B\") #> #> Std. deviate for low = 1.0141, p-value = 0.3105 #> alternative hypothesis: two.sided #> sample estimates: #> Same colour statistic Expectation Variance #> 34.00000 29.59184 18.89550 #> #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"B\") #> #> Std. deviate for high = 6.3307, p-value = 2.44e-10 #> alternative hypothesis: two.sided #> sample estimates: #> Same colour statistic Expectation Variance #> 54.00000 27.22449 17.88838 #>"},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":null,"dir":"Reference","previous_headings":"","what":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"function tallying join counts -colour different colour spatial objects, neighbour relations defined weights list. Given global counts colour, expected counts variances calculated non-free sampling, z-value reported. Since multiple tests reported, p-values given, allowing user adjust significance level applied. Jtot count different-colour joins.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"","code":"joincount.multi(fx, listw, zero.policy = attr(listw, \"zero.policy\"), spChk = NULL, adjust.n=TRUE) # S3 method for class 'jcmulti' print(x, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"fx factor length neighbours weights objects listw listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted consistently (including spdep 0.3-28 adjustment inconsistent - thanks Tomoki NAKAYA careful bug report) spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() x object printed ... arguments passed printing","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"matrix class jcmulti row column names observed expected counts, variance, z-value.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 20; Upton, G., Fingleton, B. 1985 Spatial data analysis example: point pattern qualitative data, Wiley, pp. 158–170.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"derivation test (Cliff Ord, 1981, p. 18) assumes weights matrix symmetric. inherently non-symmetric matrices, k-nearest neighbour matrices, listw2U() can used make matrix symmetric. non-symmetric weights matrix cases, variance test statistic may negative.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) HICRIME <- cut(columbus$CRIME, breaks=c(0,35,80), labels=c(\"low\",\"high\")) (nb <- poly2nb(columbus)) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 236 #> Percentage nonzero weights: 9.829238 #> Average number of links: 4.816327 lw <- nb2listw(nb, style=\"B\") joincount.multi(HICRIME, lw) #> Joincount Expected Variance z-value #> low:low 35.000 30.102 19.247 1.1164 #> high:high 54.000 27.694 18.219 6.1630 #> high:low 29.000 60.204 26.630 -6.0468 #> Jtot 29.000 60.204 26.630 -6.0468 col_geoms <- st_geometry(columbus) col_geoms[21] <- st_buffer(col_geoms[21], dist=-0.05) st_geometry(columbus) <- col_geoms (nb <- poly2nb(columbus)) #> Warning: some observations have no neighbours; #> if this seems unexpected, try increasing the snap argument. #> Warning: neighbour object has 3 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> 1 region with no links: #> 21 #> 3 disjoint connected subgraphs lw <- nb2listw(nb, style=\"B\", zero.policy=TRUE) joincount.multi(HICRIME, lw) #> Joincount Expected Variance z-value #> low:low 35.000 30.585 19.350 1.0036 #> high:high 52.000 28.138 18.342 5.5716 #> high:low 28.000 61.170 25.882 -6.5200 #> Jtot 28.000 61.170 33.190 -5.7577 # \\dontrun{ data(oldcol) HICRIME <- cut(COL.OLD$CRIME, breaks=c(0,35,80), labels=c(\"low\",\"high\")) names(HICRIME) <- rownames(COL.OLD) joincount.multi(HICRIME, nb2listw(COL.nb, style=\"B\")) #> Joincount Expected Variance z-value #> low:low 34.000 29.592 18.895 1.0141 #> high:high 54.000 27.224 17.888 6.3307 #> high:low 28.000 59.184 26.233 -6.0884 #> Jtot 28.000 59.184 26.233 -6.0884 data(hopkins, package=\"spData\") image(1:32, 1:32, hopkins[5:36,36:5], breaks=c(-0.5, 3.5, 20), col=c(\"white\", \"black\")) box() hopkins.rook.nb <- cell2nb(32, 32, type=\"rook\") unlist(spweights.constants(nb2listw(hopkins.rook.nb, style=\"B\"))) #> n n1 n2 n3 nn S0 S1 S2 #> 1024 1023 1022 1021 1048576 3968 7936 61984 hopkins.queen.nb <- cell2nb(32, 32, type=\"queen\") hopkins.bishop.nb <- diffnb(hopkins.rook.nb, hopkins.queen.nb, verbose=FALSE) #> Warning: neighbour object has 2 sub-graphs hopkins4 <- hopkins[5:36,36:5] hopkins4[which(hopkins4 > 3, arr.ind=TRUE)] <- 4 hopkins4.f <- factor(hopkins4) table(hopkins4.f) #> hopkins4.f #> 0 1 2 3 4 #> 657 215 98 30 24 joincount.multi(hopkins4.f, nb2listw(hopkins.rook.nb, style=\"B\")) #> Joincount Expected Variance z-value #> 0:0 864.00000 816.27273 116.05233 4.4304 #> 1:1 94.00000 87.14015 55.25216 0.9229 #> 2:2 18.00000 18.00379 14.81562 -0.0010 #> 3:3 2.00000 1.64773 1.55539 0.2825 #> 4:4 5.00000 1.04545 0.99845 3.9576 #> 1:0 503.00000 535.05682 227.76750 -2.1241 #> 2:0 213.00000 243.88636 97.21769 -3.1325 #> 2:1 99.00000 79.81061 59.01930 2.4978 #> 3:0 61.00000 74.65909 28.58592 -2.5547 #> 3:1 28.00000 24.43182 18.99976 0.8186 #> 3:2 15.00000 11.13636 9.82411 1.2327 #> 4:0 40.00000 59.72727 22.78583 -4.1327 #> 4:1 23.00000 19.54545 15.26564 0.8842 #> 4:2 14.00000 8.90909 7.90051 1.8112 #> 4:3 5.00000 2.72727 2.58616 1.4133 #> Jtot 1001.00000 1059.89015 273.78610 -3.5591 cat(\"replicates Upton & Fingleton table 3.4 (p. 166)\\n\") #> replicates Upton & Fingleton table 3.4 (p. 166) joincount.multi(hopkins4.f, nb2listw(hopkins.bishop.nb, style=\"B\")) #> Joincount Expected Variance z-value #> 0:0 823.00000 790.76420 144.44877 2.6821 #> 1:1 101.00000 84.41702 55.98143 2.2164 #> 2:2 19.00000 17.44117 14.61542 0.4077 #> 3:3 3.00000 1.59624 1.51444 1.1407 #> 4:4 3.00000 1.01278 0.97111 2.0166 #> 1:0 497.00000 518.33629 234.93545 -1.3920 #> 2:0 216.00000 236.26491 104.42142 -1.9831 #> 2:1 81.00000 77.31652 58.70829 0.4807 #> 3:0 58.00000 72.32599 31.49151 -2.5529 #> 3:1 21.00000 23.66832 18.85316 -0.6145 #> 3:2 17.00000 10.78835 9.62487 2.0022 #> 4:0 48.00000 57.86080 25.15973 -1.9659 #> 4:1 21.00000 18.93466 15.14473 0.5307 #> 4:2 10.00000 8.63068 7.73708 0.4923 #> 4:3 4.00000 2.64205 2.51686 0.8560 #> Jtot 973.00000 1026.76858 284.51030 -3.1877 cat(\"replicates Upton & Fingleton table 3.6 (p. 168)\\n\") #> replicates Upton & Fingleton table 3.6 (p. 168) joincount.multi(hopkins4.f, nb2listw(hopkins.queen.nb, style=\"B\")) #> Joincount Expected Variance z-value #> 0:0 1687.0000 1607.0369 303.8034 4.5877 #> 1:1 195.0000 171.5572 114.2057 2.1936 #> 2:2 37.0000 35.4450 29.6821 0.2854 #> 3:3 5.0000 3.2440 3.0687 1.0024 #> 4:4 8.0000 2.0582 1.9674 4.2361 #> 1:0 1000.0000 1053.3931 480.6959 -2.4353 #> 2:0 429.0000 480.1513 215.0360 -3.4882 #> 2:1 180.0000 157.1271 119.3987 2.0932 #> 3:0 119.0000 146.9851 65.1029 -3.4684 #> 3:1 49.0000 48.1001 38.3268 0.1454 #> 3:2 32.0000 21.9247 19.5237 2.2802 #> 4:0 88.0000 117.5881 52.0312 -4.1019 #> 4:1 44.0000 38.4801 30.7868 0.9948 #> 4:2 24.0000 17.5398 15.6933 1.6308 #> 4:3 9.0000 5.3693 5.0994 1.6078 #> Jtot 1974.0000 2086.6587 582.8326 -4.6665 cat(\"replicates Upton & Fingleton table 3.7 (p. 169)\\n\") #> replicates Upton & Fingleton table 3.7 (p. 169) # } GDAL37 <- numeric_version(unname(sf::sf_extSoftVersion()[\"GDAL\"]), strict=FALSE) (GDAL37 <- ifelse(is.na(GDAL37), FALSE, GDAL37 >= \"3.7.0\")) #> [1] TRUE file <- \"etc/shapes/GB_2024_southcoast_50m.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) { sc50m <- st_read(zipfile) } else { td <- tempdir() bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE) target <- unzip(zipfile, files=bn, exdir=td) sc50m <- st_read(target) } #> Reading layer `GB_2024_southcoast_50m' from data source #> `/tmp/Rtmp5vVziX/temp_libpath224d25059ed81/spdep/etc/shapes/GB_2024_southcoast_50m.gpkg.zip' #> using driver `GPKG' #> Simple feature collection with 119 features and 19 fields #> Geometry type: MULTIPOLYGON #> Dimension: XY #> Bounding box: xmin: 82643.12 ymin: 5342.9 xmax: 640301.6 ymax: 187226.2 #> Projected CRS: OSGB36 / British National Grid sc50m$Winner <- factor(sc50m$Winner, levels=c(\"Con\", \"Green\", \"Lab\", \"LD\")) plot(sc50m[,\"Winner\"], pal=c(\"#2297E6\", \"#61D04F\", \"#DF536B\", \"#F5C710\")) nb_sc_50m <- poly2nb(sc50m, row.names=as.character(sc50m$Constituency)) #> Warning: neighbour object has 2 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. sub2 <- attr(nb_sc_50m, \"region.id\")[attr(nb_sc_50m, \"ncomp\")$comp.id == 2L] iowe <- match(sub2[1], attr(nb_sc_50m, \"region.id\")) diowe <- c(st_distance(sc50m[iowe,], sc50m)) meet_criterion <- sum(diowe <= units::set_units(5000, \"m\")) cands <- attr(nb_sc_50m, \"region.id\")[order(diowe)[1:meet_criterion]] nb_sc_50m_iowe <- addlinks1(nb_sc_50m, from = cands[1], to = cands[3:meet_criterion]) ioww <- match(sub2[2], attr(nb_sc_50m, \"region.id\")) dioww <- c(st_distance(sc50m[ioww,], sc50m)) meet_criterion <- sum(dioww <= units::set_units(5000, \"m\")) cands <- attr(nb_sc_50m, \"region.id\")[order(dioww)[1:meet_criterion]] nb_sc_50m_iow <- addlinks1(nb_sc_50m_iowe, from = cands[2], to = cands[3:meet_criterion]) nb_sc_1_2 <- nblag_cumul(nblag(nb_sc_50m_iow, 2)) joincount.multi(sc50m$Winner, nb2listw(nb_sc_1_2, style=\"B\")) #> Joincount Expected Variance z-value #> Con:Con 146.0000 84.4324 116.3530 5.7077 #> Green:Green 0.0000 0.0000 0.0000 NaN #> Lab:Lab 63.0000 98.1057 136.0379 -3.0099 #> LD:LD 100.0000 75.8866 103.9440 2.3651 #> Green:Con 4.0000 4.4438 5.8532 -0.1834 #> Lab:Con 184.0000 186.6401 180.9233 -0.1963 #> Lab:Green 3.0000 4.7856 6.4663 -0.7022 #> LD:Con 198.0000 164.4210 166.3583 2.6034 #> LD:Green 4.0000 4.2159 5.4573 -0.0924 #> LD:Lab 98.0000 177.0688 175.2035 -5.9736 #> Jtot 491.0000 541.5753 153.6123 -4.0806"},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":null,"dir":"Reference","previous_headings":"","what":"BB join count statistic for k-coloured factors — joincount.test","title":"BB join count statistic for k-coloured factors — joincount.test","text":"BB join count test spatial autocorrelation using spatial weights matrix weights list form testing whether -colour joins occur frequently expected zones labelled spatially random way. assumptions underlying test sensitive form graph neighbour relationships factors, results may checked joincount.mc permutations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"BB join count statistic for k-coloured factors — joincount.test","text":"","code":"joincount.test(fx, listw, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\", sampling=\"nonfree\", spChk=NULL, adjust.n=TRUE) # S3 method for class 'jclist' print(x, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"BB join count statistic for k-coloured factors — joincount.test","text":"fx factor length neighbours weights objects listw listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"less\" \"two.sided\". sampling default “nonfree”, may “free” adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted consistently (including spdep 0.3-28 adjustment inconsistent - thanks Tomoki NAKAYA careful bug report) spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() x object printed ... arguments passed printing","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"BB join count statistic for k-coloured factors — joincount.test","text":"list class jclist lists class htest k colours containing following components: statistic value standard deviate join count statistic. p.value p-value test. estimate value observed statistic, expectation variance non-free sampling. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"BB join count statistic for k-coloured factors — joincount.test","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, pp. 19-20.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"BB join count statistic for k-coloured factors — joincount.test","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"BB join count statistic for k-coloured factors — joincount.test","text":"derivation test (Cliff Ord, 1981, p. 18) assumes weights matrix symmetric. inherently non-symmetric matrices, k-nearest neighbour matrices, listw2U() can used make matrix symmetric. non-symmetric weights matrix cases, variance test statistic may negative.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"BB join count statistic for k-coloured factors — joincount.test","text":"","code":"data(oldcol) HICRIME <- cut(COL.OLD$CRIME, breaks=c(0,35,80), labels=c(\"low\",\"high\")) names(HICRIME) <- rownames(COL.OLD) joincount.test(HICRIME, nb2listw(COL.nb, style=\"B\")) #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"B\") #> #> Std. deviate for low = 1.0141, p-value = 0.1553 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 34.00000 29.59184 18.89550 #> #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"B\") #> #> Std. deviate for high = 6.3307, p-value = 1.22e-10 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 54.00000 27.22449 17.88838 #> joincount.test(HICRIME, nb2listw(COL.nb, style=\"B\"), sampling=\"free\") #> #> \tJoin count test under free sampling #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"B\") #> #> Std. deviate for low = 0.3993, p-value = 0.3448 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 34.00000 30.19575 90.76809 #> #> #> \tJoin count test under free sampling #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"B\") #> #> Std. deviate for high = 2.8518, p-value = 0.002173 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 54.0000 27.8284 84.2198 #> joincount.test(HICRIME, nb2listw(COL.nb, style=\"C\")) #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"C\") #> #> Std. deviate for low = 1.0141, p-value = 0.1553 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 7.1810345 6.2500000 0.8428969 #> #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"C\") #> #> Std. deviate for high = 6.3307, p-value = 1.22e-10 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 11.4051724 5.7500000 0.7979712 #> joincount.test(HICRIME, nb2listw(COL.nb, style=\"S\")) #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"S\") #> #> Std. deviate for low = 2.5786, p-value = 0.00496 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 8.2425673 6.2500000 0.5971141 #> #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"S\") #> #> Std. deviate for high = 6.1736, p-value = 3.337e-10 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 10.4249914 5.7500000 0.5734265 #> joincount.test(HICRIME, nb2listw(COL.nb, style=\"W\")) #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"W\") #> #> Std. deviate for low = 4.6675, p-value = 1.524e-06 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 9.5190476 6.2500000 0.4905378 #> #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"W\") #> #> Std. deviate for high = 5.1205, p-value = 1.523e-07 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 9.2920635 5.7500000 0.4784979 #> by(card(COL.nb), HICRIME, summary) #> HICRIME: low #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> 2.00 2.00 4.00 3.84 4.00 10.00 #> ------------------------------------------------------------ #> HICRIME: high #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> 3.000 4.750 6.000 5.667 7.000 9.000 print(is.symmetric.nb(COL.nb)) #> [1] TRUE coords.OLD <- cbind(COL.OLD$X, COL.OLD$Y) COL.k4.nb <- knn2nb(knearneigh(coords.OLD, 4)) print(is.symmetric.nb(COL.k4.nb)) #> [1] FALSE joincount.test(HICRIME, nb2listw(COL.k4.nb, style=\"B\")) #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: nb2listw(COL.k4.nb, style = \"B\") #> #> Std. deviate for low = 4.3698, p-value = 6.217e-06 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 36.500000 25.000000 6.925749 #> #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: nb2listw(COL.k4.nb, style = \"B\") #> #> Std. deviate for high = 6.7293, p-value = 8.523e-12 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 40.500000 23.000000 6.762918 #> cat(\"Note non-symmetric weights matrix - use listw2U()\\n\") #> Note non-symmetric weights matrix - use listw2U() joincount.test(HICRIME, listw2U(nb2listw(COL.k4.nb, style=\"B\"))) #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: listw2U(nb2listw(COL.k4.nb, style = \"B\")) #> #> Std. deviate for low = 4.3698, p-value = 6.217e-06 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 36.500000 25.000000 6.925749 #> #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: listw2U(nb2listw(COL.k4.nb, style = \"B\")) #> #> Std. deviate for high = 6.7293, p-value = 8.523e-12 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 40.500000 23.000000 6.762918 #> columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) HICRIME <- cut(columbus$CRIME, breaks=c(0,35,80), labels=c(\"low\",\"high\")) (nb <- poly2nb(columbus)) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 236 #> Percentage nonzero weights: 9.829238 #> Average number of links: 4.816327 lw <- nb2listw(nb, style=\"B\") joincount.test(HICRIME, lw) #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: lw #> #> Std. deviate for low = 1.1164, p-value = 0.1321 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 35.00000 30.10204 19.24708 #> #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: lw #> #> Std. deviate for high = 6.163, p-value = 3.57e-10 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 54.00000 27.69388 18.21936 #> col_geoms <- st_geometry(columbus) col_geoms[21] <- st_buffer(col_geoms[21], dist=-0.05) st_geometry(columbus) <- col_geoms (nb <- poly2nb(columbus)) #> Warning: some observations have no neighbours; #> if this seems unexpected, try increasing the snap argument. #> Warning: neighbour object has 3 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> 1 region with no links: #> 21 #> 3 disjoint connected subgraphs lw <- nb2listw(nb, style=\"B\", zero.policy=TRUE) joincount.test(HICRIME, lw) #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: lw #> #> Std. deviate for low = 1.0036, p-value = 0.1578 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 35.00000 30.58511 19.35032 #> #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: lw #> #> Std. deviate for high = 5.5716, p-value = 1.262e-08 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 52.00000 28.13830 18.34187 #>"},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":null,"dir":"Reference","previous_headings":"","what":"K nearest neighbours for spatial weights — knearneigh","title":"K nearest neighbours for spatial weights — knearneigh","text":"function returns matrix indices points belonging set k nearest neighbours . longlat = TRUE, Great Circle distances used. warning given identical points found.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"K nearest neighbours for spatial weights — knearneigh","text":"","code":"knearneigh(x, k=1, longlat = NULL, use_kd_tree=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"K nearest neighbours for spatial weights — knearneigh","text":"x matrix point coordinates, object inheriting SpatialPoints \"sf\" \"sfc\" object; \"sf\" \"sfc\" object geometries geographical coordinates (sf::st_is_longlat(x) == TRUE sf::sf_use_s2() == TRUE), s2 used find neighbours uses spatial indexing https://github.com/r-spatial/s2/issues/125 opposed legacy method uses brute-force k number nearest neighbours returned; identical points present, k least large largest count identical points (k smaller, error occur s2 used) longlat TRUE point coordinates longitude-latitude decimal degrees, case distances measured kilometers; x SpatialPoints object \"sf\" \"sfc\" object, value taken object ; longlat override kd_tree use_kd_tree logical value, dbscan package available, use finding k nearest neighbours coordinates planar, identical points; https://github.com/r-spatial/spdep/issues/38, input data may two columns dbscan used","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"K nearest neighbours for spatial weights — knearneigh","text":"underlying legacy C code based knn function class package.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"K nearest neighbours for spatial weights — knearneigh","text":"list class knn nn integer matrix region number ids np number input points k input required k dimension number columns x x input coordinates","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"K nearest neighbours for spatial weights — knearneigh","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"K nearest neighbours for spatial weights — knearneigh","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE) col.knn <- knearneigh(coords, k=4) plot(st_geometry(columbus), border=\"grey\") plot(knn2nb(col.knn), coords, add=TRUE) title(main=\"K nearest neighbours, k = 4\") data(state) us48.fipsno <- read.geoda(system.file(\"etc/weights/us48.txt\", package=\"spdep\")[1]) if (as.numeric(paste(version$major, version$minor, sep=\"\")) < 19) { m50.48 <- match(us48.fipsno$\"State.name\", state.name) } else { m50.48 <- match(us48.fipsno$\"State_name\", state.name) } xy <- as.matrix(as.data.frame(state.center))[m50.48,] llk4.nb <- knn2nb(knearneigh(xy, k=4, longlat=FALSE)) gck4.nb <- knn2nb(knearneigh(xy, k=4, longlat=TRUE)) plot(llk4.nb, xy) plot(diffnb(llk4.nb, gck4.nb), xy, add=TRUE, col=\"red\", lty=2) #> Warning: neighbour object has 22 sub-graphs title(main=\"Differences between Euclidean and Great Circle k=4 neighbours\") summary(llk4.nb, xy, longlat=TRUE, scale=0.5) #> Neighbour list object: #> Number of regions: 48 #> Number of nonzero links: 192 #> Percentage nonzero weights: 8.333333 #> Average number of links: 4 #> Non-symmetric neighbours list #> Link number distribution: #> #> 4 #> 48 #> 48 least connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links #> 48 most connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links summary(gck4.nb, xy, longlat=TRUE, scale=0.5) #> Neighbour list object: #> Number of regions: 48 #> Number of nonzero links: 192 #> Percentage nonzero weights: 8.333333 #> Average number of links: 4 #> Non-symmetric neighbours list #> Link number distribution: #> #> 4 #> 48 #> 48 least connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links #> 48 most connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links #xy1 <- SpatialPoints((as.data.frame(state.center))[m50.48,], # proj4string=CRS(\"+proj=longlat +ellps=GRS80\")) #gck4a.nb <- knn2nb(knearneigh(xy1, k=4)) #summary(gck4a.nb, xy1, scale=0.5) xy1 <- st_as_sf((as.data.frame(state.center))[m50.48,], coords=1:2, crs=st_crs(\"OGC:CRS84\")) old_use_s2 <- sf_use_s2() sf_use_s2(TRUE) system.time(gck4a.nb <- knn2nb(knearneigh(xy1, k=4))) #> user system elapsed #> 0.023 0.000 0.023 summary(gck4a.nb, xy1, scale=0.5) #> Neighbour list object: #> Number of regions: 48 #> Number of nonzero links: 192 #> Percentage nonzero weights: 8.333333 #> Average number of links: 4 #> Non-symmetric neighbours list #> Link number distribution: #> #> 4 #> 48 #> 48 least connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links #> 48 most connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links sf_use_s2(FALSE) #> Spherical geometry (s2) switched off system.time(gck4a.nb <- knn2nb(knearneigh(xy1, k=4))) #> user system elapsed #> 0.016 0.000 0.016 summary(gck4a.nb, xy1, scale=0.5) #> Neighbour list object: #> Number of regions: 48 #> Number of nonzero links: 192 #> Percentage nonzero weights: 8.333333 #> Average number of links: 4 #> Non-symmetric neighbours list #> Link number distribution: #> #> 4 #> 48 #> 48 least connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links #> 48 most connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links sf_use_s2(old_use_s2) #> Spherical geometry (s2) switched on # https://github.com/r-spatial/spdep/issues/38 run <- FALSE if (require(\"dbscan\", quietly=TRUE)) run <- TRUE if (run) { set.seed(1) x <- cbind(runif(50), runif(50), runif(50)) out <- knearneigh(x, k=5) knn2nb(out) } #> Neighbour list object: #> Number of regions: 50 #> Number of nonzero links: 250 #> Percentage nonzero weights: 10 #> Average number of links: 5 #> Non-symmetric neighbours list if (run) { # fails because dbscan works with > 2 dimensions but does # not work with duplicate points try(out <- knearneigh(rbind(x, x[1:10,]), k=5)) } #> Warning: knearneigh: identical points found #> Warning: knearneigh: kd_tree not available for identical points #> Error in knearneigh(rbind(x, x[1:10, ]), k = 5) : #> kd_tree required for more than 2 dimensions"},{"path":"https://r-spatial.github.io/spdep/reference/knn2nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Neighbours list from knn object — knn2nb","title":"Neighbours list from knn object — knn2nb","text":"function converts knn object returned knearneigh neighbours list class nb list integer vectors containing neighbour region number ids.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knn2nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Neighbours list from knn object — knn2nb","text":"","code":"knn2nb(knn, row.names = NULL, sym = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/knn2nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Neighbours list from knn object — knn2nb","text":"knn knn object returned knearneigh row.names character vector region ids added neighbours list attribute region.id, default seq(1, nrow(x)) sym force output neighbours list symmetry","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knn2nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Neighbours list from knn object — knn2nb","text":"function returns object class nb list integer vectors containing neighbour region number ids. See card details “nb” objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knn2nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Neighbours list from knn object — knn2nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/knn2nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Neighbours list from knn object — knn2nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries col.knn <- knearneigh(coords, k=4) plot(st_geometry(columbus), border=\"grey\") plot(knn2nb(col.knn), coords, add=TRUE) title(main=\"K nearest neighbours, k = 4\") # example of reading points with readr::read_csv() yielding a tibble load(system.file(\"etc/misc/coords.rda\", package=\"spdep\")) class(coords) #> [1] \"spec_tbl_df\" \"tbl_df\" \"tbl\" \"data.frame\" knn2nb(knearneigh(coords, k=4)) #> Neighbour list object: #> Number of regions: 100 #> Number of nonzero links: 400 #> Percentage nonzero weights: 4 #> Average number of links: 4 #> Non-symmetric neighbours list"},{"path":"https://r-spatial.github.io/spdep/reference/lag.listw.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial lag of a numeric vector — lag.listw","title":"Spatial lag of a numeric vector — lag.listw","text":"Using listw sparse representation spatial weights matrix, compute lag vector \\(V x\\)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lag.listw.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial lag of a numeric vector — lag.listw","text":"","code":"# S3 method for class 'listw' lag(x, var, zero.policy=attr(listw, \"zero.policy\"), NAOK=FALSE, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/lag.listw.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial lag of a numeric vector — lag.listw","text":"x listw object created example nb2listw var numeric vector length neighbours list listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA NAOK 'FALSE', presence 'NA' values regarded error; 'TRUE' 'NA' 'NaN' 'Inf' values var represented NA lagged value. ... additional arguments","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lag.listw.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial lag of a numeric vector — lag.listw","text":"numeric vector length var","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lag.listw.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial lag of a numeric vector — lag.listw","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lag.listw.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial lag of a numeric vector — lag.listw","text":"","code":"data(oldcol) Vx <- lag.listw(nb2listw(COL.nb, style=\"W\"), COL.OLD$CRIME) plot(Vx, COL.OLD$CRIME) plot(ecdf(COL.OLD$CRIME)) plot(ecdf(Vx), add=TRUE, col.points=\"red\", col.hor=\"red\") is.na(COL.OLD$CRIME[5]) <- TRUE VxNA <- lag.listw(nb2listw(COL.nb, style=\"W\"), COL.OLD$CRIME, NAOK=TRUE) #> Warning: NAs in lagged values"},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute Lee's statistic — lee","title":"Compute Lee's statistic — lee","text":"simple function compute Lee's L statistic bivariate spatial data; $$L(x,y) = \\frac{n}{\\sum_{=1}^{n}(\\sum_{j=1}^{n}w_{ij})^2} \\frac{\\sum_{=1}^{n}(\\sum_{j=1}^{n}w_{ij}(x_i-\\bar{x})) ((\\sum_{j=1}^{n}w_{ij}(y_j-\\bar{y}))}{\\sqrt{\\sum_{=1}^{n}(x_i - \\bar{x})^2} \\sqrt{\\sum_{=1}^{n}(y_i - \\bar{y})^2}} $$","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute Lee's statistic — lee","text":"","code":"lee(x, y, listw, n, S2, zero.policy=attr(listw, \"zero.policy\"), NAOK=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute Lee's statistic — lee","text":"x numeric vector length neighbours list listw y numeric vector length neighbours list listw listw listw object created example nb2listw n number zones S2 Sum squared sum weights rows. zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA NAOK 'TRUE' 'NA' 'NaN' 'Inf' values x passed foreign function. 'FALSE', presence 'NA' 'NaN' 'Inf' values regarded error.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute Lee's statistic — lee","text":"list L Lee's L statistic local L Lee's local L statistic","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute Lee's statistic — lee","text":"Lee (2001). Developing bivariate spatial association measure: integration Pearson's r Moran's . J Geograph Syst 3: 369-385","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute Lee's statistic — lee","text":"Roger Bivand Virgiio Gómez-Rubio Virgilio.Gomez@uclm.es","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute Lee's statistic — lee","text":"","code":"data(boston, package=\"spData\") lw<-nb2listw(boston.soi) x<-boston.c$CMEDV y<-boston.c$CRIM z<-boston.c$RAD Lxy<-lee(x, y, lw, length(x), zero.policy=TRUE) Lxz<-lee(x, z, lw, length(x), zero.policy=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Permutation test for Lee's L statistic — lee.mc","title":"Permutation test for Lee's L statistic — lee.mc","text":"permutation test Lee's L statistic calculated using nsim random permutations x y given spatial weighting scheme, establish rank observed statistic relation nsim simulated values.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Permutation test for Lee's L statistic — lee.mc","text":"","code":"lee.mc(x, y, listw, nsim, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\", na.action=na.fail, spChk=NULL, return_boot=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Permutation test for Lee's L statistic — lee.mc","text":"x numeric vector length neighbours list listw y numeric vector length neighbours list listw listw listw object created example nb2listw nsim number permutations zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"two.sided\", \"less\". na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass permitted meaningless permutation test. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() return_boot return object class boot equivalent permutation bootstrap rather object class htest","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Permutation test for Lee's L statistic — lee.mc","text":"list class htest mc.sim containing following components: statistic value observed Lee's L. parameter rank observed Lee's L. p.value pseudo p-value test. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data, number simulations. res nsim simulated values statistic, final value observed statistic","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Permutation test for Lee's L statistic — lee.mc","text":"Lee (2001). Developing bivariate spatial association measure: integration Pearson's r Moran's . J Geograph Syst 3: 369-385","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Permutation test for Lee's L statistic — lee.mc","text":"Roger Bivand, Virgilio Gómez-Rubio Virgilio.Gomez@uclm.es","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Permutation test for Lee's L statistic — lee.mc","text":"","code":"data(boston, package=\"spData\") lw<-nb2listw(boston.soi) x<-boston.c$CMEDV y<-boston.c$CRIM lee.mc(x, y, nsim=99, lw, zero.policy=TRUE, alternative=\"two.sided\") #> #> \tMonte-Carlo simulation of Lee's L #> #> data: x , y #> weights: lw #> number of simulations + 1: 100 #> #> statistic = -0.3263, observed rank = 1, p-value = 0.02 #> alternative hypothesis: two.sided #> #Test with missing values x[1:5]<-NA y[3:7]<-NA lee.mc(x, y, nsim=99, lw, zero.policy=TRUE, alternative=\"two.sided\", na.action=na.omit) #> #> \tMonte-Carlo simulation of Lee's L #> #> data: x , y #> weights: lw #> omitted: 1, 2, 3, 4, 5, 6, 7 #> number of simulations + 1: 100 #> #> statistic = -0.32447, observed rank = 1, p-value = 0.02 #> alternative hypothesis: two.sided #>"},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":null,"dir":"Reference","previous_headings":"","what":"Lee's L test for spatial autocorrelation — lee.test","title":"Lee's L test for spatial autocorrelation — lee.test","text":"Lee's L test spatial autocorrelation using spatial weights matrix weights list form. assumptions underlying test sensitive form graph neighbour relationships factors, results may checked lee.mc permutations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Lee's L test for spatial autocorrelation — lee.test","text":"","code":"lee.test(x, y, listw, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\", na.action=na.fail, spChk=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Lee's L test for spatial autocorrelation — lee.test","text":"x numeric vector length neighbours list listw y numeric vector length neighbours list listw listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one greater (default), less two.sided. na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass used, zero substituted NA values calculating spatial lag spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption()","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Lee's L test for spatial autocorrelation — lee.test","text":"list class htest containing following components: statistic value standard deviate Lee's L. p.value p-value test. estimate value observed Lee's L, expectation variance method assumption. alternative character string describing alternative hypothesis. method character string giving assumption used calculating standard deviate. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Lee's L test for spatial autocorrelation — lee.test","text":"See Lee (2004) details asymptotic expectation variance Lee's L computed. particular, check Lee (2004), table 1, page 1690. test may fail large datasets computation asymptotic expectation variance requires use dense matrices.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Lee's L test for spatial autocorrelation — lee.test","text":"Lee (2004). generalized significance testing method global measures spatial association: extension Mantel test. Environment Planning 2004, volume 36, pages 1687 - 1703","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Lee's L test for spatial autocorrelation — lee.test","text":"Roger Bivand Virgilio Gómez-Rubio Virgilio.Gomez@uclm.es","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Lee's L test for spatial autocorrelation — lee.test","text":"","code":"data(oldcol) col.W <- nb2listw(COL.nb, style=\"W\") crime <- COL.OLD$CRIME lee.test(crime, crime, col.W, zero.policy=TRUE) #> #> \tLee's L statistic randomisation #> #> data: crime , crime #> weights: col.W #> #> Lee's L statistic standard deviate = 5.2343, p-value = 8.279e-08 #> alternative hypothesis: greater #> sample estimates: #> Lee's L statistic Expectation Variance #> 0.547064219 0.239417989 0.003454459 #> #Test with missing values x<-crime y<-crime x[1:5]<-NA y[3:7]<-NA lee.test(x, y, col.W, zero.policy=TRUE, na.action=na.omit) #> #> \tLee's L statistic randomisation #> #> data: x , y #> weights: col.W #> omitted: 1, 2, 3, 4, 5, 6, 7 #> #> Lee's L statistic standard deviate = 6.6873, p-value = 1.137e-11 #> alternative hypothesis: greater #> sample estimates: #> Lee's L statistic Expectation Variance #> 0.706469726 0.260143244 0.004454563 #> # lee.test(x, y, col.W, zero.policy=TRUE)#Stops with an error data(boston, package=\"spData\") lw<-nb2listw(boston.soi) x<-boston.c$CMEDV y<-boston.c$CRIM lee.test(x, y, lw, zero.policy=TRUE, alternative=\"less\") #> #> \tLee's L statistic randomisation #> #> data: x , y #> weights: lw #> #> Lee's L statistic standard deviate = -11.54, p-value < 2.2e-16 #> alternative hypothesis: less #> sample estimates: #> Lee's L statistic Expectation Variance #> -0.326297206 -0.105040316 0.000367637 #> #Test with missing values x[1:5]<-NA y[3:7]<-NA lee.test(x, y, lw, zero.policy=TRUE, alternative=\"less\", na.action=na.omit) #> #> \tLee's L statistic randomisation #> #> data: x , y #> weights: lw #> omitted: 1, 2, 3, 4, 5, 6, 7 #> #> Lee's L statistic standard deviate = -11.284, p-value < 2.2e-16 #> alternative hypothesis: less #> sample estimates: #> Lee's L statistic Expectation Variance #> -0.3244748280 -0.1053154332 0.0003772109 #>"},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":null,"dir":"Reference","previous_headings":"","what":"Local Indicators for Categorical Data — licd_multi","title":"Local Indicators for Categorical Data — licd_multi","text":"Local indicators categorical data combine measure local composition window given per-observation set neighbouring observations, local multi-category joincount test simplified neighbours different categories compared focal observation","code":""},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Local Indicators for Categorical Data — licd_multi","text":"","code":"licd_multi(fx, listw, zero.policy = attr(listw, \"zero.policy\"), adjust.n = TRUE, nsim = 0L, iseed = NULL, no_repeat_in_row = FALSE, control = list())"},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Local Indicators for Categorical Data — licd_multi","text":"fx factor two categories, length neighbours weights objects listw listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted nsim default 0, number conditonal permutation simulations iseed default NULL, used set seed; output reproducible count CPU cores across computation distributed no_repeat_in_row default FALSE, TRUE, sample conditionally row without replacements avoid duplicate values, https://github.com/r-spatial/spdep/issues/124 control comp_binary=TRUE default TRUE, ignoring weights styles binary composition measures, binomial_punif_alternative=\"greater\", jcm_same_punif_alternative=\"less\", jcm_diff_punif_alternative=\"greater\", rank_ties.method=\"min\" default \"min\", na.last=\"keep\" leading rank NA returned observed joincount variance non-positive; TRUE joincount NAs ranked highest using rank, others see ?rank, check_reps=FALSE, unique_ceiling=1/3 used check_reps TRUE, check_reps=FALSE TRUE, check report many unique draws made among nsim draws, number unique draws less unique_ceiling, compute measures unique draws copy replicated draws, pysal_rank=FALSE use rank rank_ties.method na.last; TRUE, use pysal-style ranking find rank sum(sims <= obs, na.rm=TRUE)+1 pysal_sim_obs \"GE\", sum(sims < obs, na.rm=TRUE)+1 count observed greater \"GT\" simulated values, pysal_sim_obs=\"GT\" may also \"GE\", xtras=FALSE TRUE return calculated compostion values BW chi-squared, k-colour chi-squared, BW Anscombe","code":""},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Local Indicators for Categorical Data — licd_multi","text":"original code may found doi:10.5281/zenodo.4283766","code":""},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Local Indicators for Categorical Data — licd_multi","text":"local_comp data.frame object LICD local composition columns: ID, category_i, count_like_i, prop_i, count_nbs_i, pbinom_like_BW, pbinom_unlike_BW, pbinom_unlike_BW_alt, chi_BW_i, chi_K_i, anscombe_BW local_config data.frame object LICD local configuration columns: ID, jcm_chi_obs, jcm_count_BB_obs, jcm_count_BW_obs, jcm_count_WW_obs, pval_jcm_obs_BB, pval_jcm_obs_WW, pval_jcm_obs_BW local_comp_sim data.frame object permutation-based LICD local composition columns: ID, pbinom_like_BW, pbinom_unlike_BW, pbinom_unlike_BW_alt, rank_sim_chi_BW, rank_sim_chi_K, rank_sim_anscombe local_config_sim data.frame object permutation-based LICD local configuration columns: ID, jcm_chi_sim_rank, pval_jcm_obs_BB, pval_jcm_obs_BW, pval_jcm_obs_WW","code":""},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Local Indicators for Categorical Data — licd_multi","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 20; Upton, G., Fingleton, B. 1985 Spatial data analysis example: point pattern qualitative data, Wiley, pp. 158–170; Boots, B., 2003. Developing local measures spatial association categorical data. Journal Geographical Systems 5, 139–160; Boots, B., 2006. Local configuration measures categorical spatial data: binary regular lattices. Journal Geographical Systems 8 (1), 1–24; Pietrzak, M.B., Wilk, J., Kossowski, T., Bivand, R.S., 2014. application local indicators categorical data (LICD) spatial analysis economic development. Comparative Economic Research 17 (4), 203–220 doi:10.2478/cer-2014-0041 ; Bivand, R.S., Wilk, J., Kossowski, T., 2017. Spatial association population pyramids across Europe: application symbolic data, cluster analysis join-count tests. Spatial Statistics 21 (B), 339–361 doi:10.1016/j.spasta.2017.03.003 ; Francesco Carrer, Tomasz M. Kossowski, Justyna Wilk, Michał B. Pietrzak, Roger S. Bivand, application Local Indicators Categorical Data (LICD) explore spatial dependence archaeological spaces, Journal Archaeological Science, 126, 2021, doi:10.1016/j.jas.2020.105306","code":""},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Local Indicators for Categorical Data — licd_multi","text":"Roger Bivand Roger.Bivand@nhh.based earlier code Tomasz M. Kossowski, Justyna Wilk Michał B. Pietrzak","code":""},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Local Indicators for Categorical Data — licd_multi","text":"order increase numbers neighbours using nblag nblag_cumul advisable; use binary weights advised case used composition measure","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Local Indicators for Categorical Data — licd_multi","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) HICRIME <- cut(columbus$CRIME, breaks=c(0,35,80), labels=c(\"low\",\"high\")) (nb <- poly2nb(columbus)) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 236 #> Percentage nonzero weights: 9.829238 #> Average number of links: 4.816327 lw <- nb2listw(nblag_cumul(nblag(nb, 2)), style=\"B\") obj <- licd_multi(HICRIME, lw) str(obj) #> List of 4 #> $ local_comp :'data.frame':\t49 obs. of 11 variables: #> ..$ ID : int [1:49] 1 2 3 4 5 6 7 8 9 10 ... #> ..$ category_i : num [1:49] 1 1 1 1 2 1 1 2 1 1 ... #> ..$ count_like_i : num [1:49] 4 4 6 7 12 7 2 8 10 8 ... #> ..$ prop_i : num [1:49] 0.51 0.51 0.51 0.51 0.49 ... #> ..$ count_nbs_i : num [1:49] 5 6 11 14 22 14 11 14 25 17 ... #> ..$ pbinom_like_BW : num [1:49] 0.965 0.881 0.702 0.575 0.769 ... #> ..$ pbinom_unlike_BW : num [1:49] 0.0346 0.1192 0.2979 0.4255 0.2313 ... #> ..$ pbinom_unlike_BW_alt: num [1:49] 0.201 0.363 0.528 0.634 0.379 ... #> ..$ chi_BW_i : num [1:49] NA NA NA NA NA NA NA NA NA NA ... #> ..$ chi_K_i : num [1:49] NA NA NA NA NA NA NA NA NA NA ... #> ..$ anscombe_BW : num [1:49] NA NA NA NA NA NA NA NA NA NA ... #> $ local_config :'data.frame':\t49 obs. of 8 variables: #> ..$ ID : int [1:49] 1 2 3 4 5 6 7 8 9 10 ... #> ..$ jcm_chi_obs : num [1:49] 0 0.0625 0.625 2.7468 14.1889 ... #> ..$ jcm_count_BB_obs: num [1:49] 6 6 11 12 55 15 1 27 30 25 ... #> ..$ jcm_count_BW_obs: num [1:49] 4 7 23 31 50 36 15 31 73 53 ... #> ..$ jcm_count_WW_obs: num [1:49] 0 1 10 20 21 19 32 9 61 24 ... #> ..$ pval_jcm_obs_BB : num [1:49] 1 0.207108 0.70232 0.820405 0.000214 ... #> ..$ pval_jcm_obs_WW : num [1:49] 1 0.3946 0.0981 0.0243 0.7839 ... #> ..$ pval_jcm_obs_BW : num [1:49] 1.00 1.75e-01 2.08e-01 5.10e-02 3.52e-06 ... #> $ local_comp_sim : NULL #> $ local_config_sim: NULL #> - attr(*, \"timings\")=List of 3 #> ..$ set_up : 'proc_time' Named num [1:5] 0 0 0 0 0 #> .. ..- attr(*, \"names\")= chr [1:5] \"user.self\" \"sys.self\" \"elapsed\" \"user.child\" ... #> ..$ processing : 'proc_time' Named num [1:5] 0.104 0 0.106 0 0 #> .. ..- attr(*, \"names\")= chr [1:5] \"user.self\" \"sys.self\" \"elapsed\" \"user.child\" ... #> ..$ postprocessing: 'proc_time' Named num [1:5] 0.001 0 0.001 0 0 #> .. ..- attr(*, \"names\")= chr [1:5] \"user.self\" \"sys.self\" \"elapsed\" \"user.child\" ... #> - attr(*, \"out\")= num [1:49, 1:35] 1 1 1 1 2 1 1 2 1 1 ... #> ..- attr(*, \"ncpus\")= int 1 #> ..- attr(*, \"dimnames\")=List of 2 #> .. ..$ : NULL #> .. ..$ : chr [1:35] \"category_i\" \"count_like_i\" \"prop_i\" \"count_nbs_i\" ... #> - attr(*, \"ncpus\")= int 1 #> - attr(*, \"nsim\")= int 0 #> - attr(*, \"con\")=List of 11 #> ..$ comp_binary : logi TRUE #> ..$ binomial_punif_alternative: chr \"greater\" #> ..$ jcm_same_punif_alternative: chr \"less\" #> ..$ jcm_diff_punif_alternative: chr \"greater\" #> ..$ rank_ties.method : chr \"min\" #> ..$ unique_ceiling : num 0.333 #> ..$ check_reps : logi FALSE #> ..$ pysal_rank : logi FALSE #> ..$ pysal_sim_obs : chr \"GT\" #> ..$ na.last : chr \"keep\" #> ..$ xtras : logi FALSE #> - attr(*, \"class\")= chr [1:2] \"licd\" \"list\" h_obj <- hotspot(obj) str(h_obj) #> List of 9 #> $ ID : int [1:49] 1 2 3 4 5 6 7 8 9 10 ... #> $ local_comp : Factor w/ 2 levels \"Cluster\",\"Dispersed\": 2 2 2 2 2 2 2 2 2 2 ... #> $ local_comp_sim : NULL #> $ local_config : Factor w/ 3 levels \"Cluster\",\"Dispersed\",..: 3 3 3 3 2 3 3 2 3 3 ... #> $ local_config_sim: NULL #> $ both : Factor w/ 6 levels \"Cluster.Cluster\",..: 6 6 6 6 4 6 6 4 6 6 ... #> $ both_sim : NULL #> $ both_recode : Factor w/ 4 levels \"Clump\",\"Cluster\",..: 4 4 4 4 3 4 4 3 4 4 ... #> $ both_recode_sim : NULL table(h_obj$both_recode) #> #> Clump Cluster Dispersed No cluster #> 8 3 11 27 columbus$both <- h_obj$both_recode plot(columbus[, \"both\"]) GDAL37 <- numeric_version(unname(sf::sf_extSoftVersion()[\"GDAL\"]), strict=FALSE) (GDAL37 <- ifelse(is.na(GDAL37), FALSE, GDAL37 >= \"3.7.0\")) #> [1] TRUE file <- \"etc/shapes/GB_2024_southcoast_50m.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) { sc50m <- st_read(zipfile) } else { td <- tempdir() bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE) target <- unzip(zipfile, files=bn, exdir=td) sc50m <- st_read(target) } #> Reading layer `GB_2024_southcoast_50m' from data source #> `/tmp/Rtmp5vVziX/temp_libpath224d25059ed81/spdep/etc/shapes/GB_2024_southcoast_50m.gpkg.zip' #> using driver `GPKG' #> Simple feature collection with 119 features and 19 fields #> Geometry type: MULTIPOLYGON #> Dimension: XY #> Bounding box: xmin: 82643.12 ymin: 5342.9 xmax: 640301.6 ymax: 187226.2 #> Projected CRS: OSGB36 / British National Grid sc50m$Winner <- factor(sc50m$Winner, levels=c(\"Con\", \"Green\", \"Lab\", \"LD\")) plot(sc50m[,\"Winner\"], pal=c(\"#2297E6\", \"#61D04F\", \"#DF536B\", \"#F5C710\")) nb_sc_50m <- poly2nb(sc50m, row.names=as.character(sc50m$Constituency)) #> Warning: neighbour object has 2 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. sub2 <- attr(nb_sc_50m, \"region.id\")[attr(nb_sc_50m, \"ncomp\")$comp.id == 2L] iowe <- match(sub2[1], attr(nb_sc_50m, \"region.id\")) diowe <- c(st_distance(sc50m[iowe,], sc50m)) meet_criterion <- sum(diowe <= units::set_units(5000, \"m\")) cands <- attr(nb_sc_50m, \"region.id\")[order(diowe)[1:meet_criterion]] nb_sc_50m_iowe <- addlinks1(nb_sc_50m, from = cands[1], to = cands[3:meet_criterion]) ioww <- match(sub2[2], attr(nb_sc_50m, \"region.id\")) dioww <- c(st_distance(sc50m[ioww,], sc50m)) meet_criterion <- sum(dioww <= units::set_units(5000, \"m\")) cands <- attr(nb_sc_50m, \"region.id\")[order(dioww)[1:meet_criterion]] nb_sc_50m_iow <- addlinks1(nb_sc_50m_iowe, from = cands[2], to = cands[3:meet_criterion]) nb_sc_1_2 <- nblag_cumul(nblag(nb_sc_50m_iow, 2)) lw <- nb2listw(nb_sc_1_2, style=\"B\") licd_obj <- licd_multi(sc50m$Winner, lw) h_obj <- hotspot(licd_obj) sc50m$both <- h_obj$both_recode plot(sc50m[, \"both\"]) ljc <- local_joincount_uni(factor(sc50m$Winner == \"LD\"), chosen=\"TRUE\", lw) sc50m$LD_pv <- ljc[, 2] plot(sc50m[, \"LD_pv\"], breaks=c(0, 0.025, 0.05, 0.1, 0.5, 1))"},{"path":"https://r-spatial.github.io/spdep/reference/listw2sn.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial neighbour sparse representation — listw2sn","title":"Spatial neighbour sparse representation — listw2sn","text":"function makes \"spatial neighbour\" object representation (similar S-PLUS spatial statististics module representation \"listw\" spatial weights object. sn2listw() inverse function listw2sn(), creating \"listw\" object \"spatial neighbour\" object.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/listw2sn.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial neighbour sparse representation — listw2sn","text":"","code":"listw2sn(listw) sn2listw(sn, style = NULL, zero.policy = NULL, from_mat2listw=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/listw2sn.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial neighbour sparse representation — listw2sn","text":"listw listw object example nb2listw sn spatial.neighbour object style default NULL, missing, set \"M\" warning given; \"M\", passed nb2listw re-build object zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors from_mat2listw default FALSE, set TRUE called mat2listw","code":""},{"path":"https://r-spatial.github.io/spdep/reference/listw2sn.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial neighbour sparse representation — listw2sn","text":"listw2sn()returns data frame three columns, class spatial.neighbour: region number id start link (S-PLUS row.id) region number id end link (S-PLUS col.id) weights weight link","code":""},{"path":"https://r-spatial.github.io/spdep/reference/listw2sn.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial neighbour sparse representation — listw2sn","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/listw2sn.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial neighbour sparse representation — listw2sn","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) col.listw <- nb2listw(col.gal.nb) col.listw$neighbours[[1]] #> [1] 2 3 col.listw$weights[[1]] #> [1] 0.5 0.5 col.sn <- listw2sn(col.listw) str(col.sn) #> Classes ‘spatial.neighbour’ and 'data.frame':\t230 obs. of 3 variables: #> $ from : int 1 1 2 2 2 3 3 3 3 4 ... #> $ to : int 2 3 1 3 4 1 2 4 5 2 ... #> $ weights: num 0.5 0.5 0.333 0.333 0.333 ... #> - attr(*, \"n\")= int 49 #> - attr(*, \"region.id\")= chr [1:49] \"1\" \"2\" \"3\" \"4\" ... #> - attr(*, \"neighbours.attrs\")= chr [1:7] \"class\" \"region.id\" \"GeoDa\" \"gal\" ... #> - attr(*, \"weights.attrs\")= chr [1:3] \"mode\" \"W\" \"comp\" #> - attr(*, \"GeoDa\")=List of 2 #> ..$ shpfile: chr NA #> ..$ ind : chr NA #> - attr(*, \"listw.call\")= language nb2listw(neighbours = col.gal.nb)"},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":null,"dir":"Reference","previous_headings":"","what":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"function reports estimates tests chosen among five statistics testing spatial dependence linear models. statistics simple RS test error dependence (“RSerr”), simple RS test missing spatially lagged dependent variable (“RSlag”), variants adjusted presence (“adjRSerr” tests error dependence possible presence missing lagged dependent variable, “adjRSlag” way round), portmanteau test (“SARMA”, fact “RSerr” + “adjRSlag”). Note: spdep 1.3-2, tests re-named “RS” - Rao's score tests, rather “LM” - Lagrange multiplier tests match naming tests family SDM.RStests.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"","code":"lm.RStests(model, listw, zero.policy=attr(listw, \"zero.policy\"), test=\"RSerr\", spChk=NULL, naSubset=TRUE) lm.LMtests(model, listw, zero.policy=attr(listw, \"zero.policy\"), test=\"LMerr\", spChk=NULL, naSubset=TRUE) # S3 method for class 'RStestlist' print(x, ...) # S3 method for class 'RStestlist' summary(object, p.adjust.method=\"none\", ...) # S3 method for class 'RStestlist.summary' print(x, digits=max(3, getOption(\"digits\") - 2), ...) "},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"model object class lm returned lm, optionally vector externally calculated residuals (run though na.omit NAs present) use \"RSerr\" chosen; weights offsets used lm object listw listw object created example nb2listw, expected row-standardised (W-style) zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA test character vector tests requested chosen RSerr, RSlag, adjRSerr, adjRSlag, SARMA; test=\"\" computes tests. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() naSubset default TRUE subset listw object omitted observations model object (change earlier behaviour, model$na.action component ignored, listw object subsetted hand) x, object object printed p.adjust.method character string specifying probability value adjustment (see p.adjust) multiple tests, default \"none\" digits minimum number significant digits used numbers ... printing arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"two types dependence spatial lag \\(\\rho\\) spatial error \\(\\lambda\\): $$ \\mathbf{y} = \\mathbf{X \\beta} + \\rho \\mathbf{W_{(1)} y} + \\mathbf{u}, $$ $$ \\mathbf{u} = \\lambda \\mathbf{W_{(2)} u} + \\mathbf{e} $$ \\(\\mathbf{e}\\) well-behaved, uncorrelated error term. Tests missing spatially lagged dependent variable test \\(\\rho = 0\\), tests spatial autocorrelation error \\(\\mathbf{u}\\) test whether \\(\\lambda = 0\\). \\(\\mathbf{W}\\) spatial weights matrix; tests used identical. factors ordered factors among explanatory variables regression, coding contrasts affects outcomes significance tests.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"list class RStestlist htest objects, : statistic value Rao's score (.k.Lagrange multiplier) test. parameter number degrees freedom p.value p-value test. method character string giving method used. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"Anselin, L. 1988 Spatial econometrics: methods models. (Dordrecht: Kluwer); Anselin, L., Bera, . K., Florax, R. Yoon, M. J. 1996 Simple diagnostic tests spatial dependence. Regional Science Urban Economics, 26, 77–104 doi:10.1016/0166-0462(95)02111-6 ; Malabika Koley (2024) Specification Testing General Nesting Spatial Model, https://sites.google.com/view/malabikakoley/research.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"Roger Bivand Roger.Bivand@nhh.Andrew Bernat","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"","code":"data(oldcol) oldcrime.lm <- lm(CRIME ~ HOVAL + INC, data = COL.OLD) summary(oldcrime.lm) #> #> Call: #> lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD) #> #> Residuals: #> Min 1Q Median 3Q Max #> -34.418 -6.388 -1.580 9.052 28.649 #> #> Coefficients: #> Estimate Std. Error t value Pr(>|t|) #> (Intercept) 68.6190 4.7355 14.490 < 2e-16 *** #> HOVAL -0.2739 0.1032 -2.654 0.0109 * #> INC -1.5973 0.3341 -4.780 1.83e-05 *** #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #> #> Residual standard error: 11.43 on 46 degrees of freedom #> Multiple R-squared: 0.5524,\tAdjusted R-squared: 0.5329 #> F-statistic: 28.39 on 2 and 46 DF, p-value: 9.341e-09 #> lw <- nb2listw(COL.nb) res <- lm.RStests(oldcrime.lm, listw=lw, test=\"all\") summary(res) #> \tRao's score (a.k.a Lagrange multiplier) diagnostics for spatial #> \tdependence #> data: #> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD) #> test weights: lw #> #> statistic parameter p.value #> RSerr 5.723131 1 0.016743 * #> RSlag 9.363684 1 0.002213 ** #> adjRSerr 0.079495 1 0.777983 #> adjRSlag 3.720048 1 0.053763 . #> SARMA 9.443178 2 0.008901 ** #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 if (require(\"spatialreg\", quietly=TRUE)) { oldcrime.slx <- lmSLX(CRIME ~ HOVAL + INC, data = COL.OLD, listw=lw) summary(lm.RStests(oldcrime.slx, listw=lw, test=c(\"adjRSerr\", \"adjRSlag\"))) } #> \tRao's score (a.k.a Lagrange multiplier) diagnostics for spatial #> \tdependence #> data: #> model: lm(CRIME ~ HOVAL + INC + lag.HOVAL + lag.INC, data = COL.OLD, #> listw = lw) #> test weights: lw #> #> statistic parameter p.value #> GNM_adjRSerr 0.10933 1 0.7409 #> GNM_adjRSlag 0.61580 1 0.4326 run <- require(\"codingMatrices\", quietly=TRUE) if (run) { COL.OLD$fEW <- factor(COL.OLD$EW) COL.OLD$fDISCBD <- ordered(cut(COL.OLD$DISCBD, c(0, 1.5, 3, 4.5, 6))) f <- formula(CRIME ~ INC + HOVAL + fDISCBD*fEW) lw <- nb2listw(COL.nb, style=\"W\") # default codings summary(lm.RStests(lm(f, data=COL.OLD, contrasts=list(fDISCBD=\"contr.poly\", fEW=\"contr.treatment\")), lw, test=c(\"adjRSerr\", \"adjRSlag\"))) } #> \tRao's score (a.k.a Lagrange multiplier) diagnostics for spatial #> \tdependence #> data: #> model: lm(formula = f, data = COL.OLD, contrasts = list(fDISCBD = #> \"contr.poly\", fEW = \"contr.treatment\")) #> test weights: lw #> #> statistic parameter p.value #> adjRSerr 0.98727 1 0.3204 #> adjRSlag 1.14732 1 0.2841 if (run) { # use codingMatrices::code_diff for ordered factor summary(lm.RStests(lm(f, data=COL.OLD, contrasts=list(fDISCBD=\"code_diff\", fEW=\"contr.treatment\")), lw, test=c(\"adjRSerr\", \"adjRSlag\"))) } #> \tRao's score (a.k.a Lagrange multiplier) diagnostics for spatial #> \tdependence #> data: #> model: lm(formula = f, data = COL.OLD, contrasts = list(fDISCBD = #> \"code_diff\", fEW = \"contr.treatment\")) #> test weights: lw #> #> statistic parameter p.value #> adjRSerr 0.03415 1 0.8534 #> adjRSlag -0.01572 1 1.0000 if (run) { # use codingMatrices::code_control for both summary(lm.RStests(lm(f, data=COL.OLD, contrasts=list(fDISCBD=\"code_control\", fEW=\"code_control\")), lw, test=c(\"adjRSerr\", \"adjRSlag\"))) } #> \tRao's score (a.k.a Lagrange multiplier) diagnostics for spatial #> \tdependence #> data: #> model: lm(formula = f, data = COL.OLD, contrasts = list(fDISCBD = #> \"code_control\", fEW = \"code_control\")) #> test weights: lw #> #> statistic parameter p.value #> adjRSerr 0.0383759 1 0.8447 #> adjRSlag -0.0062517 1 1.0000"},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":null,"dir":"Reference","previous_headings":"","what":"Exact global Moran's I test — lm.morantest.exact","title":"Exact global Moran's I test — lm.morantest.exact","text":"function implements Tiefelsdorf's exact global Moran's test.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Exact global Moran's I test — lm.morantest.exact","text":"","code":"lm.morantest.exact(model, listw, zero.policy = attr(listw, \"zero.policy\"), alternative = \"greater\", spChk = NULL, resfun = weighted.residuals, zero.tol = 1e-07, Omega=NULL, save.M=NULL, save.U=NULL, useTP=FALSE, truncErr=1e-6, zeroTreat=0.1) # S3 method for class 'moranex' print(x, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Exact global Moran's I test — lm.morantest.exact","text":"model object class lm returned lm; weights may specified lm fit, offsets used listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one greater (default), less two.sided. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() resfun default: weighted.residuals; function used extract residuals lm object, may residuals, weighted.residuals, rstandard, rstudent zero.tol tolerance used find eigenvalues close absolute zero Omega SAR process matrix may passed test alternative hypothesis, example Omega <- invIrW(listw, rho=0.1); Omega <- tcrossprod(Omega), chol() taken internally save.M return full M matrix use spdep:::exactMoranAlt save.U return full U matrix use spdep:::exactMoranAlt useTP default FALSE, TRUE, use truncation point integration rather upper=Inf, see Tiefelsdorf (2000), eq. 6.7, p.69 truncErr useTP=TRUE, pass truncation error truncation point function zeroTreat useTP=TRUE, pass zero adjustment truncation point function x moranex object ... arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Exact global Moran's I test — lm.morantest.exact","text":"list class moranex following components: statistic value exact standard deviate global Moran's . p.value p-value test. estimate value observed global Moran's . method character string giving method used. alternative character string describing alternative hypothesis. gamma eigenvalues (excluding zero values) oType usually set \"E\" data.name character string giving name(s) data. df degrees freedom","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Exact global Moran's I test — lm.morantest.exact","text":"Markus Reder Roger Bivand","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Exact global Moran's I test — lm.morantest.exact","text":"Roger Bivand, Werner G. Müller Markus Reder (2009) \"Power calculations global local Moran's .\" Computational Statistics & Data Analysis 53, 2859-2872.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Exact global Moran's I test — lm.morantest.exact","text":"","code":"eire <- st_read(system.file(\"shapes/eire.gpkg\", package=\"spData\")[1]) #> Reading layer `eire' from data source #> `/home/rsb/lib/r_libs/spData/shapes/eire.gpkg' using driver `GPKG' #> Simple feature collection with 26 features and 10 fields #> Geometry type: MULTIPOLYGON #> Dimension: XY #> Bounding box: xmin: -4.12 ymin: 5768 xmax: 300.82 ymax: 6119.25 #> Projected CRS: Undefined Cartesian SRS with unknown unit row.names(eire) <- as.character(eire$names) eire.nb <- poly2nb(eire) e.lm <- lm(OWNCONS ~ ROADACC, data=eire) lm.morantest(e.lm, nb2listw(eire.nb)) #> #> \tGlobal Moran I for regression residuals #> #> data: #> model: lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #> #> Moran I statistic standard deviate = 3.2575, p-value = 0.0005619 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I Expectation Variance #> 0.33660565 -0.05877741 0.01473183 #> lm.morantest.sad(e.lm, nb2listw(eire.nb)) #> #> \tSaddlepoint approximation for global Moran's I (Barndorff-Nielsen #> \tformula) #> #> data: #> model:lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #> #> Saddlepoint approximation = 2.9395, p-value = 0.001644 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I #> 0.3366057 #> lm.morantest.exact(e.lm, nb2listw(eire.nb)) #> #> \tGlobal Moran I statistic with exact p-value #> #> data: #> model:lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #> #> Exact standard deviate = 2.9316, p-value = 0.001686 #> alternative hypothesis: greater #> sample estimates: #> [1] 0.3366057 #> lm.morantest.exact(e.lm, nb2listw(eire.nb), useTP=TRUE) #> #> \tGlobal Moran I statistic with exact p-value #> #> data: #> model:lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #> #> Exact standard deviate = 2.9315, p-value = 0.001686 #> alternative hypothesis: greater #> sample estimates: #> [1] 0.3366057 #>"},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":null,"dir":"Reference","previous_headings":"","what":"Moran's I test for residual spatial autocorrelation — lm.morantest","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"Moran's test spatial autocorrelation residuals estimated linear model (lm()).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"","code":"lm.morantest(model, listw, zero.policy=attr(listw, \"zero.policy\"), alternative = \"greater\", spChk=NULL, resfun=weighted.residuals, naSubset=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"model object class lm returned lm; weights may specified lm fit, offsets used listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"less\" \"two.sided\". spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() resfun default: weighted.residuals; function used extract residuals lm object, may residuals, weighted.residuals, rstandard, rstudent naSubset default TRUE subset listw object omitted observations model object (change earlier behaviour, model$na.action component ignored, listw object subsetted hand)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"list class htest containing following components: statistic value standard deviate Moran's . p.value p-value test. estimate value observed Moran's , expectation variance method assumption. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 203,","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"factors ordered factors among explanatory variables regression, coding contrasts affects outcomes significance tests.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"","code":"data(oldcol) oldcrime1.lm <- lm(CRIME ~ 1, data = COL.OLD) oldcrime.lm <- lm(CRIME ~ HOVAL + INC, data = COL.OLD) lm.morantest(oldcrime.lm, nb2listw(COL.nb, style=\"W\")) #> #> \tGlobal Moran I for regression residuals #> #> data: #> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD) #> weights: nb2listw(COL.nb, style = \"W\") #> #> Moran I statistic standard deviate = 2.9539, p-value = 0.001569 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I Expectation Variance #> 0.235638354 -0.033302866 0.008289408 #> lm.LMtests(oldcrime.lm, nb2listw(COL.nb, style=\"W\")) #> Please update scripts to use lm.RStests in place of lm.LMtests #> #> \tRao's score (a.k.a Lagrange multiplier) diagnostics for spatial #> \tdependence #> #> data: #> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD) #> test weights: listw #> #> RSerr = 5.7231, df = 1, p-value = 0.01674 #> lm.morantest(oldcrime.lm, nb2listw(COL.nb, style=\"S\")) #> #> \tGlobal Moran I for regression residuals #> #> data: #> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD) #> weights: nb2listw(COL.nb, style = \"S\") #> #> Moran I statistic standard deviate = 3.1745, p-value = 0.0007504 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I Expectation Variance #> 0.239317561 -0.033431740 0.007381982 #> lm.morantest(oldcrime1.lm, nb2listw(COL.nb, style=\"W\")) #> #> \tGlobal Moran I for regression residuals #> #> data: #> model: lm(formula = CRIME ~ 1, data = COL.OLD) #> weights: nb2listw(COL.nb, style = \"W\") #> #> Moran I statistic standard deviate = 5.6754, p-value = 6.92e-09 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I Expectation Variance #> 0.510951264 -0.020833333 0.008779831 #> moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"W\"), randomisation=FALSE) #> #> \tMoran I test under normality #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.nb, style = \"W\") #> #> Moran I statistic standard deviate = 5.6754, p-value = 6.92e-09 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.510951264 -0.020833333 0.008779831 #> oldcrime.wlm <- lm(CRIME ~ HOVAL + INC, data = COL.OLD, weights = I(1/AREA_PL)) lm.morantest(oldcrime.wlm, nb2listw(COL.nb, style=\"W\"), resfun=weighted.residuals) #> #> \tGlobal Moran I for regression residuals #> #> data: #> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD, weights = #> I(1/AREA_PL)) #> weights: nb2listw(COL.nb, style = \"W\") #> #> Moran I statistic standard deviate = 3.0141, p-value = 0.001289 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I Expectation Variance #> 0.241298974 -0.032224366 0.008235091 #> lm.morantest(oldcrime.wlm, nb2listw(COL.nb, style=\"W\"), resfun=rstudent) #> #> \tGlobal Moran I for regression residuals #> #> data: #> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD, weights = #> I(1/AREA_PL)) #> weights: nb2listw(COL.nb, style = \"W\") #> #> Moran I statistic standard deviate = 2.822, p-value = 0.002387 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I Expectation Variance #> 0.223860298 -0.032224366 0.008235091 #> run <- require(\"codingMatrices\", quietly=TRUE) if (run) { COL.OLD$fEW <- factor(COL.OLD$EW) COL.OLD$fDISCBD <- ordered(cut(COL.OLD$DISCBD, c(0, 1.5, 3, 4.5, 6))) f <- formula(CRIME ~ INC + HOVAL + fDISCBD*fEW) lw <- nb2listw(COL.nb, style=\"W\") # default codings lm.morantest(lm(f, data=COL.OLD, contrasts=list(fDISCBD=\"contr.poly\", fEW=\"contr.treatment\")), lw) } #> #> \tGlobal Moran I for regression residuals #> #> data: #> model: lm(formula = f, data = COL.OLD, contrasts = list(fDISCBD = #> \"contr.poly\", fEW = \"contr.treatment\")) #> weights: lw #> #> Moran I statistic standard deviate = 0.98381, p-value = 0.1626 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I Expectation Variance #> -0.020008220 -0.099678739 0.006558024 #> if (run) { # use codingMatrices::code_diff for ordered factor lm.morantest(lm(f, data=COL.OLD, contrasts=list(fDISCBD=\"code_diff\", fEW=\"contr.treatment\")), lw) } #> #> \tGlobal Moran I for regression residuals #> #> data: #> model: lm(formula = f, data = COL.OLD, contrasts = list(fDISCBD = #> \"code_diff\", fEW = \"contr.treatment\")) #> weights: lw #> #> Moran I statistic standard deviate = 1.5595, p-value = 0.05944 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I Expectation Variance #> -0.02000822 -0.23955333 0.01981926 #> if (run) { # use stats::contr.treatment for both factors lm.morantest(lm(f, data=COL.OLD, contrasts=list(fDISCBD=\"contr.treatment\", fEW=\"contr.treatment\")), lw) } #> #> \tGlobal Moran I for regression residuals #> #> data: #> model: lm(formula = f, data = COL.OLD, contrasts = list(fDISCBD = #> \"contr.treatment\", fEW = \"contr.treatment\")) #> weights: lw #> #> Moran I statistic standard deviate = 1.3866, p-value = 0.08278 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I Expectation Variance #> -0.02000822 -0.55316698 0.14784790 #> if (run) { # use codingMatrices::code_control for factor lm.morantest(lm(f, data=COL.OLD, contrasts=list(fDISCBD=\"code_diff\", fEW=\"code_control\")), lw) } #> #> \tGlobal Moran I for regression residuals #> #> data: #> model: lm(formula = f, data = COL.OLD, contrasts = list(fDISCBD = #> \"code_diff\", fEW = \"code_control\")) #> weights: lw #> #> Moran I statistic standard deviate = 1.568, p-value = 0.05844 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I Expectation Variance #> -0.02000822 -0.28007346 0.02750775 #> if (run) { # use codingMatrices::code_control for both lm.morantest(lm(f, data=COL.OLD, contrasts=list(fDISCBD=\"code_control\", fEW=\"code_control\")), lw) } #> #> \tGlobal Moran I for regression residuals #> #> data: #> model: lm(formula = f, data = COL.OLD, contrasts = list(fDISCBD = #> \"code_control\", fEW = \"code_control\")) #> weights: lw #> #> Moran I statistic standard deviate = 1.4316, p-value = 0.07613 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I Expectation Variance #> -0.02000822 -0.26418630 0.02909259 #>"},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":null,"dir":"Reference","previous_headings":"","what":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"function implements Tiefelsdorf's application Saddlepoint approximation global Moran's 's reference distribution.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"","code":"lm.morantest.sad(model, listw, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\", spChk=NULL, resfun=weighted.residuals, tol=.Machine$double.eps^0.5, maxiter=1000, tol.bounds=0.0001, zero.tol = 1e-07, Omega=NULL, save.M=NULL, save.U=NULL) # S3 method for class 'moransad' print(x, ...) # S3 method for class 'moransad' summary(object, ...) # S3 method for class 'summary.moransad' print(x, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"model object class lm returned lm; weights may specified lm fit, offsets used listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one greater (default), less two.sided. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() resfun default: weighted.residuals; function used extract residuals lm object, may residuals, weighted.residuals, rstandard, rstudent tol desired accuracy (convergence tolerance) uniroot maxiter maximum number iterations uniroot tol.bounds offset bounds uniroot zero.tol tolerance used find eigenvalues close absolute zero Omega SAR process matrix may passed test alternative hypothesis, example Omega <- invIrW(listw, rho=0.1); Omega <- tcrossprod(Omega), chol() taken internally save.M return full M matrix use spdep:::exactMoranAlt save.U return full U matrix use spdep:::exactMoranAlt x object printed object object summarised ... arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"function involves finding eigenvalues n n matrix, numerically finding root Saddlepoint approximation, therefore used care n large.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"list class moransad following components: statistic value saddlepoint approximation standard deviate global Moran's . p.value p-value test. estimate value observed global Moran's . alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data. internal1 Saddlepoint omega, r u internal2 f.root, iter estim.prec uniroot df degrees freedom tau eigenvalues (excluding zero values)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"Tiefelsdorf, M. 2002 Saddlepoint approximation Moran's local Moran's Ii reference distributions numerical evaluation. Geographical Analysis, 34, pp. 187–206; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"","code":"eire <- st_read(system.file(\"shapes/eire.gpkg\", package=\"spData\")[1]) #> Reading layer `eire' from data source #> `/home/rsb/lib/r_libs/spData/shapes/eire.gpkg' using driver `GPKG' #> Simple feature collection with 26 features and 10 fields #> Geometry type: MULTIPOLYGON #> Dimension: XY #> Bounding box: xmin: -4.12 ymin: 5768 xmax: 300.82 ymax: 6119.25 #> Projected CRS: Undefined Cartesian SRS with unknown unit row.names(eire) <- as.character(eire$names) eire.nb <- poly2nb(eire) e.lm <- lm(OWNCONS ~ ROADACC, data=eire) lm.morantest(e.lm, nb2listw(eire.nb)) #> #> \tGlobal Moran I for regression residuals #> #> data: #> model: lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #> #> Moran I statistic standard deviate = 3.2575, p-value = 0.0005619 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I Expectation Variance #> 0.33660565 -0.05877741 0.01473183 #> lm.morantest.sad(e.lm, nb2listw(eire.nb)) #> #> \tSaddlepoint approximation for global Moran's I (Barndorff-Nielsen #> \tformula) #> #> data: #> model:lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #> #> Saddlepoint approximation = 2.9395, p-value = 0.001644 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I #> 0.3366057 #> summary(lm.morantest.sad(e.lm, nb2listw(eire.nb))) #> #> \tSaddlepoint approximation for global Moran's I (Barndorff-Nielsen #> \tformula) #> #> data: #> model:lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #> #> Saddlepoint approximation = 2.9395, p-value = 0.001644 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I #> 0.3366057 #> #> Expectation Variance Std. deviate Skewness Kurtosis Minimum #> -0.05877741 0.01473183 3.25753938 0.31336881 3.05047361 -0.67545810 #> Maximum omega sad.r sad.u #> 0.89091555 0.76549075 2.77616585 4.36854629 #> f.root iter estim.prec #> 6.996834e-14 1.100000e+01 NA e.wlm <- lm(OWNCONS ~ ROADACC, data=eire, weights=RETSALE) lm.morantest(e.wlm, nb2listw(eire.nb), resfun=rstudent) #> #> \tGlobal Moran I for regression residuals #> #> data: #> model: lm(formula = OWNCONS ~ ROADACC, data = eire, weights = RETSALE) #> weights: nb2listw(eire.nb) #> #> Moran I statistic standard deviate = 3.1385, p-value = 0.0008491 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I Expectation Variance #> 0.34500329 -0.04049313 0.01508687 #> lm.morantest.sad(e.wlm, nb2listw(eire.nb), resfun=rstudent) #> #> \tSaddlepoint approximation for global Moran's I (Barndorff-Nielsen #> \tformula) #> #> data: #> model:lm(formula = OWNCONS ~ ROADACC, data = eire, weights = RETSALE) #> weights: nb2listw(eire.nb) #> #> Saddlepoint approximation = 2.8708, p-value = 0.002047 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I #> 0.3450033 #>"},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute Local Geary statistic — localC","title":"Compute Local Geary statistic — localC","text":"Local Geary local adaptation Geary's C statistic spatial autocorrelation. Local Geary uses squared differences measure dissimilarity unlike Local Moran. Low values Local Geary indicate positive spatial autocorrelation large refers negative spatial autocorrelation. Inference Local Geary based permutation approach compares observed value reference distribution spatial randomness. localC_perm() returns pseudo p-value. analytical p-value based number permutations used care.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute Local Geary statistic — localC","text":"","code":"localC(x, ..., zero.policy=NULL) # Default S3 method localC(x, listw, ..., zero.policy=attr(listw, \"zero.policy\")) # S3 method for class 'formula' localC(formula, data, listw, ..., zero.policy=attr(listw, \"zero.policy\")) # S3 method for class 'list' localC(x, listw, ..., zero.policy=attr(listw, \"zero.policy\")) # S3 method for class 'matrix' localC(x, listw, ..., zero.policy=attr(listw, \"zero.policy\")) # S3 method for class 'data.frame' localC(x, listw, ..., zero.policy=attr(listw, \"zero.policy\")) localC_perm(x, ..., zero.policy=NULL, iseed=NULL, no_repeat_in_row=FALSE) # Default S3 method localC_perm(x, listw, nsim = 499, alternative = \"two.sided\", ..., zero.policy=attr(listw, \"zero.policy\"), iseed=NULL, no_repeat_in_row=FALSE) # S3 method for class 'formula' localC_perm(formula, data, listw, nsim = 499, alternative = \"two.sided\", ..., zero.policy=attr(listw, \"zero.policy\"), iseed=NULL, no_repeat_in_row=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute Local Geary statistic — localC","text":"x numeric vector, numeric matrix, list. See details . formula one-sided formula determining variables used. listw listw object created example nb2listw. data Used formula provided. matrix data frame containing variables formula formula. nsim number simulations used permutation test. alternative character defining alternative hypothesis. Must one \"two.sided\", \"less\" \"greater\". ... arguments passed methods. zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA. iseed default NULL, used set seed;output reproducible count CPU cores across computation distributed no_repeat_in_row default FALSE, TRUE, sample conditionally row without replacements avoid duplicate values, https://github.com/r-spatial/spdep/issues/124","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Compute Local Geary statistic — localC","text":"Local Geary can extended multivariate context. x numeric vector, univariate Local Geary calculated. calculate multivariate Local Moran provide either list matrix. x list, element must numeric vector length length neighbours listw. case x matrix number rows must length neighbours listw. required univariate context, standardized Local Geary calculated. multivariate Local Geary always standardized. univariate Local Geary calculated \\(c_i = \\sum_j w_{ij}(x_i - x_j)^2\\) multivariate Local Geary calculated \\(c_{k,} = \\sum_{v=1}^{k} c_{v,}\\) described Anselin (2019).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute Local Geary statistic — localC","text":"numeric vector containing Local Geary statistic attribute pseudo-p localC_perm() used. pseudo-p 8 column matrix containing E.Ci expectation Local Geary statistic based permutation sample Var.Ci variance Local Geary based permutation sample Z.Ci standard deviate Local Geary based permutation sample Pr() p-value Local Geary statistic using pnorm() using standard deviates based permutation sample means standard deviations Pr() Sim rank() punif() observed statistic rank [0, 1] p-values using alternative= Pr(folded) Sim simulation folded [0, 0.5] range ranked p-value (based https://github.com/pysal/esda/blob/4a63e0b5df1e754b17b5f1205b8cadcbecc5e061/esda/crand.py#L211-L213) Skewness output e1071::skewness() permutation samples underlying standard deviates Kurtosis output e1071::kurtosis() permutation samples underlying standard deviates","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute Local Geary statistic — localC","text":"Anselin, L. (1995), Local Indicators Spatial Association—LISA. Geographical Analysis, 27: 93-115. doi:10.1111/j.1538-4632.1995.tb00338.x Anselin, L. (2019), Local Indicator Multivariate Spatial Association: Extending Gearys c. Geogr Anal, 51: 133-150. doi:10.1111/gean.12164","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute Local Geary statistic — localC","text":"Josiah Parry josiah.parry@gmail.com Roger Bivand","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute Local Geary statistic — localC","text":"","code":"orig <- spData::africa.rook.nb listw <- nb2listw(orig) x <- spData::afcon$totcon (A <- localC(x, listw)) #> [1] 0.39025457 0.50460439 0.15303047 2.90814878 3.40006901 0.17103368 #> [7] 0.29947832 0.72444806 2.30617282 5.70252541 2.23161263 0.17833029 #> [13] 0.18420002 0.18680408 0.37851643 0.11056720 0.14814835 0.17257920 #> [19] 0.03254150 0.18992772 0.08749322 3.71970760 0.09566918 0.26112918 #> [25] 0.09505331 2.99934478 1.17465032 1.64868780 0.87901004 0.05909537 #> [31] 2.54591475 3.85570655 2.99413462 0.96084992 0.80678832 1.56869350 #> [37] 0.86422915 0.38817470 0.23425755 1.26191610 1.34455327 1.80707481 listw1 <- nb2listw(droplinks(sym.attr.nb(orig), 3, sym=TRUE), zero.policy=TRUE) #> Warning: some observations have no neighbours #> Warning: neighbour object has 2 sub-graphs (A1 <- localC(x, listw1, zero.policy=FALSE)) #> [1] 0.39025457 0.57491918 NA 2.90814878 3.40006901 0.17103368 #> [7] 0.29947832 0.72444806 2.30617282 5.70252541 2.23161263 0.17833029 #> [13] 0.18420002 0.18680408 0.37851643 0.11056720 0.14814835 0.17257920 #> [19] 0.03254150 0.18992772 0.08749322 3.71970760 0.09566918 0.26112918 #> [25] 0.09505331 2.99934478 1.17465032 1.64868780 0.87901004 0.05909537 #> [31] 2.54591475 3.85570655 2.99413462 0.96084992 0.80678832 1.56869350 #> [37] 0.86422915 0.38817470 0.23425755 1.26191610 1.34455327 1.80707481 (A2 <- localC(x, listw1, zero.policy=TRUE)) #> [1] 0.39025457 0.57491918 0.00000000 2.90814878 3.40006901 0.17103368 #> [7] 0.29947832 0.72444806 2.30617282 5.70252541 2.23161263 0.17833029 #> [13] 0.18420002 0.18680408 0.37851643 0.11056720 0.14814835 0.17257920 #> [19] 0.03254150 0.18992772 0.08749322 3.71970760 0.09566918 0.26112918 #> [25] 0.09505331 2.99934478 1.17465032 1.64868780 0.87901004 0.05909537 #> [31] 2.54591475 3.85570655 2.99413462 0.96084992 0.80678832 1.56869350 #> [37] 0.86422915 0.38817470 0.23425755 1.26191610 1.34455327 1.80707481 run <- FALSE if (require(rgeoda, quietly=TRUE)) run <- TRUE #> #> Attaching package: ‘rgeoda’ #> The following object is masked from ‘package:spdep’: #> #> skater if (run) { W <- create_weights(as.numeric(length(x))) for (i in 1:length(listw$neighbours)) { set_neighbors_with_weights(W, i, listw$neighbours[[i]], listw$weights[[i]]) update_weights(W) } set.seed(1) B <- local_geary(W, data.frame(x)) all.equal(A, lisa_values(B)) } #> [1] TRUE if (run) { set.seed(1) C <- localC_perm(x, listw, nsim = 499, conditional=TRUE, alternative=\"two.sided\") cor(ifelse(lisa_pvalues(B) < 0.5, lisa_pvalues(B), 1-lisa_pvalues(B)), attr(C, \"pseudo-p\")[,6]) } #> [1] 0.985611 # pseudo-p values probably wrongly folded https://github.com/GeoDaCenter/rgeoda/issues/28 # \\donttest{ tmap_ok <- FALSE if (require(tmap, quietly=TRUE)) tmap_ok <- TRUE if (run) { # doi: 10.1111/gean.12164 guerry_path <- system.file(\"extdata\", \"Guerry.shp\", package = \"rgeoda\") g <- st_read(guerry_path)[, 7:12] cor(st_drop_geometry(g)) #(Tab. 1) lw <- nb2listw(poly2nb(g)) moran(g$Crm_prs, lw, n=nrow(g), S0=Szero(lw))$I moran(g$Crm_prp, lw, n=nrow(g), S0=Szero(lw))$I moran(g$Litercy, lw, n=nrow(g), S0=Szero(lw))$I moran(g$Donatns, lw, n=nrow(g), S0=Szero(lw))$I moran(g$Infants, lw, n=nrow(g), S0=Szero(lw))$I moran(g$Suicids, lw, n=nrow(g), S0=Szero(lw))$I } #> Reading layer `Guerry' from data source #> `/home/rsb/lib/r_libs/rgeoda/extdata/Guerry.shp' using driver `ESRI Shapefile' #> Simple feature collection with 85 features and 29 fields #> Geometry type: MULTIPOLYGON #> Dimension: XY #> Bounding box: xmin: 47680 ymin: 1703258 xmax: 1031401 ymax: 2677441 #> Projected CRS: NTF (Paris) / Lambert zone II #> [1] 0.4016812 if (run) { o <- prcomp(st_drop_geometry(g), scale.=TRUE) cor(st_drop_geometry(g), o$x[,1:2])^2 #(Tab. 2) } #> PC1 PC2 #> Crm_prs 0.009286863 0.418851254 #> Crm_prp 0.561825664 0.009377232 #> Litercy 0.560570048 0.020095011 #> Donatns 0.024138865 0.586720363 #> Infants 0.436025658 0.012817054 #> Suicids 0.548623327 0.152958961 if (run) { g$PC1 <- o$x[, \"PC1\"] brks <- c(min(g$PC1), natural_breaks(k=6, g[\"PC1\"]), max(g$PC1)) if (tmap_ok) { tmap4 <- packageVersion(\"tmap\") >= \"3.99\" if (tmap4) { tm_shape(g) + tm_polygons(fill=\"PC1\", fill.scale=tm_scale(values=\"brewer.rd_yl_gn\", breaks=brks, midpoint=0), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"PC1\", breaks=brks, midpoint=0) + tm_borders() # Fig. 1 } } else { plot(g[\"PC1\"], breaks=brks) } } if (run) { g$PC2 <- -1*o$x[, \"PC2\"] # eigenvalue sign arbitrary brks <- c(min(g$PC2), natural_breaks(k=6, g[\"PC2\"]), max(g$PC2)) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"PC2\", fill.scale=tm_scale(values=\"brewer.rd_yl_gn\", breaks=brks, midpoint=0), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"PC2\", breaks=brks, midpoint=0) + tm_borders() # Fig. 2 } } else { plot(g[\"PC2\"], breaks=brks) } } if (run) { w <- queen_weights(g) lm_PC1 <- local_moran(w, g[\"PC1\"], significance_cutoff=0.01, permutations=99999) g$lm_PC1 <- factor(lisa_clusters(lm_PC1), levels=0:4, labels=lisa_labels(lm_PC1)[1:5]) is.na(g$lm_PC1) <- g$lm_PC1 == \"Not significant\" g$lm_PC1 <- droplevels(g$lm_PC1) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lm_PC1\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lm_PC1\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # Fig. 3 } } else { plot(g[\"lm_PC1\"]) } } if (run) { set.seed(1) lm_PC1_spdep <- localmoran_perm(g$PC1, lw, nsim=9999) q <- attr(lm_PC1_spdep, \"quadr\")$pysal g$lm_PC1_spdep <- q is.na(g$lm_PC1_spdep) <- lm_PC1_spdep[,6] > 0.02 # note folded p-values g$lm_PC1_spdep <- droplevels(g$lm_PC1_spdep) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lm_PC1_spdep\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lm_PC1_spdep\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # rep. Fig. 3 } } else { plot(g[\"lm_PC1_spdep\"]) } } if (run) { lg_PC1 <- local_g(w, g[\"PC1\"], significance_cutoff=0.01, permutations=99999) g$lg_PC1 <- factor(lisa_clusters(lg_PC1), levels=0:2, labels=lisa_labels(lg_PC1)[0:3]) is.na(g$lg_PC1) <- g$lg_PC1 == \"Not significant\" g$lg_PC1 <- droplevels(g$lg_PC1) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lg_PC1\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lg_PC1\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # Fig. 4 (wrong) } } else { plot(g[\"lg_PC1\"]) } g$lg_PC1a <- cut(g$PC1, c(-Inf, mean(g$PC1), Inf), labels=c(\"Low\", \"High\")) is.na(g$lg_PC1a) <- lisa_pvalues(lg_PC1) >= 0.01 g$lg_PC1a <- droplevels(g$lg_PC1a) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lg_PC1a\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lg_PC1a\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # Fig. 4 (guess) } } else { plot(g[\"lg_PC1\"]) } } if (run) { lc_PC1 <- local_geary(w, g[\"PC1\"], significance_cutoff=0.01, permutations=99999) g$lc_PC1 <- factor(lisa_clusters(lc_PC1), levels=0:4, labels=lisa_labels(lc_PC1)[1:5]) is.na(g$lc_PC1) <- g$lc_PC1 == \"Not significant\" g$lc_PC1 <- droplevels(g$lc_PC1) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lc_PC1\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lc_PC1\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # Fig. 5 } } else { plot(g[\"lc_PC1\"]) } } if (run) { set.seed(1) system.time(lc_PC1_spdep <- localC_perm(g$PC1, lw, nsim=9999, alternative=\"two.sided\")) } #> user system elapsed #> 0.352 0.004 0.364 if (run) { if (require(parallel, quietly=TRUE)) { ncpus <- max(2L, detectCores(logical=FALSE), na.rm = TRUE)-1L # test with single core if (ncpus > 1L) ncpus <- 1L cores <- get.coresOption() set.coresOption(ncpus) system.time(lmc_PC1_spdep1 <- localC_perm(g$PC1, lw, nsim=9999, alternative=\"two.sided\", iseed=1)) set.coresOption(cores) } } #> [1] 1 if (run) { g$lc_PC1_spdep <- attr(lc_PC1_spdep, \"cluster\") is.na(g$lc_PC1_spdep) <- attr(lc_PC1_spdep, \"pseudo-p\")[,6] > 0.01 g$lc_PC1_spdep <- droplevels(g$lc_PC1_spdep) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lc_PC1_spdep\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lc_PC1_spdep\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # rep. Fig. 5 } } else { plot(g[\"lc_PC1_spdep\"]) } } if (run) { g$both_PC1 <- interaction(g$lc_PC1, g$lm_PC1) g$both_PC1 <- droplevels(g$both_PC1) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"both_PC1\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"both_PC1\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # Fig. 6 } } else { plot(g[\"both_PC1\"]) } } if (run) { lc005_PC1 <- local_geary(w, g[\"PC1\"], significance_cutoff=0.005, permutations=99999) g$lc005_PC1 <- factor(lisa_clusters(lc005_PC1), levels=0:4, labels=lisa_labels(lc005_PC1)[1:5]) is.na(g$lc005_PC1) <- g$lc005_PC1 == \"Not significant\" g$lc005_PC1 <- droplevels(g$lc005_PC1) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lc005_PC1\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lc005_PC1\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # Fig. 7 } } else { plot(g[\"lc005_PC1\"]) } if (run) { g$lc005_PC1_spdep <- attr(lc_PC1_spdep, \"cluster\") is.na(g$lc005_PC1_spdep) <- attr(lc_PC1_spdep, \"pseudo-p\")[,6] > 0.005 g$lc005_PC1_spdep <- droplevels(g$lc005_PC1_spdep) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lc005_PC1_spdep\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lc005_PC1_spdep\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # rep. Fig. 7 } } else { plot(g[\"lc005_PC1_spdep\"]) } } if (run) { lc001_PC1 <- local_geary(w, g[\"PC1\"], significance_cutoff=0.001, permutations=99999) g$lc001_PC1 <- factor(lisa_clusters(lc001_PC1), levels=0:4, labels=lisa_labels(lc001_PC1)[1:5]) is.na(g$lc001_PC1) <- g$lc001_PC1 == \"Not significant\" g$lc001_PC1 <- droplevels(g$lc001_PC1) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lc005_PC1\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lc001_PC1\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # Fig. 8 } } else { plot(g[\"lc001_PC1\"]) } } if (run) { g$lc001_PC1_spdep <- attr(lc_PC1_spdep, \"cluster\") is.na(g$lc001_PC1_spdep) <- attr(lc_PC1_spdep, \"pseudo-p\")[,6] > 0.001 g$lc001_PC1_spdep <- droplevels(g$lc001_PC1_spdep) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lc005_PC1_spdep\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lc001_PC1_spdep\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # rep. Fig. 8 } } else { plot(g[\"lc001_PC1_spdep\"]) } } } if (run) { lc_PC2 <- local_geary(w, g[\"PC2\"], significance_cutoff=0.01, permutations=99999) g$lc_PC2 <- factor(lisa_clusters(lc_PC2), levels=0:4, labels=lisa_labels(lc_PC2)[1:5]) is.na(g$lc_PC2) <- g$lc_PC2 == \"Not significant\" g$lc_PC2 <- droplevels(g$lc_PC2) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lc_PC2\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lc_PC2\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # Fig. 9 } } else { plot(g[\"lc_PC2\"]) } } if (run) { lmc_PC <- local_multigeary(w, g[c(\"PC1\",\"PC2\")], significance_cutoff=0.00247, permutations=99999) g$lmc_PC <- factor(lisa_clusters(lmc_PC), levels=0:1, labels=lisa_labels(lmc_PC)[1:2]) is.na(g$lmc_PC) <- g$lmc_PC == \"Not significant\" g$lmc_PC <- droplevels(g$lmc_PC) table(interaction((p.adjust(lisa_pvalues(lmc_PC), \"fdr\") < 0.01), g$lmc_PC)) } #> #> FALSE.Positive TRUE.Positive #> 0 21 if (run) { if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lmc_PC\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lmc_PC\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # Fig. 10 } } else { plot(g[\"lmc_PC\"]) } } #> The visual variable \"fill\" of the layer \"polygons\" contains a unique value. Therefore a categorical scale is applied (tm_scale_categorical). if (run) { set.seed(1) lmc_PC_spdep <- localC_perm(g[c(\"PC1\",\"PC2\")], lw, nsim=9999, alternative=\"two.sided\") all.equal(lisa_values(lmc_PC), c(lmc_PC_spdep)) } #> [1] TRUE if (run) { cor(attr(lmc_PC_spdep, \"pseudo-p\")[,6], lisa_pvalues(lmc_PC)) } #> [1] 0.9905202 if (run) { g$lmc_PC_spdep <- attr(lmc_PC_spdep, \"cluster\") is.na(g$lmc_PC_spdep) <- p.adjust(attr(lmc_PC_spdep, \"pseudo-p\")[,6], \"fdr\") > 0.01 g$lmc_PC_spdep <- droplevels(g$lmc_PC_spdep) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lmc_PC_spdep\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lmc_PC_spdep\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # rep. Fig. 10 } } else { plot(g[\"lmc_PC_spdep\"]) } } #> The visual variable \"fill\" of the layer \"polygons\" contains a unique value. Therefore a categorical scale is applied (tm_scale_categorical). if (run) { lmc_vars <- local_multigeary(w, st_drop_geometry(g)[, 1:6], significance_cutoff=0.00247, permutations=99999) g$lmc_vars <- factor(lisa_clusters(lmc_vars), levels=0:1, labels=lisa_labels(lmc_vars)[1:2]) is.na(g$lmc_vars) <- g$lmc_vars == \"Not significant\" g$lmc_vars <- droplevels(g$lmc_vars) table(interaction((p.adjust(lisa_pvalues(lmc_vars), \"fdr\") < 0.01), g$lmc_vars)) } #> #> FALSE.Positive TRUE.Positive #> 0 21 if (run) { if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lmc_vars\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lmc_vars\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # Fig. 11 } } else { plot(g[\"lmc_vars\"]) } } #> The visual variable \"fill\" of the layer \"polygons\" contains a unique value. Therefore a categorical scale is applied (tm_scale_categorical). if (run) { set.seed(1) system.time(lmc_vars_spdep <- localC_perm(st_drop_geometry(g)[, 1:6], lw, nsim=9999, alternative=\"two.sided\")) } #> user system elapsed #> 0.648 0.000 0.651 if (run) { all.equal(lisa_values(lmc_vars), c(lmc_vars_spdep)) } #> [1] TRUE if (run) { cor(attr(lmc_vars_spdep, \"pseudo-p\")[,6], lisa_pvalues(lmc_vars)) } #> [1] 0.9938141 if (run) { if (require(parallel, quietly=TRUE)) { ncpus <- max(2L, detectCores(logical=FALSE), na.rm = TRUE)-1L # test with single core if (ncpus > 1L) ncpus <- 1L cores <- get.coresOption() set.coresOption(ncpus) system.time(lmc_vars_spdep1 <- localC_perm(st_drop_geometry(g)[, 1:6], lw, nsim=9999, alternative=\"two.sided\", iseed=1)) set.coresOption(cores) } } #> [1] 1 if (run) { all.equal(lisa_values(lmc_vars), c(lmc_vars_spdep1)) } #> [1] TRUE if (run) { cor(attr(lmc_vars_spdep1, \"pseudo-p\")[,6], lisa_pvalues(lmc_vars)) } #> [1] 0.9938141 if (run) { g$lmc_vars_spdep <- attr(lmc_vars_spdep1, \"cluster\") is.na(g$lmc_vars_spdep) <- p.adjust(attr(lmc_vars_spdep1, \"pseudo-p\")[,6], \"fdr\") > 0.01 g$lmc_vars_spdep <- droplevels(g$lmc_vars_spdep) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lmc_vars_spdep\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lmc_vars_spdep\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # rep. Fig. 11 } } else { plot(g[\"lmc_vars_spdep\"]) } } #> The visual variable \"fill\" of the layer \"polygons\" contains a unique value. Therefore a categorical scale is applied (tm_scale_categorical). # } # \\dontrun{ library(reticulate) use_python(\"/usr/bin/python\", required = TRUE) gp <- import(\"geopandas\") ps <- import(\"libpysal\") W <- listw2mat(listw) w <- ps$weights$full2W(W, rownames(W)) w$transform <- \"R\" esda <- import(\"esda\") lM <- esda$Moran_Local(x, w) all.equal(unname(localmoran(x, listw, mlvar=FALSE)[,1]), c(lM$Is)) #> [1] TRUE # confirm x and w the same lC <- esda$Geary_Local(connectivity=w)$fit(scale(x)) # np$std missing ddof=1 n <- length(x) D0 <- spdep:::geary.intern((x - mean(x)) / sqrt(var(x)*(n-1)/n), listw, n=n) # lC components probably wrongly ordered https://github.com/pysal/esda/issues/192 o <- match(round(D0, 6), round(lC$localG, 6)) all.equal(c(lC$localG)[o], D0) #> [1] TRUE # simulation order not retained lC$p_sim[o] #> [1] 0.272 0.486 0.124 0.018 0.110 0.024 0.315 0.419 0.136 0.001 0.125 0.123 #> [13] 0.175 0.240 0.487 0.211 0.105 0.328 0.001 0.028 0.031 0.094 0.057 0.293 #> [25] 0.173 0.027 0.096 0.249 0.465 0.001 0.058 0.106 0.074 0.225 0.285 0.001 #> [37] 0.301 0.482 0.351 0.205 0.231 0.255 attr(C, \"pseudo-p\")[,6] #> [1] 0.408 0.374 0.144 0.056 0.010 0.284 0.032 0.264 0.186 0.004 0.150 0.224 #> [13] 0.022 0.150 0.438 0.084 0.126 0.184 0.002 0.238 0.126 0.100 0.068 0.372 #> [25] 0.124 0.234 0.230 0.016 0.318 0.176 0.272 0.164 0.164 0.206 0.402 0.250 #> [37] 0.410 0.402 0.328 0.294 0.438 0.248 # }"},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":null,"dir":"Reference","previous_headings":"","what":"G and Gstar local spatial statistics — localG","title":"G and Gstar local spatial statistics — localG","text":"local spatial statistic G calculated zone based spatial weights object used. value returned Z-value, may used diagnostic tool. High positive values indicate posibility local cluster high values variable analysed, low relative values similar cluster low values. inference, Bonferroni-type test suggested references, tables critical values may found (see also details ).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"G and Gstar local spatial statistics — localG","text":"","code":"localG(x, listw, zero.policy=attr(listw, \"zero.policy\"), spChk=NULL, GeoDa=FALSE, alternative = \"two.sided\", return_internals=TRUE) localG_perm(x, listw, nsim=499, zero.policy=attr(listw, \"zero.policy\"), spChk=NULL, alternative = \"two.sided\", iseed=NULL, fix_i_in_Gstar_permutations=TRUE, no_repeat_in_row=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"G and Gstar local spatial statistics — localG","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw zero.policy default NULL, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() GeoDa default FALSE, TRUE, drop x values -neighbour self-neighbour observations summations nsim default 499, number conditonal permutation simulations alternative character string specifying alternative hypothesis, must one \"two.sided\" (default), \"greater\" \"less\". return_internals default TRUE, unused iseed default NULL, used set seed; output reproducible count CPU cores across computation distributed fix_i_in_Gstar_permutations default TRUE (fix x self permutations local G-star), set FALSE use pre-1.2-8 behaviour no_repeat_in_row default FALSE, TRUE, sample conditionally row without replacements avoid duplicate values, https://github.com/r-spatial/spdep/issues/124","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"G and Gstar local spatial statistics — localG","text":"neighbours member listw \"self.included\" attribute set TRUE, Gstar variant, including self-weight \\(w_{ii} > 0\\), calculated returned. returned vector \"gstari\" attribute set TRUE. Self-weights must included using include.self function converting neighbour list spatial weights list nb2listw shown example. critical values statistic assumptions given references 95th percentile n=1: 1.645, n=50: 3.083, n=100: 3.289, n=1000: 3.886.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"G and Gstar local spatial statistics — localG","text":"vector G Gstar standard deviate values, attributes \"gstari\" set TRUE FALSE, \"call\" set function call, class \"localG\". conditional permutation, returned value localG(), simulated standard deviate returned column \"StdDev.Gi\" attr(., \"internals\").","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"G and Gstar local spatial statistics — localG","text":"Conditional permutations added comparative purposes; permutations whole data vector omitting observation , 1.2-8 fixing observation neighbour local G-star.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"G and Gstar local spatial statistics — localG","text":"Ord, J. K. Getis, . 1995 Local spatial autocorrelation statistics: distributional issues application. Geographical Analysis, 27, 286–306; Getis, . Ord, J. K. 1996 Local spatial statistics: overview. P. Longley M. Batty (eds) Spatial analysis: modelling GIS environment (Cambridge: Geoinformation International), 261–277; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"G and Gstar local spatial statistics — localG","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"G and Gstar local spatial statistics — localG","text":"","code":"data(getisord, package=\"spData\") # spData 0.3.2 changes x, y, xyz object names to go_x, go_y, go_xyz to # avoid putting these objects into the global environment via lazy loading if (exists(\"go_xyz\") && packageVersion(\"spData\") >= \"0.3.2\") { xyz <- go_xyz x <- go_x y <- go_y } xycoords <- cbind(xyz$x, xyz$y) nb30 <- dnearneigh(xycoords, 0, 30) G30 <- localG(xyz$val, nb2listw(nb30, style=\"B\")) G30[length(xyz$val)-136] #> [1] 1.221979 set.seed(1) G30_sim <- localG_perm(xyz$val, nb2listw(nb30, style=\"B\")) G30_sim[length(xyz$val)-136] #> [1] 1.221979 nb60 <- dnearneigh(xycoords, 0, 60) G60 <- localG(xyz$val, nb2listw(nb60, style=\"B\")) G60[length(xyz$val)-136] #> [1] 1.748098 nb90 <- dnearneigh(xycoords, 0, 90) G90 <- localG(xyz$val, nb2listw(nb90, style=\"B\")) G90[length(xyz$val)-136] #> [1] 1.986135 nb120 <- dnearneigh(xycoords, 0, 120) G120 <- localG(xyz$val, nb2listw(nb120, style=\"B\")) G120[length(xyz$val)-136] #> [1] 1.893374 nb150 <- dnearneigh(xycoords, 0, 150) G150 <- localG(xyz$val, nb2listw(nb150, style=\"B\")) G150[length(xyz$val)-136] #> [1] 1.237454 brks <- seq(-5,5,1) cm.col <- cm.colors(length(brks)-1) image(x, y, t(matrix(G30, nrow=16, ncol=16, byrow=TRUE)), breaks=brks, col=cm.col, asp=1) text(xyz$x, xyz$y, round(G30, digits=1), cex=0.7) polygon(c(195,225,225,195), c(195,195,225,225), lwd=2) title(main=expression(paste(\"Values of the \", G[i], \" statistic\"))) G30s <- localG(xyz$val, nb2listw(include.self(nb30), style=\"B\")) cat(\"value according to Getis and Ord's eq. 14.2, p. 263 (1996)\\n\") #> value according to Getis and Ord's eq. 14.2, p. 263 (1996) G30s[length(xyz$val)-136] #> [1] 1.45078 cat(paste(\"value given by Getis and Ord (1996), p. 267\", \"(division by n-1 rather than n \\n in variance)\\n\")) #> value given by Getis and Ord (1996), p. 267 (division by n-1 rather than n #> in variance) G30s[length(xyz$val)-136] * (sqrt(sum(scale(xyz$val, scale=FALSE)^2)/length(xyz$val)) / sqrt(var(xyz$val))) #> [1] 1.447943 image(x, y, t(matrix(G30s, nrow=16, ncol=16, byrow=TRUE)), breaks=brks, col=cm.col, asp=1) text(xyz$x, xyz$y, round(G30s, digits=1), cex=0.7) polygon(c(195,225,225,195), c(195,195,225,225), lwd=2) title(main=expression(paste(\"Values of the \", G[i]^\"*\", \" statistic\")))"},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":null,"dir":"Reference","previous_headings":"","what":"A local hotspot statistic for analysing multiscale datasets — localGS","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"function implements \\(GS_i\\) test statistic local hotspots specific pairwise evaluated distance bands, proposed Westerholt et al. (2015). Like hotspot estimator \\(G_i^*\\), \\(GS_i\\) statistic given z-scores can evaluated accordingly. idea method identify hotspots datasets comprise several, difficult--separate processes operating different scales. often case complex user-generated datasets Twitter feeds. example, football match reflected tweets pubs, homes, stadium vicinity. exemplified phenomena represent different processes may detected different geometric scales. \\(GS_i\\) method enables identification specifying geometric scale band strictly calculating statistical quantities mean variance solely respective relevant observations interact range adjusted scale band. addition, neighbourhood relationships respective central unit, scale-relevant relationships considered. way, hotspots can detected specific scale ranges independently scales. statistic given : $$GS_i = \\frac{\\displaystyle\\sum_{j; k < j}{w_{ij}w_{ik}\\phi_{jk}a_{jk}} - \\frac{W_i}{\\Phi} \\displaystyle\\sum_{j; k < j}{\\phi_{jk}a_{jk}}}{\\sqrt{\\frac{W_i}{\\Phi}\\displaystyle\\sum_{j; k < j}{\\phi_{jk}a_{jk}^2} + \\frac{W_i\\left(W_i-1\\right)}{\\Phi\\left(\\Phi-1\\right)}\\left(\\Gamma^2 -\\!\\! \\displaystyle\\sum_{j; k < j}{\\left(\\phi_{jk}a_{jk}\\right)^2}\\right) - \\left(\\frac{W_i}{\\Phi}\\displaystyle\\sum_{j; k < j}{\\phi_{jk}a_{jk}}\\right)^2}}$$ $$a_{jk} = x_j + x_k,\\;\\;\\; W_i = \\displaystyle\\sum_{j; k < j}{w_{ij}w_{ik}\\phi_{jk}},\\;\\;\\; \\Phi = \\displaystyle\\sum_{j; k < j}{\\phi_{jk}},\\;\\;\\; \\textrm{} \\;\\;\\; \\Gamma = \\displaystyle\\sum_{j; k < j}{\\phi_{jk}a_{jk}}.$$","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"","code":"localGS(x, listw, dmin, dmax, attr, longlat = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"x sf sp object listw listw object dmin lower distance bound (greater equal) dmax upper distance bound (less equal) attr name attribute interest longlat default NULL; TRUE point coordinates longitude-latitude decimal degrees, case distances measured kilometres; x SpatialPoints object, value taken object , overrides argument NULL; distances measured map units FALSE NULL","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"pairs observations shared distance (map units) interval [dmin, dmax] within maximum radius dmax around corresponding output observation considered. Thereby, also mean values variance terms estimated within measure adjusted scale range consideration. application examples method see Westerholt et al. (2015) (applied tweets) Sonea & Westerholt (2021) (applied access banking scenario).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"vector \\(GS_i\\) values given z-scores.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"Westerholt, R., Resch, B. & Zipf, . 2015. local scale-sensitive indicator spatial autocorrelation assessing high-low-value clusters multiscale datasets. International Journal Geographical Information Science, 29(5), 868–887, doi:10.1080/13658816.2014.1002499 . Sonea, . Westerholt, R. (2021): Geographic temporal access basic banking services Wales. Applied Spatial Analysis Policy, 14 (4), 879–905, doi:10.1007/s12061-021-09386-3 .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"René Westerholt rene.westerholt@tu-dortmund.de","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"","code":"# \\donttest{ boston.tr <- sf::st_read(system.file(\"shapes/boston_tracts.gpkg\", package=\"spData\")[1]) #> Reading layer `boston_tracts' from data source #> `/home/rsb/lib/r_libs/spData/shapes/boston_tracts.gpkg' using driver `GPKG' #> Simple feature collection with 506 features and 36 fields #> Geometry type: POLYGON #> Dimension: XY #> Bounding box: xmin: -71.52311 ymin: 42.00305 xmax: -70.63823 ymax: 42.67307 #> Geodetic CRS: NAD27 boston.tr_utm <- st_transform(boston.tr, 32619) #26786 boston_listw1 <- nb2listwdist(dnearneigh(st_centroid(boston.tr_utm), 1, 2000), boston.tr_utm, type = \"dpd\", alpha = 2, zero.policy = TRUE, dmax = 9500) #> Warning: st_centroid assumes attributes are constant over geometries #> Warning: neighbour object has 120 sub-graphs boston_listw2 <- nb2listwdist(dnearneigh(st_centroid(boston.tr_utm), 5000, 9500), boston.tr_utm, type = \"dpd\", alpha = 2, zero.policy = TRUE, dmax = 9500) #> Warning: st_centroid assumes attributes are constant over geometries boston_RM_gsi_1 <- localGS(boston.tr_utm, boston_listw1, 1, 2000, \"RM\", FALSE) boston_RM_gsi_2 <- localGS(boston.tr_utm, boston_listw2, 2000, 9500, \"RM\", FALSE) # }"},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate the local bivariate join count — local_joincount_bv","title":"Calculate the local bivariate join count — local_joincount_bv","text":"bivariate join count (BJC) evaluates event occurrences predefined regions tests co-occurrence events deviates complete spatial randomness.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate the local bivariate join count — local_joincount_bv","text":"","code":"local_joincount_bv( x, z, listw, nsim = 199, alternative = \"two.sided\" )"},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate the local bivariate join count — local_joincount_bv","text":"x binary variable either numeric logical z binary variable either numeric logical length x listw listw object containing binary weights created, example, nb2listw(nb, style = \"B\") nsim number conditional permutation simulations alternative default \"greater\". One \"less\" \"greater\".","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Calculate the local bivariate join count — local_joincount_bv","text":"two cases evaluated bivariate join count. first -situ colocation (CLC) xi = 1 zi = 1. second general form bivariate join count (BJC) used -situ colocation. BJC case \"useful x z occur location, x z correspond two different values single categorical variable\" \"x z can co-locate, \" (Anselin Li, 2019). Whereas CLC case useful evaluating simultaneous occurrences events. local bivariate join count statistic requires binary weights list can generated nb2listw(nb, style = \"B\"). P-values reported regions match CLC BJC criteria. Others associated p-value. P-values estimated using conditional permutation approach. creates reference distribution observed statistic compared.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate the local bivariate join count — local_joincount_bv","text":"data.frame two columns join_count p_sim number rows equal length arguments x.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Calculate the local bivariate join count — local_joincount_bv","text":"Anselin, L., & Li, X. (2019). Operational Local Join Count Statistics Cluster Detection. Journal geographical systems, 21(2), 189–210. doi:10.1007/s10109-019-00299-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Calculate the local bivariate join count — local_joincount_bv","text":"Josiah Parry josiah.parry@gmail.com","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate the local bivariate join count — local_joincount_bv","text":"","code":"data(\"oldcol\") listw <- nb2listw(COL.nb, style = \"B\") # Colocation case x <- COL.OLD[[\"CP\"]] z <- COL.OLD[[\"EW\"]] set.seed(1) res <- local_joincount_bv(x, z, listw) na.omit(res) #> join_count p_sim #> 9 2 0.480 #> 19 3 0.180 #> 20 4 0.020 #> 21 3 0.040 #> 22 3 0.060 #> 23 4 0.070 #> 24 5 0.005 #> 27 2 0.300 #> 28 3 0.050 #> 29 5 0.010 #> 30 5 0.010 #> 31 9 0.005 #> 32 4 0.090 #> 33 4 0.055 # no colocation case z <- 1 - x set.seed(1) res <- local_joincount_bv(x, z, listw) na.omit(res) #> join_count p_sim #> 9 2 0.065 #> 19 3 0.300 #> 20 1 0.015 #> 21 1 0.040 #> 22 1 0.045 #> 23 3 0.165 #> 24 1 0.000 #> 27 2 0.230 #> 28 1 0.050 #> 29 1 0.000 #> 36 1 0.000 #> 37 2 0.005 #> 38 2 0.185 #> 39 2 0.265 #> 40 1 0.005 #> 43 1 0.070"},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate the local univariate join count — local_joincount_uni","title":"Calculate the local univariate join count — local_joincount_uni","text":"univariate local join count statistic used identify clusters rarely occurring binary variables. binary variable interest occur less half time.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate the local univariate join count — local_joincount_uni","text":"","code":"local_joincount_uni( fx, chosen, listw, alternative = \"two.sided\", nsim = 199, iseed = NULL, no_repeat_in_row=FALSE )"},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate the local univariate join count — local_joincount_uni","text":"fx binary variable either numeric logical chosen scalar character containing level fx considered observed value (1). listw listw object containing binary weights created, example, nbwlistw(nb, style = \"B\") alternative default \"greater\". One \"less\" \"greater\". nsim number conditional permutation simulations iseed default NULL, used set seed; output reproducible count CPU cores across computation distributed no_repeat_in_row default FALSE, TRUE, sample conditionally row without replacements avoid duplicate values, https://github.com/r-spatial/spdep/issues/124","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate the local univariate join count — local_joincount_uni","text":"data.frame two columns BB Pr() number rows equal length x.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Calculate the local univariate join count — local_joincount_uni","text":"local join count statistic requires binary weights list can generated nb2listw(nb, style = \"B\"). Additionally, ensure binary variable interest rarely occurring half observations. P-values estimated using conditional permutation approach. creates reference distribution observed statistic compared. see Geoda Glossary.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Calculate the local univariate join count — local_joincount_uni","text":"Anselin, L., & Li, X. (2019). Operational Local Join Count Statistics Cluster Detection. Journal geographical systems, 21(2), 189–210. doi:10.1007/s10109-019-00299-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Calculate the local univariate join count — local_joincount_uni","text":"Josiah Parry josiah.parry@gmail.com","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate the local univariate join count — local_joincount_uni","text":"","code":"data(oldcol) fx <- as.factor(ifelse(COL.OLD$CRIME < 35, \"low-crime\", \"high-crime\")) listw <- nb2listw(COL.nb, style = \"B\") set.seed(1) (res <- local_joincount_uni(fx, chosen = \"high-crime\", listw)) #> BB Pr(z != E(BBi)) #> 1 0 NA #> 2 0 NA #> 3 4 0.50 #> 4 0 NA #> 5 0 NA #> 6 0 NA #> 7 4 0.89 #> 8 0 NA #> 9 5 0.11 #> 10 0 NA #> 11 0 NA #> 12 0 NA #> 13 0 NA #> 14 0 NA #> 15 0 NA #> 16 0 NA #> 17 0 NA #> 18 0 NA #> 19 0 NA #> 20 3 0.55 #> 21 2 0.84 #> 22 3 0.30 #> 23 4 0.61 #> 24 5 0.12 #> 25 0 NA #> 26 0 NA #> 27 0 NA #> 28 0 NA #> 29 3 0.98 #> 30 5 0.09 #> 31 8 0.01 #> 32 7 0.02 #> 33 6 0.02 #> 34 5 0.04 #> 35 7 0.03 #> 36 8 0.02 #> 37 6 0.05 #> 38 5 0.04 #> 39 3 0.44 #> 40 5 0.14 #> 41 3 0.13 #> 42 5 0.05 #> 43 2 0.63 #> 44 0 NA #> 45 0 NA #> 46 0 NA #> 47 0 NA #> 48 0 NA #> 49 0 NA"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":null,"dir":"Reference","previous_headings":"","what":"Exact local Moran's Ii tests — localmoran.exact","title":"Exact local Moran's Ii tests — localmoran.exact","text":"localmoran.exact provides exact local Moran's Ii tests null hypothesis, localmoran.exact.alt provides exact local Moran's Ii tests alternative hypothesis. case, model may fitted model derived model fitted spatialreg::errorsarlm, covariance matrix can passed Omega= argument.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Exact local Moran's Ii tests — localmoran.exact","text":"","code":"localmoran.exact(model, select, nb, glist = NULL, style = \"W\", zero.policy = NULL, alternative = \"two.sided\", spChk = NULL, resfun = weighted.residuals, save.Vi = FALSE, useTP=FALSE, truncErr=1e-6, zeroTreat=0.1) localmoran.exact.alt(model, select, nb, glist = NULL, style = \"W\", zero.policy = NULL, alternative = \"two.sided\", spChk = NULL, resfun = weighted.residuals, Omega = NULL, save.Vi = FALSE, save.M = FALSE, useTP=FALSE, truncErr=1e-6, zeroTreat=0.1) # S3 method for class 'localmoranex' print(x, ...) # S3 method for class 'localmoranex' as.data.frame(x, row.names=NULL, optional=FALSE, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Exact local Moran's Ii tests — localmoran.exact","text":"model object class lm returned lm (assuming global spatial autocorrelation), object class sarlm returned spatial simultaneous autoregressive model fit (assuming global spatial autocorrelation represented model spatial coefficient); weights may specified lm fit, offsets used select integer vector id. numbers zones tested; missing, zones nb list neighbours class nb glist list general weights corresponding neighbours style can take values W, B, C, S zero.policy default NULL, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one greater (default), less two.sided. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() resfun default: weighted.residuals; function used extract residuals lm object, may residuals, weighted.residuals, rstandard, rstudent Omega SAR process matrix may passed test alternative hypothesis, example Omega <- invIrW(listw, rho=0.1); Omega <- tcrossprod(Omega), chol() taken internally save.Vi TRUE, return star-shaped weights lists zone tested save.M TRUE, save list left right M products useTP default FALSE, TRUE, use truncation point integration rather upper=Inf, see Tiefelsdorf (2000), eq. 6.7, p.69 truncErr useTP=TRUE, pass truncation error truncation point function zeroTreat useTP=TRUE, pass zero adjustment truncation point function x object printed row.names ignored argument .data.frame.localmoranex; row names assigned localmoranex object optional ignored argument .data.frame.localmoranex; row names assigned localmoranex object ... arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Exact local Moran's Ii tests — localmoran.exact","text":"list class localmoranex containing \"select\" lists, class moranex following components: statistic value exact standard deviate global Moran's . p.value p-value test. estimate value observed local Moran's Ii. method character string giving method used. alternative character string describing alternative hypothesis. gamma eigenvalues (two extreme values null, vector alternative) oType usually set \"E\", set \"N\" integration leads domain value qnorm, Normal assumption substituted. occurs output p-value close zero data.name character string giving name(s) data. df degrees freedom zone tested Vi zone tested alternative tested, list left right M products attribute M.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Exact local Moran's Ii tests — localmoran.exact","text":"Bivand RS, Müller W, Reder M (2009) Power calculations global local Moran’s . Comput Stat Data Anal 53:2859–2872; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Exact local Moran's Ii tests — localmoran.exact","text":"Markus Reder Roger Bivand","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Exact local Moran's Ii tests — localmoran.exact","text":"","code":"eire <- st_read(system.file(\"shapes/eire.gpkg\", package=\"spData\")[1]) #> Reading layer `eire' from data source #> `/home/rsb/lib/r_libs/spData/shapes/eire.gpkg' using driver `GPKG' #> Simple feature collection with 26 features and 10 fields #> Geometry type: MULTIPOLYGON #> Dimension: XY #> Bounding box: xmin: -4.12 ymin: 5768 xmax: 300.82 ymax: 6119.25 #> Projected CRS: Undefined Cartesian SRS with unknown unit row.names(eire) <- as.character(eire$names) eire.nb <- poly2nb(eire) e.lm <- lm(OWNCONS ~ ROADACC, data=eire) localmoran.sad(e.lm, nb=eire.nb) #> Local Morans I Saddlepoint Pr. (Sad) #> 1 Carlow 0.21699668 0.95074844 3.417321e-01 #> 2 Cavan -0.37257361 -1.00603119 3.144006e-01 #> 3 Clare 0.23197510 0.67166518 5.017969e-01 #> 4 Cork 0.78193548 1.74761575 8.053059e-02 #> 5 Donegal -1.69064059 -1.72031078 8.537596e-02 #> 6 Dublin -0.16069692 -0.35212627 7.247436e-01 #> 7 Galway 1.31371473 2.66849536 7.619183e-03 #> 8 Kerry 0.36534866 0.78073279 4.349597e-01 #> 9 Kildare -0.02557544 0.04167665 9.667565e-01 #> 10 Kilkenny 0.57684331 1.70897697 8.745521e-02 #> 11 Laoghis -0.05951798 -0.12155465 9.032517e-01 #> 12 Leitrim 0.38484587 1.47227033 1.409479e-01 #> 13 Limerick 0.11817987 0.45727712 6.474719e-01 #> 14 Longford 1.41643200 2.51113769 1.203427e-02 #> 15 Louth 0.56242920 1.07441571 2.826364e-01 #> 16 Mayo 0.87572704 2.05251226 4.011990e-02 #> 17 Meath 0.00367856 0.12813539 8.980418e-01 #> 18 Monaghan 0.55098311 1.23999193 2.149784e-01 #> 19 Offaly 0.15155556 0.80786519 4.191682e-01 #> 20 Roscommon 2.04368839 4.53187292 5.846302e-06 #> 21 Sligo -0.47579871 -0.94578114 3.442602e-01 #> 22 Tipperary -0.03454106 -0.06919691 9.448329e-01 #> 23 Waterford 0.85723423 1.91385108 5.563919e-02 #> 24 Westmeath 0.45138572 1.36017204 1.737755e-01 #> 25 Wexford 0.64371834 1.63188492 1.027037e-01 #> 26 Wicklow 0.02441950 0.21197000 8.321304e-01 localmoran.exact(e.lm, nb=eire.nb) #> Local Morans I Exact SD Pr. (exact) #> 1 Carlow 0.21699668 1.02706083 3.043918e-01 #> 2 Cavan -0.37257361 -1.04864802 2.943401e-01 #> 3 Clare 0.23197510 0.76362894 4.450884e-01 #> 4 Cork 0.78193548 1.77727656 7.552275e-02 #> 5 Donegal -1.69064059 -1.74428756 8.110896e-02 #> 6 Dublin -0.16069692 -0.44236119 6.582279e-01 #> 7 Galway 1.31371473 2.69199974 7.102500e-03 #> 8 Kerry 0.36534866 0.85742696 3.912090e-01 #> 9 Kildare -0.02557544 -0.03475476 9.722753e-01 #> 10 Kilkenny 0.57684331 1.74146177 8.160267e-02 #> 11 Laoghis -0.05951798 -0.21824035 8.272419e-01 #> 12 Leitrim 0.38484587 1.51434641 1.299380e-01 #> 13 Limerick 0.11817987 0.56922630 5.692026e-01 #> 14 Longford 1.41643200 2.53491837 1.124735e-02 #> 15 Louth 0.56242920 1.12775107 2.594251e-01 #> 16 Mayo 0.87572704 2.08125803 3.741029e-02 #> 17 Meath 0.00367856 0.16372685 8.699462e-01 #> 18 Monaghan 0.55098311 1.28435459 1.990179e-01 #> 19 Offaly 0.15155556 0.89537870 3.705847e-01 #> 20 Roscommon 2.04368839 4.55244870 5.302509e-06 #> 21 Sligo -0.47579871 -0.98101752 3.265841e-01 #> 22 Tipperary -0.03454106 -0.16132608 8.718366e-01 #> 23 Waterford 0.85723423 1.94188723 5.215075e-02 #> 24 Westmeath 0.45138572 1.40091422 1.612397e-01 #> 25 Wexford 0.64371834 1.66488051 9.593660e-02 #> 26 Wicklow 0.02441950 0.29717701 7.663314e-01 localmoran.exact(e.lm, nb=eire.nb, useTP=TRUE) #> Local Morans I Exact SD Pr. (exact) #> 1 Carlow 0.21699668 1.02706127 3.043916e-01 #> 2 Cavan -0.37257361 -1.04864834 2.943400e-01 #> 3 Clare 0.23197510 0.76362936 4.450881e-01 #> 4 Cork 0.78193548 1.77727666 7.552273e-02 #> 5 Donegal -1.69064059 -1.74428741 8.110899e-02 #> 6 Dublin -0.16069692 -0.44236158 6.582276e-01 #> 7 Galway 1.31371473 2.69199162 7.102673e-03 #> 8 Kerry 0.36534866 0.85742736 3.912087e-01 #> 9 Kildare -0.02557544 -0.03540278 9.717586e-01 #> 10 Kilkenny 0.57684331 1.74146192 8.160264e-02 #> 11 Laoghis -0.05951798 -0.21823772 8.272439e-01 #> 12 Leitrim 0.38484587 1.51434680 1.299379e-01 #> 13 Limerick 0.11817987 0.56922674 5.692023e-01 #> 14 Longford 1.41643200 2.53491383 1.124750e-02 #> 15 Louth 0.56242920 1.12775145 2.594249e-01 #> 16 Mayo 0.87572704 2.08125778 3.741032e-02 #> 17 Meath 0.00367856 0.15714487 8.751307e-01 #> 18 Monaghan 0.55098311 1.28435495 1.990178e-01 #> 19 Offaly 0.15155556 0.89537914 3.705844e-01 #> 20 Roscommon 2.04368839 4.53362873 5.797890e-06 #> 21 Sligo -0.47579871 -0.98101780 3.265840e-01 #> 22 Tipperary -0.03454106 -0.16116590 8.719627e-01 #> 23 Waterford 0.85723423 1.94188711 5.215077e-02 #> 24 Westmeath 0.45138572 1.40091457 1.612396e-01 #> 25 Wexford 0.64371834 1.66488069 9.593656e-02 #> 26 Wicklow 0.02441950 0.29790569 7.657751e-01 run <- FALSE if (requireNamespace(\"spatialreg\", quietly=TRUE)) run <- TRUE if (run) { e.errorsar <- spatialreg::errorsarlm(OWNCONS ~ ROADACC, data=eire, listw=nb2listw(eire.nb)) lm.target <- lm(e.errorsar$tary ~ e.errorsar$tarX - 1) localmoran.exact.alt(lm.target, nb=eire.nb) } #> Local Morans I Exact SD Pr. (exact) #> 1 Carlow 0.17958462 0.83313548 0.404768327 #> 2 Cavan -0.24752628 -0.82861508 0.407322251 #> 3 Clare -0.27901334 -0.72313220 0.469598670 #> 4 Cork 0.37808655 1.15083938 0.249798320 #> 5 Donegal -1.01894688 -1.50937607 0.131202704 #> 6 Dublin -0.18171297 -0.50995181 0.610085224 #> 7 Galway 1.02193390 2.27605549 0.022842689 #> 8 Kerry -0.94967914 -1.46954733 0.141684395 #> 9 Kildare 0.07005053 0.56174770 0.574287931 #> 10 Kilkenny 0.43022231 1.39078833 0.164289622 #> 11 Laoghis -0.12239133 -0.45750046 0.647311369 #> 12 Leitrim -0.24203970 -0.84925558 0.395739092 #> 13 Limerick -0.03214546 -0.13098232 0.895789292 #> 14 Longford 0.38307454 1.17909760 0.238359315 #> 15 Louth 0.21301552 0.62068302 0.534808204 #> 16 Mayo 0.93971200 1.94079901 0.052282661 #> 17 Meath 0.12484415 0.78747315 0.431004937 #> 18 Monaghan -0.16109919 -0.48277561 0.629255068 #> 19 Offaly -0.00632492 0.03008421 0.975999892 #> 20 Roscommon 1.02089429 2.64333471 0.008209384 #> 21 Sligo -2.01629233 -2.54211789 0.011018300 #> 22 Tipperary -0.10810709 -0.51063241 0.609608478 #> 23 Waterford 0.44099279 1.28152280 0.200010096 #> 24 Westmeath -0.06329661 -0.26575204 0.790430182 #> 25 Wexford 0.30764883 1.02115599 0.307180540 #> 26 Wicklow -0.01696406 -0.04109885 0.967217095 if (run) { Omega <- spatialreg::invIrW(nb2listw(eire.nb), rho=e.errorsar$lambda) Omega1 <- tcrossprod(Omega) localmoran.exact.alt(lm.target, nb=eire.nb, Omega=Omega1) } #> Local Morans I Exact SD Pr. (exact) #> 1 Carlow 0.17958462 0.009413917 0.9924888917 #> 2 Cavan -0.24752628 -1.416786314 0.1565454123 #> 3 Clare -0.27901334 -1.512813055 0.1303271518 #> 4 Cork 0.37808655 0.078686494 0.9372819882 #> 5 Donegal -1.01894688 -1.935314161 0.0529517556 #> 6 Dublin -0.18171297 -1.226543250 0.2199943101 #> 7 Galway 1.02193390 1.477322295 0.1395892645 #> 8 Kerry -0.94967914 -2.427948363 0.0151845050 #> 9 Kildare 0.07005053 -0.042522018 0.9660825597 #> 10 Kilkenny 0.43022231 0.488471215 0.6252161095 #> 11 Laoghis -0.12239133 -1.091910862 0.2748722828 #> 12 Leitrim -0.24203970 -1.631825829 0.1027161825 #> 13 Limerick -0.03214546 -0.921751556 0.3566581814 #> 14 Longford 0.38307454 0.183273193 0.8545836668 #> 15 Louth 0.21301552 -0.184065307 0.8539622228 #> 16 Mayo 0.93971200 1.182398032 0.2370478039 #> 17 Meath 0.12484415 -0.060499926 0.9517574751 #> 18 Monaghan -0.16109919 -1.342787508 0.1793407894 #> 19 Offaly -0.00632492 -0.409598788 0.6821002864 #> 20 Roscommon 1.02089429 1.238387417 0.2155724439 #> 21 Sligo -2.01629233 -3.623597237 0.0002905339 #> 22 Tipperary -0.10810709 -1.227333133 0.2196974073 #> 23 Waterford 0.44099279 0.433358039 0.6647546795 #> 24 Westmeath -0.06329661 -0.956519228 0.3388099749 #> 25 Wexford 0.30764883 0.141381249 0.8875687669 #> 26 Wicklow -0.01696406 -0.783977878 0.4330530912 if (run) { localmoran.exact.alt(lm.target, nb=eire.nb, Omega=Omega1, useTP=TRUE) } #> Local Morans I Exact SD Pr. (exact) #> 1 Carlow 0.17958462 0.009414171 0.9924886890 #> 2 Cavan -0.24752628 -1.416786809 0.1565452674 #> 3 Clare -0.27901334 -1.512813519 0.1303270339 #> 4 Cork 0.37808655 0.078686628 0.9372818820 #> 5 Donegal -1.01894688 -1.935314436 0.0529517219 #> 6 Dublin -0.18171297 -1.226543734 0.2199941280 #> 7 Galway 1.02193390 1.477322399 0.1395892366 #> 8 Kerry -0.94967914 -2.427949220 0.0151844692 #> 9 Kildare 0.07005053 -0.042526750 0.9660787872 #> 10 Kilkenny 0.43022231 0.488471349 0.6252160151 #> 11 Laoghis -0.12239133 -1.091912026 0.2748717712 #> 12 Leitrim -0.24203970 -1.631826543 0.1027160320 #> 13 Limerick -0.03214546 -0.921785589 0.3566404260 #> 14 Longford 0.38307454 0.183273325 0.8545835633 #> 15 Louth 0.21301552 -0.184065128 0.8539623632 #> 16 Mayo 0.93971200 1.182398127 0.2370477660 #> 17 Meath 0.12484415 -0.060499243 0.9517580191 #> 18 Monaghan -0.16109919 -1.342788191 0.1793405683 #> 19 Offaly -0.00632492 -0.407816672 0.6834082724 #> 20 Roscommon 1.02089429 1.238387488 0.2155724176 #> 21 Sligo -2.01629233 -3.623590126 0.0002905419 #> 22 Tipperary -0.10810709 -1.227335007 0.2196967034 #> 23 Waterford 0.44099279 0.433358168 0.6647545856 #> 24 Westmeath -0.06329661 -0.956505669 0.3388168216 #> 25 Wexford 0.30764883 0.141381402 0.8875686458 #> 26 Wicklow -0.01696406 -0.784451760 0.4327750770"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":null,"dir":"Reference","previous_headings":"","what":"Local Moran's I statistic — localmoran","title":"Local Moran's I statistic — localmoran","text":"local spatial statistic Moran's calculated zone based spatial weights object used. values returned include Z-value, may used diagnostic tool. statistic : $$I_i = \\frac{(x_i-\\bar{x})}{{\\sum_{k=1}^{n}(x_k-\\bar{x})^2}/(n-1)}{\\sum_{j=1}^{n}w_{ij}(x_j-\\bar{x})}$$, expectation variance given Anselin (1995), Sokal et al. (1998) implemented .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Local Moran's I statistic — localmoran","text":"","code":"localmoran(x, listw, zero.policy=attr(listw, \"zero.policy\"), na.action=na.fail, conditional=TRUE, alternative = \"two.sided\", mlvar=TRUE, spChk=NULL, adjust.x=FALSE) localmoran_perm(x, listw, nsim=499, zero.policy=attr(listw, \"zero.policy\"), na.action=na.fail, alternative = \"two.sided\", mlvar=TRUE, spChk=NULL, adjust.x=FALSE, sample_Ei=TRUE, iseed=NULL, no_repeat_in_row=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Local Moran's I statistic — localmoran","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw zero.policy default default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass used, zero substituted NA values calculating spatial lag. (Note na.exclude work properly starting R 1.9.0, na.omit na.exclude assign wrong classes 1.8.*) conditional default TRUE: expectation variance calculated using conditional randomization null (Sokal 1998 Eqs. A7 & A8). Elaboration changes available Sauer et al. (2021). FALSE: expectation variance calculated using total randomization null (Sokal 1998 Eqs. A3 & A4). alternative character string specifying alternative hypothesis, must one greater, less two.sided (default). mlvar default TRUE: values local Moran's reported using variance variable interest (sum squared deviances n), can reported sample variance, dividing (n-1) instead; used implementations. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() adjust.x default FALSE, TRUE, x values observations neighbours omitted mean x nsim default 499, number conditonal permutation simulations sample_Ei default TRUE; conditional permutation, use sample $E_i$ values, analytical values, leaving variances calculated simulation. iseed default NULL, used set seed; output reproducible count CPU cores across computation distributed no_repeat_in_row default FALSE, TRUE, sample conditionally row without replacements avoid duplicate values, https://github.com/r-spatial/spdep/issues/124","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Local Moran's I statistic — localmoran","text":"values local Moran's divided variance (sample variance) variable interest accord Table 1, p. 103, formula (12), p. 99, Anselin (1995), rather formula (7), p. 98. variance local Moran statistic taken Sokal et al. (1998) p. 334, equations 4 & 5 equations 7 & 8 located depending user specification. default, implementation divides n, (n-1) calculating variance higher moments. Conditional code contributed Jeff Sauer Levi Wolf.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Local Moran's I statistic — localmoran","text":"Ii local moran statistic E.Ii expectation local moran statistic; localmoran_permthe permutation sample means Var.Ii variance local moran statistic; localmoran_permthe permutation sample standard deviations Z.Ii standard deviate local moran statistic; localmoran_perm based permutation sample means standard deviations Pr() p-value local moran statistic using pnorm(); localmoran_perm using standard deviatse based permutation sample means standard deviations Pr() Sim localmoran_perm, rank() punif() observed statistic rank [0, 1] p-values using alternative= Pr(folded) Sim simulation folded [0, 0.5] range ranked p-value (based https://github.com/pysal/esda/blob/4a63e0b5df1e754b17b5f1205b8cadcbecc5e061/esda/crand.py#L211-L213) Skewness localmoran_perm, output e1071::skewness() permutation samples underlying standard deviates Kurtosis localmoran_perm, output e1071::kurtosis() permutation samples underlying standard deviates addition, attribute data frame \"quadr\" mean median quadrant columns, column splitting demeaned variable lagged demeaned variable zero.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Local Moran's I statistic — localmoran","text":"Conditional permutations added comparative purposes; permutations whole data vector omitting observation . p-value adjustment, use p.adjust() p.adjustSP() output vector.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Local Moran's I statistic — localmoran","text":"Anselin, L. 1995. Local indicators spatial association, Geographical Analysis, 27, 93–115; Getis, . Ord, J. K. 1996 Local spatial statistics: overview. P. Longley M. Batty (eds) Spatial analysis: modelling GIS environment (Cambridge: Geoinformation International), 261–277; Sokal, R. R, Oden, N. L. Thomson, B. . 1998. Local Spatial Autocorrelation Biological Model. Geographical Analysis, 30. 331–354; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x ; Sauer, J., Oshan, T. M., Rey, S., & Wolf, L. J. 2021. Importance Null Hypotheses: Understanding Differences Local Moran’s Heteroskedasticity. Geographical Analysis. doi:10.1111/gean.12304 Bivand, R. (2022), R Packages Analyzing Spatial Data: Comparative Case Study Areal Data. Geographical Analysis, 54(3), 488-518. doi:10.1111/gean.12319","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Local Moran's I statistic — localmoran","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Local Moran's I statistic — localmoran","text":"","code":"data(afcon, package=\"spData\") oid <- order(afcon$id) resI <- localmoran(afcon$totcon, nb2listw(paper.nb)) printCoefmat(data.frame(resI[oid,], row.names=afcon$name[oid]), check.names=FALSE) #> Ii E.Ii Var.Ii Z.Ii #> THE GAMBIA 3.7523e-01 -2.4317e-02 9.9646e-01 4.0025e-01 #> MALI 4.6363e-01 -2.1841e-02 1.0896e-01 1.4708e+00 #> SENEGAL 2.5670e-01 -3.4444e-03 3.3339e-02 1.4248e+00 #> BENIN 1.9412e-01 -2.4556e-03 2.3792e-02 1.2744e+00 #> MAURITANIA 9.7053e-02 -5.7508e-03 5.5533e-02 4.3625e-01 #> NIGER 2.3071e-01 -1.9459e-02 9.7310e-02 8.0198e-01 #> IVORY COAST 2.9004e-01 -6.9359e-03 5.2072e-02 1.3014e+00 #> GUINEA 1.8263e-01 -2.2246e-03 1.6780e-02 1.4270e+00 #> BURKINA FASO 5.0828e-01 -1.9893e-02 1.1942e-01 1.5284e+00 #> LIBERIA 1.8565e-01 -2.7127e-03 3.5982e-02 9.9300e-01 #> SIERRA LEONE 2.6523e-01 -1.6994e-02 3.4204e-01 4.8257e-01 #> GHANA 1.4764e-01 -1.3414e-03 1.7817e-02 1.1161e+00 #> TOGO 2.1934e-01 -4.9892e-03 6.6025e-02 8.7305e-01 #> CAMEROON 2.5925e-01 -1.1009e-02 8.2313e-02 9.4198e-01 #> NIGERIA 1.1377e-01 -9.6126e-04 9.3272e-03 1.1880e+00 #> GABON 2.0366e-01 -5.4771e-03 1.1153e-01 6.2625e-01 #> CENTRAL AFRICAN REPUBLIC -4.4206e-01 -1.0600e-02 7.9287e-02 -1.5323e+00 #> CHAD -1.0528e-01 -4.0998e-03 2.5008e-02 -6.3985e-01 #> CONGO 1.1380e-02 -8.5953e-04 8.3410e-03 1.3402e-01 #> ZAIRE 7.0978e-01 -5.9545e-02 2.0906e-01 1.6826e+00 #> ANGOLA 1.1797e-01 -6.2140e-04 8.2594e-03 1.3050e+00 #> UGANDA 1.9425e+00 -6.2812e-02 4.4503e-01 3.0060e+00 #> KENYA 1.1969e+00 -1.6803e-02 1.2489e-01 3.4344e+00 #> TANZANIA 2.7185e-01 -4.6254e-02 1.9107e-01 7.2774e-01 #> BURUNDI -4.8428e-01 -1.1009e-02 1.4481e-01 -1.2437e+00 #> RWANDA -7.5236e-01 -1.4730e-02 1.4096e-01 -1.9647e+00 #> SOMALIA 4.5277e-01 -1.1751e-02 2.3778e-01 9.5260e-01 #> ETHIOPIA 7.2512e-01 -5.4929e-03 7.2655e-02 2.7106e+00 #> ZAMBIA 4.2160e-02 -8.1691e-04 3.5354e-03 7.2280e-01 #> ZIMBABWE -9.5068e-03 -6.0969e-03 5.8855e-02 -1.4056e-02 #> MALAWI -2.2888e-01 -1.0284e-02 1.3537e-01 -5.9413e-01 #> MOZAMBIQUE 1.6790e-02 -6.1629e-03 3.7515e-02 1.1850e-01 #> SOUTH AFRICA -1.8254e-01 -5.4306e-03 2.7546e-02 -1.0671e+00 #> LESOTHO -4.1935e-01 -1.9263e-02 7.9348e-01 -4.4914e-01 #> BOTSWANA -3.9316e-03 -1.4141e-04 1.8805e-03 -8.7403e-02 #> SWAZILAND 1.6684e-02 -2.8611e-02 5.6905e-01 6.0045e-02 #> MOROCCO -9.6961e-02 -5.1445e-03 1.0479e-01 -2.8363e-01 #> ALGERIA -1.0037e-02 -9.7828e-05 5.9914e-04 -4.0605e-01 #> TUNISIA 5.3873e-03 -3.0273e-06 6.1985e-05 6.8466e-01 #> LIBYA 8.0382e-01 -1.9923e-02 1.1960e-01 2.3820e+00 #> SUDAN 2.9878e+00 -2.2835e-01 7.6320e-01 3.6814e+00 #> EGYPT 6.9467e+00 -2.9968e-01 4.2971e+00 3.4957e+00 #> Pr.z....E.Ii.. #> THE GAMBIA 0.6890 #> MALI 0.1414 #> SENEGAL 0.1542 #> BENIN 0.2025 #> MAURITANIA 0.6627 #> NIGER 0.4226 #> IVORY COAST 0.1931 #> GUINEA 0.1536 #> BURKINA FASO 0.1264 #> LIBERIA 0.3207 #> SIERRA LEONE 0.6294 #> GHANA 0.2644 #> TOGO 0.3826 #> CAMEROON 0.3462 #> NIGERIA 0.2348 #> GABON 0.5312 #> CENTRAL AFRICAN REPUBLIC 0.1255 #> CHAD 0.5223 #> CONGO 0.8934 #> ZAIRE 0.0925 #> ANGOLA 0.1919 #> UGANDA 0.0026 #> KENYA 0.0006 #> TANZANIA 0.4668 #> BURUNDI 0.2136 #> RWANDA 0.0494 #> SOMALIA 0.3408 #> ETHIOPIA 0.0067 #> ZAMBIA 0.4698 #> ZIMBABWE 0.9888 #> MALAWI 0.5524 #> MOZAMBIQUE 0.9057 #> SOUTH AFRICA 0.2859 #> LESOTHO 0.6533 #> BOTSWANA 0.9304 #> SWAZILAND 0.9521 #> MOROCCO 0.7767 #> ALGERIA 0.6847 #> TUNISIA 0.4936 #> LIBYA 0.0172 #> SUDAN 0.0002 #> EGYPT 0.0005 hist(resI[,5]) mean(resI[,1]) #> [1] 0.4167956 sum(resI[,1])/Szero(nb2listw(paper.nb)) #> [1] 0.4167956 moran.test(afcon$totcon, nb2listw(paper.nb)) #> #> \tMoran I test under randomisation #> #> data: afcon$totcon #> weights: nb2listw(paper.nb) #> #> Moran I statistic standard deviate = 4.3485, p-value = 6.854e-06 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.41679563 -0.02439024 0.01029358 #> # note equality for mean() only when the sum of weights equals # the number of observations (thanks to Juergen Symanzik) resI <- localmoran(afcon$totcon, nb2listw(paper.nb)) printCoefmat(data.frame(resI[oid,], row.names=afcon$name[oid]), check.names=FALSE) #> Ii E.Ii Var.Ii Z.Ii #> THE GAMBIA 3.7523e-01 -2.4317e-02 9.9646e-01 4.0025e-01 #> MALI 4.6363e-01 -2.1841e-02 1.0896e-01 1.4708e+00 #> SENEGAL 2.5670e-01 -3.4444e-03 3.3339e-02 1.4248e+00 #> BENIN 1.9412e-01 -2.4556e-03 2.3792e-02 1.2744e+00 #> MAURITANIA 9.7053e-02 -5.7508e-03 5.5533e-02 4.3625e-01 #> NIGER 2.3071e-01 -1.9459e-02 9.7310e-02 8.0198e-01 #> IVORY COAST 2.9004e-01 -6.9359e-03 5.2072e-02 1.3014e+00 #> GUINEA 1.8263e-01 -2.2246e-03 1.6780e-02 1.4270e+00 #> BURKINA FASO 5.0828e-01 -1.9893e-02 1.1942e-01 1.5284e+00 #> LIBERIA 1.8565e-01 -2.7127e-03 3.5982e-02 9.9300e-01 #> SIERRA LEONE 2.6523e-01 -1.6994e-02 3.4204e-01 4.8257e-01 #> GHANA 1.4764e-01 -1.3414e-03 1.7817e-02 1.1161e+00 #> TOGO 2.1934e-01 -4.9892e-03 6.6025e-02 8.7305e-01 #> CAMEROON 2.5925e-01 -1.1009e-02 8.2313e-02 9.4198e-01 #> NIGERIA 1.1377e-01 -9.6126e-04 9.3272e-03 1.1880e+00 #> GABON 2.0366e-01 -5.4771e-03 1.1153e-01 6.2625e-01 #> CENTRAL AFRICAN REPUBLIC -4.4206e-01 -1.0600e-02 7.9287e-02 -1.5323e+00 #> CHAD -1.0528e-01 -4.0998e-03 2.5008e-02 -6.3985e-01 #> CONGO 1.1380e-02 -8.5953e-04 8.3410e-03 1.3402e-01 #> ZAIRE 7.0978e-01 -5.9545e-02 2.0906e-01 1.6826e+00 #> ANGOLA 1.1797e-01 -6.2140e-04 8.2594e-03 1.3050e+00 #> UGANDA 1.9425e+00 -6.2812e-02 4.4503e-01 3.0060e+00 #> KENYA 1.1969e+00 -1.6803e-02 1.2489e-01 3.4344e+00 #> TANZANIA 2.7185e-01 -4.6254e-02 1.9107e-01 7.2774e-01 #> BURUNDI -4.8428e-01 -1.1009e-02 1.4481e-01 -1.2437e+00 #> RWANDA -7.5236e-01 -1.4730e-02 1.4096e-01 -1.9647e+00 #> SOMALIA 4.5277e-01 -1.1751e-02 2.3778e-01 9.5260e-01 #> ETHIOPIA 7.2512e-01 -5.4929e-03 7.2655e-02 2.7106e+00 #> ZAMBIA 4.2160e-02 -8.1691e-04 3.5354e-03 7.2280e-01 #> ZIMBABWE -9.5068e-03 -6.0969e-03 5.8855e-02 -1.4056e-02 #> MALAWI -2.2888e-01 -1.0284e-02 1.3537e-01 -5.9413e-01 #> MOZAMBIQUE 1.6790e-02 -6.1629e-03 3.7515e-02 1.1850e-01 #> SOUTH AFRICA -1.8254e-01 -5.4306e-03 2.7546e-02 -1.0671e+00 #> LESOTHO -4.1935e-01 -1.9263e-02 7.9348e-01 -4.4914e-01 #> BOTSWANA -3.9316e-03 -1.4141e-04 1.8805e-03 -8.7403e-02 #> SWAZILAND 1.6684e-02 -2.8611e-02 5.6905e-01 6.0045e-02 #> MOROCCO -9.6961e-02 -5.1445e-03 1.0479e-01 -2.8363e-01 #> ALGERIA -1.0037e-02 -9.7828e-05 5.9914e-04 -4.0605e-01 #> TUNISIA 5.3873e-03 -3.0273e-06 6.1985e-05 6.8466e-01 #> LIBYA 8.0382e-01 -1.9923e-02 1.1960e-01 2.3820e+00 #> SUDAN 2.9878e+00 -2.2835e-01 7.6320e-01 3.6814e+00 #> EGYPT 6.9467e+00 -2.9968e-01 4.2971e+00 3.4957e+00 #> Pr.z....E.Ii.. #> THE GAMBIA 0.6890 #> MALI 0.1414 #> SENEGAL 0.1542 #> BENIN 0.2025 #> MAURITANIA 0.6627 #> NIGER 0.4226 #> IVORY COAST 0.1931 #> GUINEA 0.1536 #> BURKINA FASO 0.1264 #> LIBERIA 0.3207 #> SIERRA LEONE 0.6294 #> GHANA 0.2644 #> TOGO 0.3826 #> CAMEROON 0.3462 #> NIGERIA 0.2348 #> GABON 0.5312 #> CENTRAL AFRICAN REPUBLIC 0.1255 #> CHAD 0.5223 #> CONGO 0.8934 #> ZAIRE 0.0925 #> ANGOLA 0.1919 #> UGANDA 0.0026 #> KENYA 0.0006 #> TANZANIA 0.4668 #> BURUNDI 0.2136 #> RWANDA 0.0494 #> SOMALIA 0.3408 #> ETHIOPIA 0.0067 #> ZAMBIA 0.4698 #> ZIMBABWE 0.9888 #> MALAWI 0.5524 #> MOZAMBIQUE 0.9057 #> SOUTH AFRICA 0.2859 #> LESOTHO 0.6533 #> BOTSWANA 0.9304 #> SWAZILAND 0.9521 #> MOROCCO 0.7767 #> ALGERIA 0.6847 #> TUNISIA 0.4936 #> LIBYA 0.0172 #> SUDAN 0.0002 #> EGYPT 0.0005 hist(p.adjust(resI[,5], method=\"bonferroni\")) totcon <-afcon$totcon is.na(totcon) <- sample(1:length(totcon), 5) totcon #> [1] 1363 1421 1861 2355 5246 811 299 358 895 NA NA 933 347 1130 241 #> [16] 604 1015 998 2122 1090 NA NA 758 423 NA 3087 2273 3134 1142 824 #> [31] 2881 487 604 1528 1554 629 792 795 1266 1875 147 363 resI.na <- localmoran(totcon, nb2listw(paper.nb), na.action=na.exclude, zero.policy=TRUE) if (class(attr(resI.na, \"na.action\")) == \"exclude\") { print(data.frame(resI.na[oid,], row.names=afcon$name[oid]), digits=2) } else print(resI.na, digits=2) #> Ii E.Ii Var.Ii Z.Ii Pr.z....E.Ii.. #> THE GAMBIA 0.3528 -2.9e-02 1.03887 0.37 0.708 #> MALI 0.4524 -2.6e-02 0.11007 1.44 0.149 #> SENEGAL 0.2347 -3.3e-03 0.02800 1.42 0.155 #> BENIN 0.1862 -2.2e-03 0.02572 1.17 0.240 #> MAURITANIA 0.0722 -6.0e-03 0.05043 0.35 0.728 #> NIGER 0.1981 -2.3e-02 0.09763 0.71 0.480 #> IVORY COAST 0.3020 -7.4e-03 0.06218 1.24 0.215 #> GUINEA 0.1774 -2.0e-03 0.01658 1.39 0.164 #> BURKINA FASO 0.5248 -2.3e-02 0.14950 1.42 0.156 #> LIBERIA NA NA NA NA NA #> SIERRA LEONE 0.2241 -2.0e-02 0.71575 0.29 0.773 #> GHANA 0.1382 -1.0e-03 0.01854 1.02 0.307 #> TOGO NA NA NA NA NA #> CAMEROON 0.1884 -1.2e-02 0.10306 0.63 0.532 #> NIGERIA 0.0861 -6.6e-04 0.00556 1.16 0.245 #> GABON 0.1828 -5.7e-03 0.10144 0.59 0.554 #> CENTRAL AFRICAN REPUBLIC NA NA NA NA NA #> CHAD 0.0657 -4.1e-03 0.03430 0.38 0.706 #> CONGO -0.0301 -5.6e-04 0.00652 -0.37 0.715 #> ZAIRE 0.5651 -8.5e-02 0.34207 1.11 0.266 #> ANGOLA 0.2017 -1.5e-03 0.01766 1.53 0.126 #> UGANDA 1.5678 -9.0e-02 0.69207 1.99 0.046 #> KENYA 1.3328 -2.6e-02 0.29012 2.52 0.012 #> TANZANIA 0.4269 -6.7e-02 0.23117 1.03 0.304 #> BURUNDI -0.5611 -1.2e-02 0.14171 -1.46 0.145 #> RWANDA -0.8661 -1.7e-02 0.14069 -2.26 0.024 #> SOMALIA 0.7805 -1.8e-02 0.66673 0.98 0.328 #> ETHIOPIA NA NA NA NA NA #> ZAMBIA 0.0806 -1.9e-03 0.00690 0.99 0.321 #> ZIMBABWE -0.0393 -6.4e-03 0.05385 -0.14 0.887 #> MALAWI -0.2844 -1.1e-02 0.13166 -0.75 0.452 #> MOZAMBIQUE -0.0121 -6.5e-03 0.03407 -0.03 0.976 #> SOUTH AFRICA -0.2047 -9.1e-03 0.03947 -0.98 0.325 #> LESOTHO -0.5158 -2.3e-02 0.81614 -0.55 0.585 #> BOTSWANA -0.0025 -1.3e-05 0.00015 -0.20 0.838 #> SWAZILAND -0.0494 -3.4e-02 0.59593 -0.02 0.984 #> MOROCCO -0.0936 -8.7e-03 0.15440 -0.22 0.829 #> ALGERIA -0.0143 -4.7e-04 0.00247 -0.28 0.780 #> TUNISIA 0.0428 -1.5e-04 0.00268 0.83 0.406 #> LIBYA 0.5764 -3.0e-02 0.19100 1.39 0.165 #> SUDAN NA NA NA NA NA #> EGYPT 4.0118 -4.1e-01 8.97211 1.48 0.140 resG <- localG(afcon$totcon, nb2listw(include.self(paper.nb))) print(data.frame(resG[oid], row.names=afcon$name[oid]), digits=2) #> resG.oid. #> THE GAMBIA -0.984 #> MALI -1.699 #> SENEGAL -1.463 #> BENIN -1.301 #> MAURITANIA -0.605 #> NIGER -1.049 #> IVORY COAST -1.417 #> GUINEA -1.449 #> BURKINA FASO -1.751 #> LIBERIA -1.041 #> SIERRA LEONE -0.870 #> GHANA -1.103 #> TOGO -0.991 #> CAMEROON -1.133 #> NIGERIA -1.173 #> GABON -0.789 #> CENTRAL AFRICAN REPUBLIC 1.173 #> CHAD 0.463 #> CONGO -0.203 #> ZAIRE 2.023 #> ANGOLA 1.235 #> UGANDA 3.336 #> KENYA 3.503 #> TANZANIA 1.098 #> BURUNDI 0.774 #> RWANDA 1.457 #> SOMALIA 1.183 #> ETHIOPIA 2.627 #> ZAMBIA 0.753 #> ZIMBABWE -0.200 #> MALAWI 0.212 #> MOZAMBIQUE -0.288 #> SOUTH AFRICA -0.868 #> LESOTHO -0.298 #> BOTSWANA 0.041 #> SWAZILAND -0.659 #> MOROCCO 0.022 #> ALGERIA -0.363 #> TUNISIA 0.579 #> LIBYA 2.553 #> SUDAN 4.039 #> EGYPT 4.421 set.seed(1) resI_p <- localmoran_perm(afcon$totcon, nb2listw(paper.nb)) printCoefmat(data.frame(resI_p[oid,], row.names=afcon$name[oid]), check.names=FALSE) #> Ii E.Ii Var.Ii Z.Ii #> THE GAMBIA 3.7523e-01 -3.0853e-02 9.0476e-01 4.2692e-01 #> MALI 4.6363e-01 -2.1690e-02 1.2192e-01 1.3899e+00 #> SENEGAL 2.5670e-01 -1.1288e-02 3.2719e-02 1.4816e+00 #> BENIN 1.9412e-01 -6.5012e-03 2.6046e-02 1.2431e+00 #> MAURITANIA 9.7053e-02 -2.0574e-03 5.7209e-02 4.1437e-01 #> NIGER 2.3071e-01 -2.8428e-02 1.1981e-01 7.4867e-01 #> IVORY COAST 2.9004e-01 -8.1011e-03 5.5564e-02 1.2648e+00 #> GUINEA 1.8263e-01 5.3454e-04 1.8397e-02 1.3425e+00 #> BURKINA FASO 5.0828e-01 -2.9727e-02 1.4019e-01 1.4369e+00 #> LIBERIA 1.8565e-01 -1.9247e-03 3.6524e-02 9.8147e-01 #> SIERRA LEONE 2.6523e-01 1.0225e-02 3.1505e-01 4.5432e-01 #> GHANA 1.4764e-01 -6.7639e-03 1.8646e-02 1.1307e+00 #> TOGO 2.1934e-01 -1.8012e-03 6.5187e-02 8.6616e-01 #> CAMEROON 2.5925e-01 -1.0726e-02 9.4789e-02 8.7688e-01 #> NIGERIA 1.1377e-01 -2.5672e-03 8.7720e-03 1.2421e+00 #> GABON 2.0366e-01 -3.5024e-03 1.0958e-01 6.2584e-01 #> CENTRAL AFRICAN REPUBLIC -4.4206e-01 2.3901e-02 8.1700e-02 -1.6302e+00 #> CHAD -1.0528e-01 5.9042e-03 3.0168e-02 -6.4016e-01 #> CONGO 1.1380e-02 7.0349e-03 8.9435e-03 4.5949e-02 #> ZAIRE 7.0978e-01 -2.9589e-02 2.9068e-01 1.3714e+00 #> ANGOLA 1.1797e-01 -3.0421e-04 8.6526e-03 1.2716e+00 #> UGANDA 1.9425e+00 -7.0491e-02 5.2046e-01 2.7903e+00 #> KENYA 1.1969e+00 -1.6362e-02 1.3644e-01 3.2847e+00 #> TANZANIA 2.7185e-01 -7.3309e-02 2.3454e-01 7.1272e-01 #> BURUNDI -4.8428e-01 9.5351e-03 1.4866e-01 -1.2807e+00 #> RWANDA -7.5236e-01 -4.0426e-02 1.7628e-01 -1.6956e+00 #> SOMALIA 4.5277e-01 -1.1165e-02 2.6266e-01 9.0523e-01 #> ETHIOPIA 7.2512e-01 8.3618e-04 7.8477e-02 2.5855e+00 #> ZAMBIA 4.2160e-02 -5.1840e-03 3.6852e-03 7.7989e-01 #> ZIMBABWE -9.5068e-03 -6.5338e-03 6.5357e-02 -1.1629e-02 #> MALAWI -2.2888e-01 3.6276e-03 1.3417e-01 -6.3477e-01 #> MOZAMBIQUE 1.6790e-02 -2.0694e-03 4.5436e-02 8.8476e-02 #> SOUTH AFRICA -1.8254e-01 -1.1611e-02 3.0240e-02 -9.8293e-01 #> LESOTHO -4.1935e-01 -6.6258e-02 8.7314e-01 -3.7787e-01 #> BOTSWANA -3.9316e-03 -4.7713e-03 2.2167e-03 1.7833e-02 #> SWAZILAND 1.6684e-02 -8.4486e-02 6.4807e-01 1.2567e-01 #> MOROCCO -9.6961e-02 -2.1623e-03 1.1253e-01 -2.8260e-01 #> ALGERIA -1.0037e-02 -3.4326e-04 6.3541e-04 -3.8456e-01 #> TUNISIA 5.3873e-03 -1.6456e-04 6.4187e-05 6.9298e-01 #> LIBYA 8.0382e-01 -2.9038e-02 1.3319e-01 2.2821e+00 #> SUDAN 2.9878e+00 -2.5952e-01 8.2522e-01 3.5747e+00 #> EGYPT 6.9467e+00 -3.7869e-01 4.1318e+00 3.6038e+00 #> Pr.z....E.Ii.. Pr.z....E.Ii...Sim Pr.folded..Sim #> THE GAMBIA 6.6944e-01 8.3200e-01 4.2800e-01 #> MALI 1.6455e-01 8.8000e-02 4.4000e-02 #> SENEGAL 1.3846e-01 6.4000e-02 3.2000e-02 #> BENIN 2.1384e-01 1.3200e-01 6.6000e-02 #> MAURITANIA 6.7860e-01 7.5600e-01 3.7800e-01 #> NIGER 4.5406e-01 5.0000e-01 2.5000e-01 #> IVORY COAST 2.0595e-01 1.1600e-01 5.8000e-02 #> GUINEA 1.7943e-01 7.2000e-02 3.6000e-02 #> BURKINA FASO 1.5075e-01 9.2000e-02 4.6000e-02 #> LIBERIA 3.2636e-01 3.0400e-01 1.5200e-01 #> SIERRA LEONE 6.4960e-01 8.2400e-01 4.1200e-01 #> GHANA 2.5816e-01 1.8400e-01 9.2000e-02 #> TOGO 3.8640e-01 3.6800e-01 1.8400e-01 #> CAMEROON 3.8055e-01 4.3200e-01 2.1600e-01 #> NIGERIA 2.1418e-01 1.4400e-01 7.2000e-02 #> GABON 5.3142e-01 5.8400e-01 2.9600e-01 #> CENTRAL AFRICAN REPUBLIC 1.0306e-01 1.8400e-01 9.2000e-02 #> CHAD 5.2207e-01 4.5200e-01 2.2600e-01 #> CONGO 9.6335e-01 8.5600e-01 4.2800e-01 #> ZAIRE 1.7026e-01 2.0000e-01 1.0000e-01 #> ANGOLA 2.0353e-01 2.3600e-01 1.1800e-01 #> UGANDA 5.2662e-03 4.0000e-02 2.0000e-02 #> KENYA 1.0210e-03 8.0000e-03 4.0000e-03 #> TANZANIA 4.7602e-01 4.2400e-01 2.1200e-01 #> BURUNDI 2.0029e-01 2.6800e-01 1.3400e-01 #> RWANDA 8.9953e-02 1.4000e-01 7.0000e-02 #> SOMALIA 3.6535e-01 2.8800e-01 1.4600e-01 #> ETHIOPIA 9.7244e-03 3.6000e-02 1.8000e-02 #> ZAMBIA 4.3546e-01 4.1200e-01 2.0600e-01 #> ZIMBABWE 9.9072e-01 8.6800e-01 4.3400e-01 #> MALAWI 5.2558e-01 4.5600e-01 2.2800e-01 #> MOZAMBIQUE 9.2950e-01 9.4400e-01 4.7200e-01 #> SOUTH AFRICA 3.2564e-01 3.5200e-01 1.7600e-01 #> LESOTHO 7.0553e-01 4.6800e-01 2.2400e-01 #> BOTSWANA 9.8577e-01 8.4400e-01 4.2200e-01 #> SWAZILAND 8.9999e-01 8.8400e-01 4.4200e-01 #> MOROCCO 7.7749e-01 9.7600e-01 4.8800e-01 #> ALGERIA 7.0057e-01 8.0400e-01 4.0200e-01 #> TUNISIA 4.8832e-01 4.2800e-01 2.1600e-01 #> LIBYA 2.2482e-02 4.8000e-02 2.4000e-02 #> SUDAN 3.5067e-04 8.0000e-03 4.0000e-03 #> EGYPT 3.1358e-04 1.6000e-02 8.0000e-03 #> Skewness Kurtosis #> THE GAMBIA -1.7643e+00 3.3422 #> MALI -8.2875e-01 0.8397 #> SENEGAL -7.1779e-01 0.3689 #> BENIN -8.5318e-01 0.5520 #> MAURITANIA -9.6301e-01 1.3949 #> NIGER -6.3767e-01 0.2577 #> IVORY COAST -8.3750e-01 0.6786 #> GUINEA -8.8298e-01 0.7691 #> BURKINA FASO -7.7665e-01 0.5911 #> LIBERIA -9.7191e-01 1.2327 #> SIERRA LEONE -1.0737e+00 0.6367 #> GHANA -9.6554e-01 0.8587 #> TOGO -1.0772e+00 1.2283 #> CAMEROON -8.1844e-01 1.1746 #> NIGERIA -6.3061e-01 0.1168 #> GABON -1.1947e+00 1.1977 #> CENTRAL AFRICAN REPUBLIC -6.7964e-01 -0.1428 #> CHAD -9.5123e-01 0.8025 #> CONGO -9.5359e-01 0.9288 #> ZAIRE 6.6929e-01 0.5829 #> ANGOLA 1.0230e+00 1.0841 #> UGANDA 9.6607e-01 1.3331 #> KENYA 8.5205e-01 0.5240 #> TANZANIA 8.5767e-01 1.2127 #> BURUNDI -1.0634e+00 0.9779 #> RWANDA -9.5905e-01 0.8365 #> SOMALIA 1.5185e+00 2.7876 #> ETHIOPIA 9.9587e-01 0.7374 #> ZAMBIA 4.9495e-01 0.1900 #> ZIMBABWE -8.0240e-01 0.4192 #> MALAWI -1.1246e+00 1.7228 #> MOZAMBIQUE -7.6989e-01 0.5793 #> SOUTH AFRICA 5.6394e-01 0.1988 #> LESOTHO -1.7905e+00 2.9865 #> BOTSWANA -9.4637e-01 0.5722 #> SWAZILAND -1.3081e+00 1.7612 #> MOROCCO 1.2705e+00 1.5574 #> ALGERIA 6.3958e-01 0.2677 #> TUNISIA 1.2498e+00 1.2249 #> LIBYA 7.3453e-01 0.5219 #> SUDAN 4.3993e-01 -0.1019 #> EGYPT 1.1875e+00 1.6480"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":null,"dir":"Reference","previous_headings":"","what":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"function implements Tiefelsdorf's application Saddlepoint approximation local Moran's Ii's reference distribution. model object class \"lm\", global independence assumed; class \"sarlm\", global dependence assumed represented spatial parameter model. Tests reported separately zone selected, may summarised using summary.localmoransad. Values local Moran's Ii agree localmoran(), function, standard deviate - Saddlepoint approximation - based randomisation assumption.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"","code":"localmoran.sad(model, select, nb, glist=NULL, style=\"W\", zero.policy=NULL, alternative=\"two.sided\", spChk=NULL, resfun=weighted.residuals, save.Vi=FALSE, tol = .Machine$double.eps^0.5, maxiter = 1000, tol.bounds=0.0001, save.M=FALSE, Omega = NULL) # S3 method for class 'localmoransad' print(x, ...) # S3 method for class 'localmoransad' summary(object, ...) # S3 method for class 'summary.localmoransad' print(x, ...) listw2star(listw, ireg, style, n, D, a, zero.policy=attr(listw, \"zero.policy\"))"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"model object class lm returned lm (assuming global spatial autocorrelation), object class sarlm returned spatial simultaneous autoregressive model fit (assuming global spatial autocorrelation represented model spatial coefficient); weights may specified lm fit, offsets used select integer vector id. numbers zones tested; missing, zones nb list neighbours class nb glist list general weights corresponding neighbours style can take values W, B, C, S zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one greater (default), less two.sided. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() resfun default: weighted.residuals; function used extract residuals lm object, may residuals, weighted.residuals, rstandard, rstudent save.Vi TRUE, return star-shaped weights lists zone tested tol desired accuracy (convergence tolerance) uniroot maxiter maximum number iterations uniroot tol.bounds offset bounds uniroot save.M TRUE, save list left right M products list conditional tests, list regression model matrix components Omega SAR process matrix may passed test alternative hypothesis, example Omega <- invIrW(listw, rho=0.1); Omega <- tcrossprod(Omega), chol() taken internally x object printed object object summarised ... arguments passed listw listw object created example nb2listw ireg zone number n internal value depending listw style D internal value depending listw style internal value depending listw style","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"function implements analytical eigenvalue calculation together trace shortcuts given suggested Tiefelsdorf (2002), partly following remarks J. Keith Ord, uses Saddlepoint analytical solution Tiefelsdorf's SPSS code. histogram probability values saddlepoint estimate assumption global independence approximately flat, assumption probably unjustified, re-estimation global dependence recommended. n n matrices needed point test assuming global dependence, star-shaped weights matrices handled listw lists. test made residuals spatial regression, taking global process account. n n matrices necessary, memory constraints may reached large lattices.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"list class localmoransad containing \"select\" lists, class moransad following components: statistic value saddlepoint approximation standard deviate local Moran's Ii. p.value p-value test. estimate value observed local Moran's Ii. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data. internal1 Saddlepoint omega, r u df degrees freedom tau maximum minimum analytical eigenvalues zone tested","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"Tiefelsdorf, M. 2002 Saddlepoint approximation Moran's local Moran's Ii reference distributions numerical evaluation. Geographical Analysis, 34, pp. 187–206.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"","code":"eire <- st_read(system.file(\"shapes/eire.gpkg\", package=\"spData\")[1]) #> Reading layer `eire' from data source #> `/home/rsb/lib/r_libs/spData/shapes/eire.gpkg' using driver `GPKG' #> Simple feature collection with 26 features and 10 fields #> Geometry type: MULTIPOLYGON #> Dimension: XY #> Bounding box: xmin: -4.12 ymin: 5768 xmax: 300.82 ymax: 6119.25 #> Projected CRS: Undefined Cartesian SRS with unknown unit row.names(eire) <- as.character(eire$names) eire.nb <- poly2nb(eire) lw <- nb2listw(eire.nb) e.lm <- lm(OWNCONS ~ ROADACC, data=eire) e.locmor <- summary(localmoran.sad(e.lm, nb=eire.nb)) e.locmor #> Local Morans I Stand. dev. (N) Pr. (N) Saddlepoint #> 1 Carlow 0.21699668 0.74177148 4.582258e-01 0.95074844 #> 2 Cavan -0.37257361 -0.81297374 1.583767e+00 -1.00603119 #> 3 Clare 0.23197510 0.49502499 6.205825e-01 0.67166518 #> 4 Cork 0.78193548 1.75999915 7.840795e-02 1.74761575 #> 5 Donegal -1.69064059 -1.98244914 1.952571e+00 -1.72031078 #> 6 Dublin -0.16069692 -0.15041940 1.119566e+00 -0.35212627 #> 7 Galway 1.31371473 3.34305297 8.286208e-04 2.66849536 #> 8 Kerry 0.36534866 0.58147812 5.609183e-01 0.78073279 #> 9 Kildare -0.02557544 0.15146558 8.796085e-01 0.04167665 #> 10 Kilkenny 0.57684331 1.62868431 1.033799e-01 1.70897697 #> 11 Laoghis -0.05951798 0.01724651 9.862400e-01 -0.12155465 #> 12 Leitrim 0.38484587 1.27548777 2.021367e-01 1.47227033 #> 13 Limerick 0.11817987 0.34038037 7.335701e-01 0.45727712 #> 14 Longford 1.41643200 3.10732224 1.887905e-03 2.51113769 #> 15 Louth 0.56242920 0.87665682 3.806731e-01 1.07441571 #> 16 Mayo 0.87572704 2.02375701 4.299516e-02 2.05251226 #> 17 Meath 0.00367856 0.16081712 8.722374e-01 0.12813539 #> 18 Monaghan 0.55098311 1.06684464 2.860420e-01 1.23999193 #> 19 Offaly 0.15155556 0.61933942 5.356928e-01 0.80786519 #> 20 Roscommon 2.04368839 6.66107106 2.718381e-11 4.53187292 #> 21 Sligo -0.47579871 -0.73430274 1.537236e+00 -0.94578114 #> 22 Tipperary -0.03454106 0.04843351 9.613708e-01 -0.06919691 #> 23 Waterford 0.85723423 1.98516133 4.712653e-02 1.91385108 #> 24 Westmeath 0.45138572 1.20305006 2.289569e-01 1.36017204 #> 25 Wexford 0.64371834 1.55468550 1.200210e-01 1.63188492 #> 26 Wicklow 0.02441950 0.21823347 8.272472e-01 0.21197000 #> Pr. (Sad) Expectation Variance Skewness Kurtosis Minimum #> 1 Carlow 3.417321e-01 -0.06471134 0.14423085 -0.7895263 7.059116 -5.461326 #> 2 Cavan 3.144006e-01 -0.04030838 0.16703857 -0.4622793 6.813004 -5.567356 #> 3 Clare 5.017969e-01 -0.04219377 0.30674823 -0.3579185 6.761932 -7.406885 #> 4 Cork 8.053059e-02 -0.04363826 0.22003250 -0.4363325 6.799081 -6.360927 #> 5 Donegal 8.537596e-02 -0.11935726 0.62821008 -0.7004303 6.979051 -11.236382 #> 6 Dublin 7.247436e-01 -0.08240217 0.27093033 -0.7352902 7.009201 -7.420687 #> 7 Galway 7.619183e-03 -0.04389010 0.16491503 -0.5059997 6.838308 -5.573707 #> 8 Kerry 4.349597e-01 -0.03212369 0.46724761 -0.2212594 6.714810 -8.915104 #> 9 Kildare 9.667565e-01 -0.07623733 0.11187546 -1.0416026 7.339962 -4.999621 #> 10 Kilkenny 8.745521e-02 -0.05911601 0.15247016 -0.7040737 6.982131 -5.538889 #> 11 Laoghis 9.032517e-01 -0.06620117 0.15016408 -0.7915137 7.061015 -5.574277 #> 12 Leitrim 1.409479e-01 -0.06828680 0.12621127 -0.8864130 7.157471 -5.186756 #> 13 Limerick 6.474719e-01 -0.04172917 0.22070746 -0.4167943 6.789132 -6.348870 #> 14 Longford 1.203427e-02 -0.04055162 0.21985521 -0.4059156 6.783792 -6.324457 #> 15 Louth 2.826364e-01 -0.04386717 0.47831137 -0.2983105 6.738631 -9.149779 #> 16 Mayo 4.011990e-02 -0.10340651 0.23408152 -0.9804377 7.264328 -7.165847 #> 17 Meath 8.980418e-01 -0.04799533 0.10324707 -0.6949022 6.974408 -4.551176 #> 18 Monaghan 2.149784e-01 -0.04136950 0.30828917 -0.3501006 6.758633 -7.415047 #> 19 Offaly 4.191682e-01 -0.04662212 0.10238870 -0.6782821 6.960676 -4.519986 #> 20 Roscommon 5.846302e-06 -0.04435301 0.09826301 -0.6591526 6.945294 -4.414164 #> 21 Sligo 3.442602e-01 -0.11041170 0.24760301 -1.0156782 7.307311 -7.409091 #> 22 Tipperary 9.448329e-01 -0.04872132 0.08571886 -0.7716947 7.042300 -4.198353 #> 23 Waterford 5.563919e-02 -0.05435079 0.21086415 -0.5533724 6.868342 -6.353514 #> 24 Westmeath 1.737755e-01 -0.04181671 0.16806722 -0.4779156 6.821788 -5.599610 #> 25 Wexford 1.027037e-01 -0.05432673 0.20159596 -0.5654870 6.876461 -6.225016 #> 26 Wicklow 8.321304e-01 -0.07022471 0.18808122 -0.7515626 7.023792 -6.198974 #> Maximum omega sad.r sad.u #> 1 Carlow 3.908254 0.071122863 0.71853146 0.84900467 #> 2 Cavan 4.599954 -0.051532330 -0.69003582 -0.85816092 #> 3 Clare 6.394234 0.031939551 0.46982957 0.51656357 #> 4 Cork 5.313609 0.083281515 1.43928884 2.24323856 #> 5 Donegal 8.371808 -0.039371561 -1.39288713 -2.19776923 #> 6 Dublin 5.443035 -0.010354512 -0.14127218 -0.14554367 #> 7 Galway 4.520344 0.134873939 2.39189491 4.63522665 #> 8 Kerry 8.144135 0.028431952 0.54051534 0.61545648 #> 9 Kildare 3.169925 0.018723213 0.14926096 0.14688325 #> 10 Kilkenny 4.120105 0.105365819 1.40668493 2.15214600 #> 11 Laoghis 3.985449 0.001724096 0.01660985 0.01657177 #> 12 Leitrim 3.547872 0.109608339 1.18229964 1.66578026 #> 13 Limerick 5.347370 0.027585567 0.32820959 0.34241163 #> 14 Longford 5.351218 0.108368224 2.22687206 4.19385821 #> 15 Louth 8.096967 0.037745731 0.78968254 0.98878788 #> 16 Mayo 4.684091 0.105317102 1.75922892 2.94711915 #> 17 Meath 3.399289 0.020074178 0.15693992 0.15623206 #> 18 Monaghan 6.422179 0.053418031 0.94193428 1.24723730 #> 19 Offaly 3.401055 0.071432961 0.59871278 0.67858124 #> 20 Roscommon 3.349691 0.357114199 4.33885200 10.02517077 #> 21 Sligo 4.759210 -0.036185300 -0.60775394 -0.74635955 #> 22 Tipperary 3.029041 0.006482570 0.04683010 0.04657633 #> 23 Waterford 5.049095 0.093409563 1.61022194 2.62552879 #> 24 Westmeath 4.596009 0.080097979 1.05978192 1.45704611 #> 25 Wexford 4.921174 0.085478829 1.32647942 1.98902088 #> 26 Wicklow 4.513581 0.020437514 0.21417067 0.21406975 mean(e.locmor[,1]) #> [1] 0.3366057 sum(e.locmor[,1])/Szero(lw) #> [1] 0.3366057 lm.morantest(e.lm, lw) #> #> \tGlobal Moran I for regression residuals #> #> data: #> model: lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: lw #> #> Moran I statistic standard deviate = 3.2575, p-value = 0.0005619 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I Expectation Variance #> 0.33660565 -0.05877741 0.01473183 #> # note equality for mean() only when the sum of weights equals # the number of observations (thanks to Juergen Symanzik) hist(e.locmor[,\"Pr. (Sad)\"]) e.wlm <- lm(OWNCONS ~ ROADACC, data=eire, weights=RETSALE) e.locmorw1 <- summary(localmoran.sad(e.wlm, nb=eire.nb, resfun=weighted.residuals)) e.locmorw1 #> Local Morans I Stand. dev. (N) Pr. (N) Saddlepoint #> 1 Carlow 0.160490657 0.41009538 6.817360e-01 0.57729730 #> 2 Cavan -0.144663771 -0.27825575 1.219184e+00 -0.45305168 #> 3 Clare 0.301676582 0.59021701 5.550452e-01 0.78987327 #> 4 Cork 1.520488153 3.49016956 4.827142e-04 2.83665634 #> 5 Donegal -0.435899664 -0.44665946 1.344879e+00 -0.67136090 #> 6 Dublin -0.340222996 -0.60886675 1.457387e+00 -0.85658016 #> 7 Galway 1.469009037 3.64546192 2.669119e-04 2.82274510 #> 8 Kerry 0.268957279 0.49517211 6.204786e-01 0.66861012 #> 9 Kildare 0.002996577 0.12659200 8.992633e-01 0.09978249 #> 10 Kilkenny 0.497968801 1.20610829 2.277757e-01 1.34091379 #> 11 Laoghis -0.026328708 -0.01713904 1.013674e+00 -0.06511750 #> 12 Leitrim 0.277306386 0.80644537 4.199861e-01 1.01176491 #> 13 Limerick 0.263122939 0.67591893 4.990921e-01 0.87759628 #> 14 Longford 0.605211711 1.23874274 2.154408e-01 1.35375850 #> 15 Louth 0.359469683 0.53572990 5.921452e-01 0.73280188 #> 16 Mayo 1.742480472 3.68118786 2.321499e-04 3.01500163 #> 17 Meath -0.112171618 -0.26680698 1.210382e+00 -0.45470531 #> 18 Monaghan 0.241044892 0.46013751 6.454175e-01 0.64094159 #> 19 Offaly 0.129191178 0.40988983 6.818868e-01 0.57205532 #> 20 Roscommon 1.469671750 4.39927211 1.086146e-05 3.13215267 #> 21 Sligo 0.095559559 0.31036587 7.562827e-01 0.38503064 #> 22 Tipperary 0.088352646 0.39958273 6.894639e-01 0.52592105 #> 23 Waterford 1.212658861 2.69846035 6.966104e-03 2.29292584 #> 24 Westmeath 0.256165310 0.61222265 5.403905e-01 0.81620859 #> 25 Wexford 0.619197906 1.31967483 1.869436e-01 1.42553832 #> 26 Wicklow 0.006531073 0.13142161 8.954418e-01 0.10986725 #> Pr. (Sad) Expectation Variance Skewness Kurtosis Minimum #> 1 Carlow 0.563738639 -0.01840558 0.19029731 -0.1986977 6.709176 -5.665283 #> 2 Cavan 0.650511526 -0.02184465 0.19482455 -0.2329761 6.717975 -5.769371 #> 3 Clare 0.429601786 -0.02782578 0.31166901 -0.2346279 6.718435 -7.299407 #> 4 Cork 0.004558865 -0.07147410 0.20805228 -0.7280203 7.002789 -6.495227 #> 5 Donegal 0.501990650 -0.07638800 0.64784767 -0.4450323 6.803659 -10.931345 #> 6 Dublin 0.391676955 -0.11187469 0.14065367 -1.3324828 7.767845 -5.846924 #> 7 Galway 0.004761441 -0.04407925 0.17227545 -0.4973247 6.833103 -5.688263 #> 8 Kerry 0.503744214 -0.05644300 0.43184063 -0.4031537 6.782459 -8.859407 #> 9 Kildare 0.920517009 -0.04145378 0.12329287 -0.5519841 6.867423 -4.857131 #> 10 Kilkenny 0.179948446 -0.02321457 0.18672759 -0.2528322 6.723714 -5.669156 #> 11 Laoghis 0.948080445 -0.01882531 0.19166504 -0.2024943 6.710081 -5.689691 #> 12 Leitrim 0.311650473 -0.03314655 0.14819776 -0.4041387 6.782933 -5.190860 #> 13 Limerick 0.380162847 -0.04800976 0.21188592 -0.4885390 6.827925 -6.298874 #> 14 Longford 0.175813436 -0.01321709 0.24923967 -0.1247567 6.694960 -6.392250 #> 15 Louth 0.463679274 -0.02272663 0.50895713 -0.1500895 6.699098 -9.179410 #> 16 Mayo 0.002569779 -0.09458039 0.24904116 -0.8745463 7.144787 -7.272523 #> 17 Meath 0.649321260 -0.02548973 0.10555100 -0.3685280 6.766525 -4.353122 #> 18 Monaghan 0.521560632 -0.02333303 0.33012248 -0.1912612 6.707452 -7.451275 #> 19 Offaly 0.567284497 -0.01927989 0.13120470 -0.2505068 6.723017 -4.750083 #> 20 Roscommon 0.001735296 -0.02385522 0.11525625 -0.3302939 6.750604 -4.517676 #> 21 Sligo 0.700214717 -0.06927688 0.28207107 -0.6087587 6.906925 -7.416881 #> 22 Tipperary 0.598943063 -0.03719246 0.09871568 -0.5534442 6.868390 -4.347214 #> 23 Waterford 0.021852275 -0.04027429 0.21558757 -0.4070996 6.784366 -6.264083 #> 24 Westmeath 0.414380842 -0.01522814 0.19650786 -0.1618342 6.701275 -5.716689 #> 25 Wexford 0.154001651 -0.02786850 0.24041626 -0.2674357 6.728234 -6.450174 #> 26 Wicklow 0.912514660 -0.04751424 0.16911517 -0.5404006 6.859847 -5.677417 #> Maximum omega sad.r sad.u #> 1 Carlow 5.223549 0.033637462 0.38794383 0.41751442 #> 2 Cavan 5.245099 -0.022294725 -0.26091513 -0.27432856 #> 3 Clare 6.631589 0.035302524 0.54866959 0.62630505 #> 4 Cork 4.779848 0.134384022 2.56890121 5.11058941 #> 5 Donegal 9.098033 -0.017507303 -0.40402088 -0.45010348 #> 6 Dublin 3.161931 -0.040828131 -0.50710580 -0.60543071 #> 7 Galway 4.630361 0.138454493 2.55314856 5.08170760 #> 8 Kerry 7.504775 0.027195108 0.47167584 0.51758880 #> 9 Kildare 3.862240 0.014230854 0.12280697 0.12246022 #> 10 Kilkenny 5.112007 0.071351828 1.03314661 1.41988761 #> 11 Laoghis 5.237883 -0.001502568 -0.01645549 -0.01646868 #> 12 Leitrim 4.395343 0.066207108 0.74158109 0.90609823 #> 13 Limerick 5.146640 0.050265468 0.63703133 0.74253221 #> 14 Longford 6.075040 0.060534639 1.04112815 1.44165700 #> 15 Louth 8.633971 0.025231866 0.49793592 0.55971045 #> 16 Mayo 5.002594 0.135902733 2.75603129 5.62669411 #> 17 Meath 3.741368 -0.028724497 -0.24912602 -0.26221742 #> 18 Monaghan 6.891283 0.028042744 0.43280552 0.47360371 #> 19 Offaly 4.287365 0.040883462 0.38909358 0.41780262 #> 20 Roscommon 3.945151 0.180270100 2.87643937 6.00202551 #> 21 Sligo 5.754236 0.023145822 0.30299868 0.31062426 #> 22 Tipperary 3.454595 0.048932861 0.38768333 0.40902706 #> 23 Waterford 5.297500 0.101874758 1.99944904 3.59542986 #> 24 Westmeath 5.351214 0.044919886 0.56403221 0.65024353 #> 25 Wexford 5.781330 0.066083430 1.11524637 1.57637406 #> 26 Wicklow 4.537075 0.012609906 0.12748740 0.12720134 e.locmorw2 <- summary(localmoran.sad(e.wlm, nb=eire.nb, resfun=rstudent)) e.locmorw2 #> Local Morans I Stand. dev. (N) Pr. (N) Saddlepoint #> 1 Carlow 0.121997164 0.32185426 0.7475631028 0.45871930 #> 2 Cavan -0.110588620 -0.20105599 1.1593452023 -0.34808741 #> 3 Clare 0.308759283 0.60290381 0.5465726820 0.80379674 #> 4 Cork 1.404203115 3.23522979 0.0012154487 2.69598105 #> 5 Donegal -0.421182109 -0.42837428 1.3316213558 -0.65187732 #> 6 Dublin -0.443534307 -0.88433550 1.6234848706 -1.05167518 #> 7 Galway 1.376190254 3.42183495 0.0006220006 2.70663064 #> 8 Kerry 0.241623387 0.45357724 0.6501331373 0.61515126 #> 9 Kildare 0.008842913 0.14324202 0.8860990418 0.12690939 #> 10 Kilkenny 0.382893124 0.93980330 0.3473184643 1.12810394 #> 11 Laoghis -0.019904450 -0.00246494 1.0019667357 -0.04176107 #> 12 Leitrim 0.200483743 0.60688769 0.5439254449 0.80241456 #> 13 Limerick 0.238810092 0.62310059 0.5332184222 0.81824678 #> 14 Longford 0.466942853 0.96178354 0.3361583457 1.14088225 #> 15 Louth 0.271710988 0.41271732 0.6798137369 0.58520655 #> 16 Mayo 1.705850161 3.60778634 0.0003088206 2.97346461 #> 17 Meath -0.160603054 -0.41587901 1.3225014587 -0.63254531 #> 18 Monaghan 0.181378604 0.35629110 0.7216225742 0.50697175 #> 19 Offaly 0.107919508 0.35116431 0.7254650854 0.49312417 #> 20 Roscommon 1.249826037 3.75170355 0.0001756371 2.81402777 #> 21 Sligo 0.079431883 0.27999953 0.7794778655 0.33741411 #> 22 Tipperary 0.085153638 0.38940098 0.6969795442 0.51126046 #> 23 Waterford 1.022922345 2.28982205 0.0220316342 2.06385578 #> 24 Westmeath 0.201539331 0.48899468 0.6248454598 0.67791734 #> 25 Wexford 0.481114325 1.03805702 0.2992435100 1.21094348 #> 26 Wicklow -0.011694661 0.08710223 0.9305902563 0.03786608 #> Pr. (Sad) Expectation Variance Skewness Kurtosis Minimum #> 1 Carlow 0.646435751 -0.01840558 0.19029731 -0.1986977 6.709176 -5.665283 #> 2 Cavan 0.727774542 -0.02184465 0.19482455 -0.2329761 6.717975 -5.769371 #> 3 Clare 0.421514374 -0.02782578 0.31166901 -0.2346279 6.718435 -7.299407 #> 4 Cork 0.007018166 -0.07147410 0.20805228 -0.7280203 7.002789 -6.495227 #> 5 Donegal 0.514480318 -0.07638800 0.64784767 -0.4450323 6.803659 -10.931345 #> 6 Dublin 0.292948602 -0.11187469 0.14065367 -1.3324828 7.767845 -5.846924 #> 7 Galway 0.006796983 -0.04407925 0.17227545 -0.4973247 6.833103 -5.688263 #> 8 Kerry 0.538454834 -0.05644300 0.43184063 -0.4031537 6.782459 -8.859407 #> 9 Kildare 0.899012117 -0.04145378 0.12329287 -0.5519841 6.867423 -4.857131 #> 10 Kilkenny 0.259276027 -0.02321457 0.18672759 -0.2528322 6.723714 -5.669156 #> 11 Laoghis 0.966689170 -0.01882531 0.19166504 -0.2024943 6.710081 -5.689691 #> 12 Leitrim 0.422313193 -0.03314655 0.14819776 -0.4041387 6.782933 -5.190860 #> 13 Limerick 0.413216288 -0.04800976 0.21188592 -0.4885390 6.827925 -6.298874 #> 14 Longford 0.253918927 -0.01321709 0.24923967 -0.1247567 6.694960 -6.392250 #> 15 Louth 0.558408841 -0.02272663 0.50895713 -0.1500895 6.699098 -9.179410 #> 16 Mayo 0.002944584 -0.09458039 0.24904116 -0.8745463 7.144787 -7.272523 #> 17 Meath 0.527030613 -0.02548973 0.10555100 -0.3685280 6.766525 -4.353122 #> 18 Monaghan 0.612174643 -0.02333303 0.33012248 -0.1912612 6.707452 -7.451275 #> 19 Offaly 0.621924855 -0.01927989 0.13120470 -0.2505068 6.723017 -4.750083 #> 20 Roscommon 0.004892500 -0.02385522 0.11525625 -0.3302939 6.750604 -4.517676 #> 21 Sligo 0.735804747 -0.06927688 0.28207107 -0.6087587 6.906925 -7.416881 #> 22 Tipperary 0.609168686 -0.03719246 0.09871568 -0.5534442 6.868390 -4.347214 #> 23 Waterford 0.039031392 -0.04027429 0.21558757 -0.4070996 6.784366 -6.264083 #> 24 Westmeath 0.497824103 -0.01522814 0.19650786 -0.1618342 6.701275 -5.716689 #> 25 Wexford 0.225917068 -0.02786850 0.24041626 -0.2674357 6.728234 -6.450174 #> 26 Wicklow 0.969794461 -0.04751424 0.16911517 -0.5404006 6.859847 -5.677417 #> Maximum omega sad.r sad.u #> 1 Carlow 5.223549 0.0272472954 0.306852385 0.321490350 #> 2 Cavan 5.245099 -0.0166242430 -0.190223798 -0.196022741 #> 3 Clare 6.631589 0.0358559846 0.559584155 0.641527095 #> 4 Cork 4.779848 0.1283688794 2.421993662 4.702934834 #> 5 Donegal 9.098033 -0.0169574018 -0.388662370 -0.430528174 #> 6 Dublin 3.161931 -0.0507848831 -0.696824139 -0.892299501 #> 7 Galway 4.630361 0.1333224875 2.431707338 4.745166958 #> 8 Kerry 7.504775 0.0252982005 0.433626352 0.469138111 #> 9 Kildare 3.862240 0.0161278548 0.139072871 0.138837812 #> 10 Kilkenny 5.112007 0.0622219791 0.835166590 1.066654825 #> 11 Laoghis 5.237883 -0.0002164925 -0.002368023 -0.002368244 #> 12 Leitrim 4.395343 0.0543844388 0.571625643 0.652237768 #> 13 Limerick 5.146640 0.0473787285 0.590605630 0.675595582 #> 14 Longford 6.075040 0.0528365356 0.840671447 1.082014178 #> 15 Louth 8.633971 0.0204960239 0.389078238 0.419930705 #> 16 Mayo 5.002594 0.1340509166 2.712635049 5.503894365 #> 17 Meath 3.741368 -0.0415411327 -0.379736494 -0.417998694 #> 18 Monaghan 6.891283 0.0226076552 0.338579266 0.358443998 #> 19 Offaly 4.287365 0.0357600182 0.335019324 0.353243066 #> 20 Roscommon 3.945151 0.1623235556 2.543240406 5.063795948 #> 21 Sligo 5.754236 0.0209568244 0.273376649 0.278204612 #> 22 Tipperary 3.454595 0.0478130890 0.377982061 0.397511387 #> 23 Waterford 5.297500 0.0941811771 1.762051071 2.998984773 #> 24 Westmeath 5.351214 0.0379323563 0.457473561 0.506014991 #> 25 Wexford 5.781330 0.0582538352 0.911459483 1.197527949 #> 26 Wicklow 4.537075 0.0083101099 0.084281843 0.083952776 run <- FALSE if (requireNamespace(\"spatialreg\", quietly=TRUE)) run <- TRUE if (run) { e.errorsar <- spatialreg::errorsarlm(OWNCONS ~ ROADACC, data=eire, listw=lw) if (packageVersion(\"spatialreg\") < \"1.1.7\") spatialreg::print.sarlm(e.errorsar) else print(e.errorsar) } #> #> Call: #> spatialreg::errorsarlm(formula = OWNCONS ~ ROADACC, data = eire, #> listw = lw) #> Type: error #> #> Coefficients: #> lambda (Intercept) ROADACC #> 0.783970988 2.892719568 0.002800913 #> #> Log likelihood: -64.12465 if (run) { lm.target <- lm(e.errorsar$tary ~ e.errorsar$tarX - 1) Omega <- tcrossprod(spatialreg::invIrW(lw, rho=e.errorsar$lambda)) e.clocmor <- summary(localmoran.sad(lm.target, nb=eire.nb, Omega=Omega)) e.clocmor } #> Local Morans I Stand. dev. (N) Pr. (N) Saddlepoint Pr. (Sad) #> 1 Carlow 0.17958462 -0.5947094 1.4479623 -0.01890335 0.9849182099 #> 2 Cavan -0.24752628 -0.9775195 1.6716880 -1.30903979 0.1905208729 #> 3 Clare -0.27901334 -0.9987481 1.6820833 -1.41535136 0.1569655036 #> 4 Cork 0.37808655 -0.5304596 1.4042067 0.06399747 0.9489722429 #> 5 Donegal -1.01894688 -1.4634181 1.8566470 -1.88871177 0.0589304608 #> 6 Dublin -0.18171297 -0.9790853 1.6724621 -1.11436912 0.2651208632 #> 7 Galway 1.02193390 0.9527103 0.3407369 1.44844014 0.1474939944 #> 8 Kerry -0.94967914 -1.1410950 1.7461696 -2.37909992 0.0173549707 #> 9 Kildare 0.07005053 -0.6531380 1.4863327 -0.10338270 0.9176592422 #> 10 Kilkenny 0.43022231 -0.3097714 1.2432652 0.46873471 0.6392592764 #> 11 Laoghis -0.12239133 -0.9818401 1.6738214 -0.97718184 0.3284791347 #> 12 Leitrim -0.24203970 -0.9591963 1.6625401 -1.53246533 0.1254076471 #> 13 Limerick -0.03214546 -0.7729433 1.5604441 -0.80301568 0.4219656706 #> 14 Longford 0.38307454 -0.4899146 1.3758057 0.16621954 0.8679841830 #> 15 Louth 0.21301552 -0.6509309 1.4849089 -0.21224290 0.8319175423 #> 16 Mayo 0.93971200 0.3895188 0.6968924 1.15011408 0.2500968881 #> 17 Meath 0.12484415 -0.6182203 1.4635699 -0.09720926 0.9225602153 #> 18 Monaghan -0.16109919 -0.8608004 1.6106520 -1.20575831 0.2279106935 #> 19 Offaly -0.00632492 -0.7740865 1.5611204 -0.33915072 0.7344961920 #> 20 Roscommon 1.02089429 0.6454801 0.5186161 1.21215474 0.2254531514 #> 21 Sligo -2.01629233 -1.8957526 1.9420072 -3.59571732 0.0003234989 #> 22 Tipperary -0.10810709 -0.9082666 1.6362626 -1.09721448 0.2725476428 #> 23 Waterford 0.44099279 -0.3488980 1.2728341 0.41219202 0.6801986840 #> 24 Westmeath -0.06329661 -0.8267635 1.5916289 -0.81444158 0.4153920275 #> 25 Wexford 0.30764883 -0.5219835 1.3983182 0.12395154 0.9013536459 #> 26 Wicklow -0.01696406 -0.7708237 1.5591886 -0.68244661 0.4949565909 #> Expectation Variance Skewness Kurtosis Minimum Maximum #> 1 Carlow 0.8594106 1.3067303 2.362830 10.416149 8.621901e-17 20.625856 #> 2 Cavan 1.1247112 1.9706416 2.347202 10.347468 1.645654e+00 25.347414 #> 3 Clare 1.2679076 2.3989670 2.334022 10.287656 2.485514e+00 27.944268 #> 4 Cork 1.2841620 2.9175890 2.362830 10.416149 -1.812003e-16 30.819888 #> 5 Donegal 1.7253177 3.5165365 2.172101 9.492322 8.227735e+00 33.179890 #> 6 Dublin 0.9462667 1.3272768 2.331563 10.276363 1.928660e+00 20.781740 #> 7 Galway 0.4507425 0.3594525 2.362830 10.416149 5.907989e-16 10.817821 #> 8 Kerry 2.6933183 10.1923447 2.307813 10.165571 7.170614e+00 57.469026 #> 9 Kildare 0.5337376 0.5040110 2.362830 10.416149 -1.337526e-16 12.809701 #> 10 Kilkenny 0.7317135 0.9472545 2.362830 10.416149 1.706968e-15 17.561125 #> 11 Laoghis 0.6035313 0.5466372 2.336004 10.296727 1.143655e+00 13.341096 #> 12 Leitrim 1.2258674 2.3419747 2.347302 10.347916 1.788145e+00 27.632674 #> 13 Limerick 1.5147254 4.0050955 2.362668 10.415466 2.341575e-01 36.119253 #> 14 Longford 1.0996747 2.1395031 2.362830 10.416149 1.538224e-16 26.392192 #> 15 Louth 1.5875248 4.4588771 2.362830 10.416149 -9.743415e-17 38.100594 #> 16 Mayo 0.6190019 0.6779043 2.362830 10.416149 -8.612978e-16 14.856045 #> 17 Meath 0.7025948 0.8733620 2.362830 10.416149 1.089845e-16 16.862274 #> 18 Monaghan 1.5519577 3.9603958 2.357838 10.394611 1.306155e+00 35.940829 #> 19 Offaly 0.3048481 0.1615939 2.362560 10.415009 6.073803e-02 7.255616 #> 20 Roscommon 0.5492905 0.5338125 2.362830 10.416149 7.680029e-16 13.182973 #> 21 Sligo 2.3130311 5.2152695 1.886102 7.938452 1.739456e+01 38.118185 #> 22 Tipperary 0.7147979 0.8208668 2.354040 10.377921 7.922254e-01 16.362924 #> 23 Waterford 0.8228671 1.1979644 2.362830 10.416149 1.480772e-16 19.748811 #> 24 Westmeath 0.8426747 1.2007879 2.360962 10.408167 4.379239e-01 19.786270 #> 25 Wexford 1.0063848 1.7918953 2.362830 10.416149 6.041304e-16 24.153236 #> 26 Wicklow 0.9927147 1.7157589 2.362598 10.415171 1.833509e-01 23.641801 #> omega sad.r sad.u #> 1 Carlow -0.017838447 -0.38297869 -0.33313448 #> 2 Cavan -0.066132684 -1.21593175 -1.36168605 #> 3 Clare -0.066612498 -1.30513958 -1.50704646 #> 4 Cork -0.010368850 -0.33915229 -0.29581081 #> 5 Donegal -0.045800559 -1.66568212 -2.41507712 #> 6 Dublin -0.056683668 -1.03296356 -1.12358099 #> 7 Galway 0.031762997 1.14153962 1.62047125 #> 8 Kerry -0.079689480 -2.19374456 -3.29442701 #> 9 Kildare -0.025051491 -0.36678693 -0.33300845 #> 10 Kilkenny 0.003214928 0.09217308 0.09542846 #> 11 Laoghis -0.065438986 -0.89335507 -0.96282454 #> 12 Leitrim -0.092395573 -1.43474097 -1.65069014 #> 13 Limerick -0.047140362 -0.97737323 -0.82423542 #> 14 Longford -0.007176482 -0.22762630 -0.20810767 #> 15 Louth -0.018552546 -0.58005974 -0.46861210 #> 16 Mayo 0.019992304 0.84088281 1.09059594 #> 17 Meath -0.026958325 -0.44558661 -0.38151850 #> 18 Monaghan -0.062388996 -1.21509194 -1.20138917 #> 19 Offaly -0.044380046 -0.41568118 -0.40266554 #> 20 Roscommon 0.023338184 0.88169755 1.17993235 #> 21 Sligo -0.131646728 -3.40243100 -6.56750200 #> 22 Tipperary -0.089378129 -1.06748205 -1.10190609 #> 23 Waterford 0.001151041 0.03534520 0.03581914 #> 24 Westmeath -0.058470593 -0.88397327 -0.83127666 #> 25 Wexford -0.009550496 -0.26689929 -0.24045996 #> 26 Wicklow -0.050401553 -0.84395069 -0.73641410 if (run) { hist(e.clocmor[,\"Pr. (Sad)\"]) }"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"Given two continuous numeric variables, calculate bivariate Local Moran's .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"","code":"localmoran_bv(x, y, listw, nsim = 199, scale = TRUE, alternative=\"two.sided\", iseed=1L, no_repeat_in_row=FALSE, zero.policy=attr(listw, \"zero.policy\"))"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"x numeric vector length y. y numeric vector length x. listw listw object example created nb2listw(). nsim number simulations run. scale default TRUE. alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"two.sided\", \"less\". iseed default NULL, used set seed; output reproducible count CPU cores across computation distributed . no_repeat_in_row default FALSE, TRUE, sample conditionally row without replacements avoid duplicate values, https://github.com/r-spatial/spdep/issues/124 zero.policy default default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"data.frame containing two columns Ib p_sim containing local bivariate Moran's simulated p-values respectively.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"Bivariate Local Moran, like global counterpart, evaluates value x observation spatial neighbors' value y. value \\(I_i^B\\) xi * Wyi. , simpler words, local bivariate Moran result multiplying x spatial lag y. Formally defined \\( I_i^B= cx_i\\Sigma_j{w_{ij}y_j} \\)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"Anselin, Luc, Ibnu Syabri, Oleg Smirnov. 2002. “Visualizing Multivariate Spatial Correlation Dynamically Linked Windows.” New Tools Spatial Data Analysis: Proceedings Specialist Meeting, edited Luc Anselin Sergio Rey. University California, Santa Barbara: Center Spatially Integrated Social Science (CSISS).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"Josiah Parry josiah.parry@gmail.com","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"","code":"# load columbus datay columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")) #> Reading layer `columbus' from data source #> `/home/rsb/lib/r_libs/spData/shapes/columbus.gpkg' using driver `GPKG' #> Simple feature collection with 49 features and 20 fields #> Geometry type: POLYGON #> Dimension: XY #> Bounding box: xmin: 5.874907 ymin: 10.78863 xmax: 11.28742 ymax: 14.74245 #> Projected CRS: Undefined Cartesian SRS with unknown unit nb <- poly2nb(columbus) listw <- nb2listw(nb) set.seed(1) (res <- localmoran_bv(columbus$CRIME, columbus$INC, listw, nsim = 499)) #> Ibvi E.Ibvi Var.Ibvi Z.Ibvi Pr(z != E(Ibvi)) #> [1,] -0.8578252210 -1.826370e-02 0.731541578 -0.98159654 3.262987e-01 #> [2,] 0.1802618568 2.554658e-02 0.334247968 0.26760782 7.890012e-01 #> [3,] 0.0118856298 7.791116e-03 0.017162929 0.03125407 9.750669e-01 #> [4,] -0.0163525887 -3.452848e-03 0.005852145 -0.16862558 8.660912e-01 #> [5,] -0.5037734606 1.811633e-02 0.101966376 -1.63436973 1.021812e-01 #> [6,] -0.0041841415 1.293651e-02 0.139142736 -0.04589760 9.633919e-01 #> [7,] 1.5201688711 -1.466392e-04 1.099034279 1.45020069 1.470026e-01 #> [8,] -0.2016456990 7.471406e-03 0.007231278 -2.45913301 1.392730e-02 #> [9,] 0.0297432891 1.600490e-03 0.009219518 0.29309821 7.694471e-01 #> [10,] -0.0374203146 1.218906e-03 0.001100110 -1.16495823 2.440359e-01 #> [11,] -1.2368494456 7.720869e-02 0.498286158 -1.86155199 6.266627e-02 #> [12,] -1.2010054212 4.055009e-02 0.266658169 -2.40430022 1.620346e-02 #> [13,] -0.5377131737 1.218864e-02 0.122363375 -1.57202494 1.159448e-01 #> [14,] -0.9879712511 3.048475e-02 0.320475271 -1.79905736 7.200961e-02 #> [15,] -0.6057303757 2.137030e-02 0.102916086 -1.95476986 5.061024e-02 #> [16,] -0.7878039284 1.378587e-02 0.161039891 -1.99749384 4.577156e-02 #> [17,] 0.1379508106 9.352179e-04 0.003351141 2.36686570 1.793944e-02 #> [18,] -0.3253226893 1.066349e-02 0.078469609 -1.19941831 2.303653e-01 #> [19,] -0.3888822685 -7.104732e-06 0.432305953 -0.59144532 5.542221e-01 #> [20,] -0.4544889957 1.367811e-01 0.355060554 -0.99228105 3.210604e-01 #> [21,] -0.0006014046 3.919068e-03 0.031597455 -0.02543067 9.797114e-01 #> [22,] -0.0068813684 -3.664201e-03 0.001242910 -0.09125440 9.272904e-01 #> [23,] -0.8788967496 1.189579e-02 0.289002627 -1.65701209 9.751703e-02 #> [24,] -0.1256865340 -3.048451e-03 0.004692164 -1.79035349 7.339710e-02 #> [25,] -0.9307459211 4.509269e-02 0.303474056 -1.77140234 7.649382e-02 #> [26,] -0.2252775788 1.039843e-02 0.019527743 -1.68651169 9.169728e-02 #> [27,] 0.1413018326 -1.409345e-02 0.236810168 0.31932848 7.494774e-01 #> [28,] -0.7804482928 3.200178e-02 0.184987862 -1.88897002 5.889585e-02 #> [29,] -0.7654416689 5.928648e-02 0.364667175 -1.36572255 1.720261e-01 #> [30,] -0.9074829015 7.597435e-03 0.737090639 -1.06585659 2.864885e-01 #> [31,] -0.5510119267 -1.377557e-03 0.388899970 -0.88136323 3.781213e-01 #> [32,] -1.9581476375 2.561515e-02 0.239115219 -4.05682367 4.974461e-05 #> [33,] 0.0907015890 3.048227e-02 0.043681309 0.28812970 7.732475e-01 #> [34,] -0.4297843082 2.130996e-02 0.104683121 -1.39421250 1.632534e-01 #> [35,] 0.1181174820 6.746380e-04 0.008393054 1.28193663 1.998649e-01 #> [36,] -0.9901007017 2.760845e-02 0.278368628 -1.92891697 5.374117e-02 #> [37,] -0.2195812498 -7.723065e-03 0.032151838 -1.18152344 2.373948e-01 #> [38,] -0.3096268627 3.401135e-02 0.205499338 -0.75804717 4.484227e-01 #> [39,] -0.6090192229 1.689079e-02 0.308320019 -1.12722610 2.596469e-01 #> [40,] -1.2709838927 6.528265e-02 0.216905961 -2.86917707 4.115413e-03 #> [41,] -1.3940681427 9.430182e-02 0.304439982 -2.69749131 6.986411e-03 #> [42,] -0.4820987026 3.961324e-02 0.632999863 -0.65573592 5.119941e-01 #> [43,] -0.0064402410 2.939096e-03 0.001385154 -0.25201308 8.010310e-01 #> [44,] 0.0761664412 2.162964e-02 0.054095662 0.23448142 8.146113e-01 #> [45,] -0.0560342555 7.788766e-03 0.029796273 -0.36973996 7.115763e-01 #> [46,] -0.8249832451 -2.301643e-02 0.673531467 -0.97718648 3.284768e-01 #> [47,] -0.8915318222 2.294960e-02 0.095247718 -2.96310881 3.045489e-03 #> [48,] -0.1282863305 -9.674295e-03 0.061579149 -0.47798241 6.326627e-01 #> [49,] 0.0094888641 -4.828535e-03 0.222107368 0.03037964 9.757643e-01 #> Pr(z != E(Ibvi)) Sim Pr(folded) Sim #> [1,] 0.324 0.162 #> [2,] 0.880 0.440 #> [3,] 0.976 0.488 #> [4,] 0.800 0.400 #> [5,] 0.112 0.056 #> [6,] 0.864 0.430 #> [7,] 0.096 0.048 #> [8,] 0.004 0.002 #> [9,] 0.852 0.426 #> [10,] 0.260 0.130 #> [11,] 0.056 0.028 #> [12,] 0.008 0.004 #> [13,] 0.084 0.042 #> [14,] 0.064 0.032 #> [15,] 0.052 0.026 #> [16,] 0.028 0.014 #> [17,] 0.028 0.014 #> [18,] 0.192 0.096 #> [19,] 0.608 0.304 #> [20,] 0.368 0.184 #> [21,] 0.936 0.468 #> [22,] 0.928 0.464 #> [23,] 0.120 0.060 #> [24,] 0.040 0.020 #> [25,] 0.044 0.022 #> [26,] 0.076 0.038 #> [27,] 0.736 0.368 #> [28,] 0.032 0.016 #> [29,] 0.140 0.070 #> [30,] 0.284 0.142 #> [31,] 0.408 0.204 #> [32,] 0.004 0.002 #> [33,] 0.724 0.362 #> [34,] 0.188 0.094 #> [35,] 0.216 0.108 #> [36,] 0.084 0.042 #> [37,] 0.232 0.116 #> [38,] 0.464 0.232 #> [39,] 0.268 0.134 #> [40,] 0.004 0.002 #> [41,] 0.020 0.010 #> [42,] 0.468 0.234 #> [43,] 0.884 0.442 #> [44,] 0.904 0.452 #> [45,] 0.672 0.336 #> [46,] 0.344 0.172 #> [47,] 0.012 0.006 #> [48,] 0.544 0.272 #> [49,] 0.896 0.448 #> attr(,\"quadr\") #> mean median pysal #> 1 Low-High Low-High Low-High #> 2 Low-Low Low-Low Low-Low #> 3 Low-Low Low-Low Low-Low #> 4 Low-High Low-High Low-High #> 5 High-Low High-Low High-Low #> 6 Low-Low Low-High Low-High #> 7 Low-Low Low-Low Low-Low #> 8 High-Low High-Low High-Low #> 9 Low-Low Low-Low Low-Low #> 10 Low-High Low-High Low-High #> 11 High-Low High-Low High-Low #> 12 High-Low High-Low High-Low #> 13 High-Low High-Low High-Low #> 14 High-Low High-Low High-Low #> 15 High-Low High-Low High-Low #> 16 High-Low High-Low High-Low #> 17 High-High High-High High-High #> 18 High-Low High-Low High-Low #> 19 High-Low High-Low High-Low #> 20 Low-High Low-High Low-High #> 21 High-Low High-High High-Low #> 22 Low-High Low-High Low-High #> 23 Low-High Low-High Low-High #> 24 High-Low High-Low High-Low #> 25 High-Low High-Low High-Low #> 26 High-Low High-Low High-Low #> 27 High-High High-High High-High #> 28 High-Low High-Low High-Low #> 29 High-Low High-Low High-Low #> 30 High-Low High-Low High-Low #> 31 Low-High Low-High Low-High #> 32 Low-High Low-High Low-High #> 33 High-High High-High High-High #> 34 Low-High Low-High Low-High #> 35 High-High High-High High-High #> 36 Low-High Low-High Low-High #> 37 High-Low High-Low High-Low #> 38 High-Low High-Low High-Low #> 39 Low-High Low-High Low-High #> 40 Low-High Low-High Low-High #> 41 Low-High Low-High Low-High #> 42 Low-High Low-High Low-High #> 43 High-Low High-Low High-Low #> 44 Low-Low Low-Low Low-Low #> 45 Low-High Low-High Low-High #> 46 Low-High Low-High Low-High #> 47 Low-High Low-High Low-High #> 48 Low-High Low-High Low-High #> 49 Low-Low Low-Low Low-Low #> attr(,\"class\") #> [1] \"localmoran\" \"matrix\" \"array\" #> attr(,\"ncpus\") #> [1] 1 columbus$hs <- hotspot(res, Prname=\"Pr(folded) Sim\", cutoff=0.05, quadrant.type=\"pysal\", p.adjust=\"none\") # \\donttest{ if (require(\"tmap\", quietly=TRUE)) { tmap4 <- packageVersion(\"tmap\") >= \"3.99\" if (tmap4) { tm_shape(columbus) + tm_polygons(fill=\"hs\", fill.scale=tm_scale(values=\"brewer.set3\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"top\"), frame=FALSE, item.r=0), lwd=0.01) } else { tm_shape(columbus) + tm_fill(\"hs\") } } # } moran.plot(x=columbus$CRIME, y=columbus$INC, listw=listw)"},{"path":"https://r-spatial.github.io/spdep/reference/mat2listw.html","id":null,"dir":"Reference","previous_headings":"","what":"Convert a square spatial weights matrix to a weights list object — mat2listw","title":"Convert a square spatial weights matrix to a weights list object — mat2listw","text":"function converts square spatial weights matrix, optionally sparse matrix weights list object, optionally adding region IDs row names matrix, sequence numbers 1:nrow(x), given argument. style can imposed rebuilting weights list object internally.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mat2listw.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Convert a square spatial weights matrix to a weights list object — mat2listw","text":"","code":"mat2listw(x, row.names = NULL, style=NULL, zero.policy = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/mat2listw.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Convert a square spatial weights matrix to a weights list object — mat2listw","text":"x square non-negative matrix NAs representing spatial weights; may matrix class “sparseMatrix” row.names row names use region IDs style default NULL, missing, set \"M\" warning given; \"M\", passed nb2listw re-build object zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mat2listw.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Convert a square spatial weights matrix to a weights list object — mat2listw","text":"listw object following members: style \"M\", meaning matrix style, underlying style unknown, assigned style argument rebuilt object neighbours derived neighbours list weights weights neighbours derived matrix","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mat2listw.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Convert a square spatial weights matrix to a weights list object — mat2listw","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/mat2listw.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Convert a square spatial weights matrix to a weights list object — mat2listw","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col005 <- dnearneigh(st_coordinates(st_centroid(st_geometry(columbus), of_largest_polygon=TRUE)), 0, 0.5, as.character(columbus$NEIGNO)) #> Warning: neighbour object has 8 sub-graphs summary(col005) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 170 #> Percentage nonzero weights: 7.080383 #> Average number of links: 3.469388 #> 4 regions with no links: #> 1005, 1006, 1008, 1043 #> 8 disjoint connected subgraphs #> Link number distribution: #> #> 0 1 2 3 4 5 6 7 8 9 #> 4 11 5 8 3 9 2 2 3 2 #> 11 least connected regions: #> 1001 1007 1018 1010 1045 1044 1046 1047 1049 1048 1015 with 1 link #> 2 most connected regions: #> 1038 1036 with 9 links col005.w.mat <- nb2mat(col005, style=\"W\", zero.policy=TRUE) try(col005.w.b <- mat2listw(col005.w.mat, style=\"W\")) #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> Warning: neighbour object has 8 sub-graphs #> Error in nb2listw(res$neighbours, glist = res$weights, style = style, : #> Empty neighbour sets found (zero.policy: FALSE) col005.w.b <- mat2listw(col005.w.mat, style=\"W\", zero.policy=TRUE) #> Warning: neighbour object has 8 sub-graphs summary(col005.w.b$neighbours) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 170 #> Percentage nonzero weights: 7.080383 #> Average number of links: 3.469388 #> 4 regions with no links: #> 1005, 1006, 1008, 1043 #> 8 disjoint connected subgraphs #> Link number distribution: #> #> 0 1 2 3 4 5 6 7 8 9 #> 4 11 5 8 3 9 2 2 3 2 #> 11 least connected regions: #> 1001 1007 1018 1010 1045 1044 1046 1047 1049 1048 1015 with 1 link #> 2 most connected regions: #> 1038 1036 with 9 links diffnb(col005, col005.w.b$neighbours) #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 0 #> Percentage nonzero weights: 0 #> Average number of links: 0 #> 49 regions with no links: #> 1005, 1001, 1006, 1002, 1007, 1008, 1004, 1003, 1018, 1010, 1038, 1037, #> 1039, 1040, 1009, 1036, 1011, 1042, 1041, 1017, 1043, 1019, 1012, 1035, #> 1032, 1020, 1021, 1031, 1033, 1034, 1045, 1013, 1022, 1044, 1023, 1046, #> 1030, 1024, 1047, 1016, 1014, 1049, 1029, 1025, 1028, 1048, 1015, 1027, #> 1026 #> 49 disjoint connected subgraphs col005.w.mat.3T <- kronecker(diag(3), col005.w.mat) col005.w.b.3T <- mat2listw(col005.w.mat.3T, style=\"W\", zero.policy=TRUE) #> Warning: neighbour object has 24 sub-graphs summary(col005.w.b.3T$neighbours) #> Neighbour list object: #> Number of regions: 147 #> Number of nonzero links: 510 #> Percentage nonzero weights: 2.360128 #> Average number of links: 3.469388 #> 12 regions with no links: #> 1, 3, 6, 21, 50, 52, 55, 70, 99, 101, 104, 119 #> 24 disjoint connected subgraphs #> Link number distribution: #> #> 0 1 2 3 4 5 6 7 8 9 #> 12 33 15 24 9 27 6 6 9 6 #> 33 least connected regions: #> 2 5 9 10 31 34 36 39 42 46 47 51 54 58 59 80 83 85 88 91 95 96 100 103 107 108 129 132 134 137 140 144 145 with 1 link #> 6 most connected regions: #> 11 16 60 65 109 114 with 9 links run <- FALSE if (require(\"spatialreg\", quiet=TRUE)) run <- TRUE if (run) { W <- as(nb2listw(col005, style=\"W\", zero.policy=TRUE), \"CsparseMatrix\") try(col005.spM <- mat2listw(W)) col005.spM <- mat2listw(W, style=\"W\", zero.policy=TRUE) summary(col005.spM$neighbours) } #> Warning: style is M (missing); style should be set to a valid value #> Warning: style is M (missing); style should be set to a valid value #> Warning: 1005, 1006, 1008, 1043 are not origins #> Warning: neighbour object has 8 sub-graphs #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> Warning: neighbour object has 8 sub-graphs #> Warning: neighbour object has 8 sub-graphs #> Warning: neighbour object has 8 sub-graphs #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 170 #> Percentage nonzero weights: 7.080383 #> Average number of links: 3.469388 #> 4 regions with no links: #> 1005, 1006, 1008, 1043 #> 8 disjoint connected subgraphs #> Link number distribution: #> #> 0 1 2 3 4 5 6 7 8 9 #> 4 11 5 8 3 9 2 2 3 2 #> 11 least connected regions: #> 1001 1007 1018 1010 1045 1044 1046 1047 1049 1048 1015 with 1 link #> 2 most connected regions: #> 1038 1036 with 9 links if (run) { diffnb(col005, col005.spM$neighbours) } #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 0 #> Percentage nonzero weights: 0 #> Average number of links: 0 #> 49 regions with no links: #> 1005, 1001, 1006, 1002, 1007, 1008, 1004, 1003, 1018, 1010, 1038, 1037, #> 1039, 1040, 1009, 1036, 1011, 1042, 1041, 1017, 1043, 1019, 1012, 1035, #> 1032, 1020, 1021, 1031, 1033, 1034, 1045, 1013, 1022, 1044, 1023, 1046, #> 1030, 1024, 1047, 1016, 1014, 1049, 1029, 1025, 1028, 1048, 1015, 1027, #> 1026 #> 49 disjoint connected subgraphs if (run && require(\"Matrix\", quiet=TRUE)) { IW <- kronecker(Diagonal(3), W) col005.spM.3T <- mat2listw(as(IW, \"CsparseMatrix\"), style=\"W\", zero.policy=TRUE) summary(col005.spM.3T$neighbours) } #> Warning: neighbour object has 24 sub-graphs #> Warning: neighbour object has 24 sub-graphs #> Neighbour list object: #> Number of regions: 147 #> Number of nonzero links: 510 #> Percentage nonzero weights: 2.360128 #> Average number of links: 3.469388 #> 12 regions with no links: #> 1, 3, 6, 21, 50, 52, 55, 70, 99, 101, 104, 119 #> 24 disjoint connected subgraphs #> Link number distribution: #> #> 0 1 2 3 4 5 6 7 8 9 #> 12 33 15 24 9 27 6 6 9 6 #> 33 least connected regions: #> 2 5 9 10 31 34 36 39 42 46 47 51 54 58 59 80 83 85 88 91 95 96 100 103 107 108 129 132 134 137 140 144 145 with 1 link #> 6 most connected regions: #> 11 16 60 65 109 114 with 9 links"},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute Moran's I — moran","title":"Compute Moran's I — moran","text":"simple function compute Moran's , called moran.test moran.mc; $$= \\frac{n}{\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}} \\frac{\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}(x_i-\\bar{x})(x_j-\\bar{x})}{\\sum_{=1}^{n}(x_i - \\bar{x})^2} $$","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute Moran's I — moran","text":"","code":"moran(x, listw, n, S0, zero.policy=attr(listw, \"zero.policy\"), NAOK=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute Moran's I — moran","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw n number zones S0 global sum weights zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA NAOK 'TRUE' 'NA' 'NaN' 'Inf' values x passed foreign function. 'FALSE', presence 'NA' 'NaN' 'Inf' values regarded error.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute Moran's I — moran","text":"list Moran's K sample kurtosis x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute Moran's I — moran","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 17.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute Moran's I — moran","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute Moran's I — moran","text":"","code":"data(oldcol) col.W <- nb2listw(COL.nb, style=\"W\") crime <- COL.OLD$CRIME str(moran(crime, col.W, length(COL.nb), Szero(col.W))) #> List of 2 #> $ I: num 0.511 #> $ K: num 2.23 is.na(crime) <- sample(1:length(crime), 10) str(moran(crime, col.W, length(COL.nb), Szero(col.W), NAOK=TRUE)) #> Warning: NAs in lagged values #> List of 2 #> $ I: num 0.142 #> $ K: num 2.82"},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Permutation test for Moran's I statistic — moran.mc","title":"Permutation test for Moran's I statistic — moran.mc","text":"permutation test Moran's statistic calculated using nsim random permutations x given spatial weighting scheme, establish rank observed statistic relation nsim simulated values.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Permutation test for Moran's I statistic — moran.mc","text":"","code":"moran.mc(x, listw, nsim, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\", na.action=na.fail, spChk=NULL, return_boot=FALSE, adjust.n=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Permutation test for Moran's I statistic — moran.mc","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw nsim number permutations zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"two.sided\", \"less\". na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass permitted meaningless permutation test. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() return_boot return object class boot equivalent permutation bootstrap rather object class htest adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Permutation test for Moran's I statistic — moran.mc","text":"list class htest mc.sim containing following components: statistic value observed Moran's . parameter rank observed Moran's . p.value pseudo p-value test. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data, number simulations. res nsim simulated values statistic, final value observed statistic","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Permutation test for Moran's I statistic — moran.mc","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 63-5.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Permutation test for Moran's I statistic — moran.mc","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Permutation test for Moran's I statistic — moran.mc","text":"","code":"data(oldcol) colw <- nb2listw(COL.nb, style=\"W\") nsim <- 99 set.seed(1234) sim1 <- moran.mc(COL.OLD$CRIME, listw=colw, nsim=nsim) sim1 #> #> \tMonte-Carlo simulation of Moran I #> #> data: COL.OLD$CRIME #> weights: colw #> number of simulations + 1: 100 #> #> statistic = 0.51095, observed rank = 100, p-value = 0.01 #> alternative hypothesis: greater #> mean(sim1$res[1:nsim]) #> [1] -0.003196117 var(sim1$res[1:nsim]) #> [1] 0.008543554 summary(sim1$res[1:nsim]) #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> -0.180085 -0.073721 -0.009528 -0.003196 0.063865 0.206779 colold.lags <- nblag(COL.nb, 3) set.seed(1234) sim2 <- moran.mc(COL.OLD$CRIME, nb2listw(colold.lags[[2]], style=\"W\"), nsim=nsim) summary(sim2$res[1:nsim]) #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> -0.15905 -0.07503 -0.01535 -0.02060 0.03305 0.13023 sim3 <- moran.mc(COL.OLD$CRIME, nb2listw(colold.lags[[3]], style=\"W\"), nsim=nsim) summary(sim3$res[1:nsim]) #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> -0.192986 -0.055468 -0.024154 -0.026327 0.004769 0.129996 crime <- COL.OLD$CRIME is.na(crime) <- sample(1:length(crime), 10) try(moran.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, na.action=na.fail)) #> Error in na.fail.default(x) : missing values in object moran.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE, na.action=na.omit) #> #> \tMonte-Carlo simulation of Moran I #> #> data: crime #> weights: nb2listw(COL.nb, style = \"W\") #> omitted: 5, 7, 9, 15, 19, 33, 40, 45, 47, 48 #> number of simulations + 1: 100 #> #> statistic = 0.42342, observed rank = 100, p-value = 0.01 #> alternative hypothesis: greater #> moran.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE, return_boot=TRUE, na.action=na.omit) #> NA observations omitted: 5, 7, 9, 15, 19, 33, 40, 45, 47, 48 #> #> DATA PERMUTATION #> #> #> Call: #> boot(data = x, statistic = moran_boot, R = nsim, sim = \"permutation\", #> listw = listw, n = n, S0 = S0, zero.policy = zero.policy, #> parallel = parallel, ncpus = ncpus, cl = cl) #> #> #> Bootstrap Statistics : #> original bias std. error #> t1* 0.4234221 -0.4429891 0.1293935 moran.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE, na.action=na.exclude) #> #> \tMonte-Carlo simulation of Moran I #> #> data: crime #> weights: nb2listw(COL.nb, style = \"W\") #> omitted: 5, 7, 9, 15, 19, 33, 40, 45, 47, 48 #> number of simulations + 1: 100 #> #> statistic = 0.42342, observed rank = 100, p-value = 0.01 #> alternative hypothesis: greater #> moran.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE, return_boot=TRUE, na.action=na.exclude) #> NA observations omitted: 5, 7, 9, 15, 19, 33, 40, 45, 47, 48 #> #> DATA PERMUTATION #> #> #> Call: #> boot(data = x, statistic = moran_boot, R = nsim, sim = \"permutation\", #> listw = listw, n = n, S0 = S0, zero.policy = zero.policy, #> parallel = parallel, ncpus = ncpus, cl = cl) #> #> #> Bootstrap Statistics : #> original bias std. error #> t1* 0.4234221 -0.4384413 0.1243937 try(moran.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, na.action=na.pass)) #> Error in moran.mc(crime, nb2listw(COL.nb, style = \"W\"), nsim = 99, na.action = na.pass) : #> na.pass not permitted"},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":null,"dir":"Reference","previous_headings":"","what":"Moran scatterplot — moran.plot","title":"Moran scatterplot — moran.plot","text":"plot spatial data spatially lagged values, augmented reporting summary influence measures linear relationship data lag. zero policy TRUE, observations also marked occur.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Moran scatterplot — moran.plot","text":"","code":"moran.plot(x, listw, y=NULL, zero.policy=attr(listw, \"zero.policy\"), spChk=NULL, labels=NULL, xlab=NULL, ylab=NULL, quiet=NULL, plot=TRUE, return_df=TRUE, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Moran scatterplot — moran.plot","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw y optional numeric vector length neighbours list listw bi-variate plot zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() labels character labels points high influence measures, set FALSE, labels plotted points large influence xlab label x axis ylab label x axis quiet default NULL, use !verbose global option value; TRUE, output summary influence object suppressed plot default TRUE, false, plotting suppressed return_df default TRUE, invisibly return data.frame object; FALSE invisibly return influence measures object ... graphical parameters par(..)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Moran scatterplot — moran.plot","text":"function returns data.frame object coordinates influence measures return_df TRUE, influence object influence.measures.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Moran scatterplot — moran.plot","text":"Anselin, L. 1996. Moran scatterplot ESDA tool assess local instability spatial association. pp. 111–125 M. M. Fischer, H. J. Scholten D. Unwin (eds) Spatial analytical perspectives GIS, London, Taylor Francis; Anselin, L. 1995. Local indicators spatial association, Geographical Analysis, 27, 93–115","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Moran scatterplot — moran.plot","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Moran scatterplot — moran.plot","text":"","code":"data(afcon, package=\"spData\") mp <- moran.plot(afcon$totcon, nb2listw(paper.nb), labels=as.character(afcon$name), pch=19) moran.plot(as.vector(scale(afcon$totcon)), nb2listw(paper.nb), labels=as.character(afcon$name), xlim=c(-2, 4), ylim=c(-2,4), pch=19) if (require(ggplot2, quietly=TRUE)) { xname <- attr(mp, \"xname\") ggplot(mp, aes(x=x, y=wx)) + geom_point(shape=1) + geom_smooth(formula=y ~ x, method=\"lm\") + geom_hline(yintercept=mean(mp$wx), lty=2) + geom_vline(xintercept=mean(mp$x), lty=2) + theme_minimal() + geom_point(data=mp[mp$is_inf,], aes(x=x, y=wx), shape=9) + geom_text(data=mp[mp$is_inf,], aes(x=x, y=wx, label=labels, vjust=1.5)) + xlab(xname) + ylab(paste0(\"Spatially lagged \", xname)) } columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")) #> Reading layer `columbus' from data source #> `/home/rsb/lib/r_libs/spData/shapes/columbus.gpkg' using driver `GPKG' #> Simple feature collection with 49 features and 20 fields #> Geometry type: POLYGON #> Dimension: XY #> Bounding box: xmin: 5.874907 ymin: 10.78863 xmax: 11.28742 ymax: 14.74245 #> Projected CRS: Undefined Cartesian SRS with unknown unit nb <- poly2nb(columbus) listw <- nb2listw(nb) moran.plot(x=columbus$CRIME, y=columbus$INC, listw=listw) moran.plot(x=columbus$INC, y=columbus$CRIME, listw=listw)"},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":null,"dir":"Reference","previous_headings":"","what":"Moran's I test for spatial autocorrelation — moran.test","title":"Moran's I test for spatial autocorrelation — moran.test","text":"Moran's test spatial autocorrelation using spatial weights matrix weights list form. assumptions underlying test sensitive form graph neighbour relationships factors, results may checked moran.mc permutations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Moran's I test for spatial autocorrelation — moran.test","text":"","code":"moran.test(x, listw, randomisation=TRUE, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\", rank = FALSE, na.action=na.fail, spChk=NULL, adjust.n=TRUE, drop.EI2=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Moran's I test for spatial autocorrelation — moran.test","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw randomisation variance calculated assumption randomisation, FALSE normality zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one greater (default), less two.sided. rank logical value - default FALSE continuous variables, TRUE, uses adaptation Moran's ranks suggested Cliff Ord (1981, p. 46) na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass used, zero substituted NA values calculating spatial lag spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted drop.EI2 default FALSE, TRUE, emulate CrimeStat <= 4.02","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Moran's I test for spatial autocorrelation — moran.test","text":"list class htest containing following components: statistic value standard deviate Moran's . p.value p-value test. estimate value observed Moran's , expectation variance method assumption. alternative character string describing alternative hypothesis. method character string giving assumption used calculating standard deviate. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Moran's I test for spatial autocorrelation — moran.test","text":"Var() taken Cliff Ord (1969, p. 28), Goodchild's CATMOG 47 (1986), see also Upton & Fingleton (1985) p. 171; agrees SpaceStat, see Tutorial workbook Chapter 22; VI second crude moment minus square first crude moment. derivation test (Cliff Ord, 1981, p. 18) assumes weights matrix symmetric. inherently non-symmetric matrices, k-nearest neighbour matrices, listw2U() can used make matrix symmetric.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Moran's I test for spatial autocorrelation — moran.test","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 21; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Moran's I test for spatial autocorrelation — moran.test","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Moran's I test for spatial autocorrelation — moran.test","text":"","code":"data(oldcol) coords.OLD <- cbind(COL.OLD$X, COL.OLD$Y) moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"W\")) #> #> \tMoran I test under randomisation #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.nb, style = \"W\") #> #> Moran I statistic standard deviate = 5.6341, p-value = 8.797e-09 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.510951264 -0.020833333 0.008908762 #> moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"B\")) #> #> \tMoran I test under randomisation #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.nb, style = \"B\") #> #> Moran I statistic standard deviate = 6.2116, p-value = 2.622e-10 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.52063815 -0.02083333 0.00759872 #> moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"C\")) #> #> \tMoran I test under randomisation #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.nb, style = \"C\") #> #> Moran I statistic standard deviate = 6.2116, p-value = 2.622e-10 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.52063815 -0.02083333 0.00759872 #> moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"S\")) #> #> \tMoran I test under randomisation #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.nb, style = \"S\") #> #> Moran I statistic standard deviate = 5.9786, p-value = 1.125e-09 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.512957470 -0.020833333 0.007971504 #> moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"W\"), randomisation=FALSE) #> #> \tMoran I test under normality #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.nb, style = \"W\") #> #> Moran I statistic standard deviate = 5.6754, p-value = 6.92e-09 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.510951264 -0.020833333 0.008779831 #> colold.lags <- nblag(COL.nb, 3) moran.test(COL.OLD$CRIME, nb2listw(colold.lags[[2]], style=\"W\")) #> #> \tMoran I test under randomisation #> #> data: COL.OLD$CRIME #> weights: nb2listw(colold.lags[[2]], style = \"W\") #> #> Moran I statistic standard deviate = 2.6076, p-value = 0.004559 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.168485742 -0.020833333 0.005271314 #> moran.test(COL.OLD$CRIME, nb2listw(colold.lags[[3]], style=\"W\")) #> #> \tMoran I test under randomisation #> #> data: COL.OLD$CRIME #> weights: nb2listw(colold.lags[[3]], style = \"W\") #> #> Moran I statistic standard deviate = -1.7896, p-value = 0.9632 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> -0.138930745 -0.020833333 0.004354683 #> print(is.symmetric.nb(COL.nb)) #> [1] TRUE COL.k4.nb <- knn2nb(knearneigh(coords.OLD, 4)) print(is.symmetric.nb(COL.k4.nb)) #> [1] FALSE moran.test(COL.OLD$CRIME, nb2listw(COL.k4.nb, style=\"W\")) #> #> \tMoran I test under randomisation #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.k4.nb, style = \"W\") #> #> Moran I statistic standard deviate = 7.2183, p-value = 2.632e-13 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.624933667 -0.020833333 0.008003503 #> moran.test(COL.OLD$CRIME, nb2listw(COL.k4.nb, style=\"W\"), randomisation=FALSE) #> #> \tMoran I test under normality #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.k4.nb, style = \"W\") #> #> Moran I statistic standard deviate = 7.2711, p-value = 1.782e-13 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.624933667 -0.020833333 0.007887613 #> cat(\"Note: non-symmetric weights matrix, use listw2U()\") #> Note: non-symmetric weights matrix, use listw2U() moran.test(COL.OLD$CRIME, listw2U(nb2listw(COL.k4.nb, style=\"W\"))) #> #> \tMoran I test under randomisation #> #> data: COL.OLD$CRIME #> weights: listw2U(nb2listw(COL.k4.nb, style = \"W\")) #> #> Moran I statistic standard deviate = 7.2183, p-value = 2.632e-13 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.624933667 -0.020833333 0.008003503 #> moran.test(COL.OLD$CRIME, listw2U(nb2listw(COL.k4.nb, style=\"W\")), randomisation=FALSE) #> #> \tMoran I test under normality #> #> data: COL.OLD$CRIME #> weights: listw2U(nb2listw(COL.k4.nb, style = \"W\")) #> #> Moran I statistic standard deviate = 7.2711, p-value = 1.782e-13 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.624933667 -0.020833333 0.007887613 #> ranks <- rank(COL.OLD$CRIME) names(ranks) <- rownames(COL.OLD) moran.test(ranks, nb2listw(COL.nb, style=\"W\"), rank=TRUE) #> #> \tMoran I test under randomisation #> #> data: ranks using rank correction #> weights: nb2listw(COL.nb, style = \"W\") #> #> Moran I statistic standard deviate = 6.3815, p-value = 8.766e-11 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.584333495 -0.020833333 0.008992923 #> crime <- COL.OLD$CRIME is.na(crime) <- sample(1:length(crime), 10) res <- try(moran.test(crime, nb2listw(COL.nb, style=\"W\"), na.action=na.fail)) #> Error in na.fail.default(x) : missing values in object moran.test(crime, nb2listw(COL.nb, style=\"W\"), zero.policy=TRUE, na.action=na.omit) #> Warning: subsetting caused increase in subgraph count #> #> \tMoran I test under randomisation #> #> data: crime #> weights: nb2listw(COL.nb, style = \"W\") #> omitted: 7, 10, 12, 13, 14, 18, 26, 41, 42, 47 #> n reduced by no-neighbour observations #> #> Moran I statistic standard deviate = 3.9826, p-value = 3.408e-05 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.43709247 -0.02702703 0.01358066 #> moran.test(crime, nb2listw(COL.nb, style=\"W\"), zero.policy=TRUE, na.action=na.exclude) #> Warning: subsetting caused increase in subgraph count #> #> \tMoran I test under randomisation #> #> data: crime #> weights: nb2listw(COL.nb, style = \"W\") #> omitted: 7, 10, 12, 13, 14, 18, 26, 41, 42, 47 #> n reduced by no-neighbour observations #> #> Moran I statistic standard deviate = 3.9826, p-value = 3.408e-05 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.43709247 -0.02702703 0.01358066 #> moran.test(crime, nb2listw(COL.nb, style=\"W\"), na.action=na.pass) #> Warning: NAs in lagged values #> #> \tMoran I test under randomisation #> #> data: crime #> weights: nb2listw(COL.nb, style = \"W\") #> #> Moran I statistic standard deviate = 2.4925, p-value = 0.006342 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.212782897 -0.020833333 0.008784908 #> columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col_geoms <- st_geometry(columbus) col_geoms[1] <- st_buffer(col_geoms[1], dist=-0.05) st_geometry(columbus) <- col_geoms (nb1 <- poly2nb(columbus)) #> Warning: some observations have no neighbours; #> if this seems unexpected, try increasing the snap argument. #> Warning: neighbour object has 2 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 232 #> Percentage nonzero weights: 9.662641 #> Average number of links: 4.734694 #> 1 region with no links: #> 1 #> 2 disjoint connected subgraphs try(lw <- nb2listw(nb1, style=\"W\")) #> Error in nb2listw(nb1, style = \"W\") : #> Empty neighbour sets found (zero.policy: FALSE) (lw <- nb2listw(nb1, style=\"W\", zero.policy=TRUE)) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 232 #> Percentage nonzero weights: 9.662641 #> Average number of links: 4.734694 #> 1 region with no links: #> 1 #> 2 disjoint connected subgraphs #> #> Weights style: W #> Weights constants summary: #> n nn S0 S1 S2 #> W 48 2304 48 22.23035 199.8188 moran.test(COL.OLD$CRIME, lw) #> #> \tMoran I test under randomisation #> #> data: COL.OLD$CRIME #> weights: lw #> n reduced by no-neighbour observations #> #> Moran I statistic standard deviate = 2.7707, p-value = 0.002797 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.23901261 -0.02127660 0.00882535 #>"},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute the Global Bivariate Moran's I — moran_bv","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"Given two continuous numeric variables, calculate bivariate Moran's . See details .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"","code":"moran_bv(x, y, listw, nsim = 499, scale = TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"x numeric vector length y. y numeric vector length x. listw listw object example created nb2listw(). nsim number simulations run. scale default TRUE.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"object class \"boot\", observed statistic component t0.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"Global Bivariate Moran defined \\( I_B = \\frac{\\Sigma_i(\\Sigma_j{w_{ij}y_j\\times x_i})}{\\Sigma_i{x_i^2}} \\) important note measure autocorrelation X spatial lag Y. , resultant measure may overestimate amount spatial autocorrelation may product inherent correlation X Y. output object class \"boot\", plots confidence intervals available using appropriate methods.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"Wartenberg, D. (1985), Multivariate Spatial Correlation: Method Exploratory Geographical Analysis. Geographical Analysis, 17: 263-283. doi:10.1111/j.1538-4632.1985.tb00849.x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"Josiah Parry josiah.parry@gmail.com","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"","code":"data(boston, package = \"spData\") x <- boston.c$CRIM y <- boston.c$NOX listw <- nb2listw(boston.soi) set.seed(1) res_xy <- moran_bv(x, y, listw, nsim=499) res_xy$t0 #> [1] 0.4082073 boot::boot.ci(res_xy, conf=c(0.99, 0.95, 0.9), type=\"basic\") #> BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS #> Based on 499 bootstrap replicates #> #> CALL : #> boot::boot.ci(boot.out = res_xy, conf = c(0.99, 0.95, 0.9), type = \"basic\") #> #> Intervals : #> Level Basic #> 99% ( 0.7443, 0.8789 ) #> 95% ( 0.7639, 0.8673 ) #> 90% ( 0.7739, 0.8615 ) #> Calculations and Intervals on Original Scale #> Some basic intervals may be unstable plot(res_xy) set.seed(1) lee_xy <- lee.mc(x, y, listw, nsim=499, return_boot=TRUE) lee_xy$t0 #> [1] 0.3993476 boot::boot.ci(lee_xy, conf=c(0.99, 0.95, 0.9), type=\"basic\") #> BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS #> Based on 499 bootstrap replicates #> #> CALL : #> boot::boot.ci(boot.out = lee_xy, conf = c(0.99, 0.95, 0.9), type = \"basic\") #> #> Intervals : #> Level Basic #> 99% ( 0.6363, 0.7236 ) #> 95% ( 0.6538, 0.7131 ) #> 90% ( 0.6584, 0.7098 ) #> Calculations and Intervals on Original Scale #> Some basic intervals may be unstable plot(lee_xy) set.seed(1) res_yx <- moran_bv(y, x, listw, nsim=499) res_yx$t0 #> [1] 0.4029821 boot::boot.ci(res_yx, conf=c(0.99, 0.95, 0.9), type=\"basic\") #> BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS #> Based on 499 bootstrap replicates #> #> CALL : #> boot::boot.ci(boot.out = res_yx, conf = c(0.99, 0.95, 0.9), type = \"basic\") #> #> Intervals : #> Level Basic #> 99% ( 0.7301, 0.8729 ) #> 95% ( 0.7574, 0.8584 ) #> 90% ( 0.7664, 0.8541 ) #> Calculations and Intervals on Original Scale #> Some basic intervals may be unstable plot(res_yx) set.seed(1) lee_yx <- lee.mc(y, x, listw, nsim=499, return_boot=TRUE) lee_yx$t0 #> [1] 0.3993476 boot::boot.ci(lee_yx, conf=c(0.99, 0.95, 0.9), type=\"basic\") #> BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS #> Based on 499 bootstrap replicates #> #> CALL : #> boot::boot.ci(boot.out = lee_yx, conf = c(0.99, 0.95, 0.9), type = \"basic\") #> #> Intervals : #> Level Basic #> 99% ( 0.6363, 0.7236 ) #> 95% ( 0.6538, 0.7131 ) #> 90% ( 0.6584, 0.7098 ) #> Calculations and Intervals on Original Scale #> Some basic intervals may be unstable plot(lee_yx)"},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":null,"dir":"Reference","previous_headings":"","what":"Find the minimal spanning tree — mstree","title":"Find the minimal spanning tree — mstree","text":"minimal spanning tree connected graph n nodes n-1 edges. smaller class possible partitions graph pruning edges high dissimilarity. one edge removed, graph partioned two unconnected subgraphs. function implements algorithm due Prim (1987).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Find the minimal spanning tree — mstree","text":"","code":"mstree(nbw, ini = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Find the minimal spanning tree — mstree","text":"nbw object listw class returned nb2listw function. See help details. ini initial node minimal spanning tree.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Find the minimal spanning tree — mstree","text":"minimum spanning tree algorithm. Input connected graph. Begin empty set nodes. Add arbitrary note set. nodes set, find minimum cost edge connecting node set node set add node set. set edges minimum spanning tree.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Find the minimal spanning tree — mstree","text":"matrix n-1 rows tree columns. row two nodes cost, . e. edge cost.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Find the minimal spanning tree — mstree","text":"R. C. Prim (1957) Shortest connection networks generalisations. : Bell System Technical Journal, 36, pp. 1389-1401","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Find the minimal spanning tree — mstree","text":"Renato M. Assuncao Elias T. Krainski","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Find the minimal spanning tree — mstree","text":"","code":"### loading data GDAL37 <- numeric_version(unname(sf::sf_extSoftVersion()[\"GDAL\"]), strict=FALSE) (GDAL37 <- ifelse(is.na(GDAL37), FALSE, GDAL37 >= \"3.7.0\")) #> [1] TRUE file <- \"etc/shapes/bhicv.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) { bh <- st_read(zipfile) } else { td <- tempdir() bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE) target <- unzip(zipfile, files=bn, exdir=td) bh <- st_read(target) } #> Reading layer `bhicv' from data source #> `/tmp/Rtmp5vVziX/temp_libpath224d25059ed81/spdep/etc/shapes/bhicv.gpkg.zip' #> using driver `GPKG' #> Simple feature collection with 98 features and 8 fields #> Geometry type: POLYGON #> Dimension: XY #> Bounding box: xmin: -45.02175 ymin: -20.93007 xmax: -42.50321 ymax: -18.08342 #> Geodetic CRS: Corrego Alegre 1970-72 ### data padronized dpad <- data.frame(scale(as.data.frame(bh)[,5:8])) ### neighboorhod list bh.nb <- poly2nb(bh) ### calculing costs lcosts <- nbcosts(bh.nb, dpad) ### making listw nb.w <- nb2listw(bh.nb, lcosts, style=\"B\") ### find a minimum spanning tree system.time(mst.bh <- mstree(nb.w,5)) #> user system elapsed #> 0.004 0.000 0.005 dim(mst.bh) #> [1] 97 3 head(mst.bh) #> [,1] [,2] [,3] #> [1,] 5 12 1.2951120 #> [2,] 12 13 0.6141101 #> [3,] 13 11 0.7913745 #> [4,] 13 6 0.9775650 #> [5,] 11 31 0.9965625 #> [6,] 31 39 0.6915158 tail(mst.bh) #> [,1] [,2] [,3] #> [92,] 89 90 2.5743702 #> [93,] 26 56 2.6235317 #> [94,] 86 87 2.6471303 #> [95,] 87 72 0.7874461 #> [96,] 49 36 2.8743677 #> [97,] 24 25 3.4675168 ### the mstree plot par(mar=c(0,0,0,0)) plot(st_geometry(bh), border=gray(.5)) plot(mst.bh, st_coordinates(st_centroid(bh)), col=2, cex.lab=.6, cex.circles=0.035, fg=\"blue\", add=TRUE) #> Warning: st_centroid assumes attributes are constant over geometries"},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":null,"dir":"Reference","previous_headings":"","what":"Output spatial neighbours for INLA — nb2INLA","title":"Output spatial neighbours for INLA — nb2INLA","text":"Output spatial neighbours INLA","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Output spatial neighbours for INLA — nb2INLA","text":"","code":"nb2INLA(file, nb)"},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Output spatial neighbours for INLA — nb2INLA","text":"file file adjacency matrix stored nb object class nb","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Output spatial neighbours for INLA — nb2INLA","text":"Nothing returned file created representation adjacency matrix required INLA spatial models.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Output spatial neighbours for INLA — nb2INLA","text":"http://www.r-inla.org","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Output spatial neighbours for INLA — nb2INLA","text":"Virgilio Gomez-Rubio","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Output spatial neighbours for INLA — nb2INLA","text":"","code":"col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) td <- tempdir() x <- nb2INLA(paste(td, \"columbus-INLA.adj\", sep=\"/\"), col.gal.nb) readLines(paste(td, \"columbus-INLA.adj\", sep=\"/\"), n=10) #> [1] \"49\" \"1 2 2 3\" #> [3] \"2 3 1 3 4\" \"3 4 1 2 4 5\" #> [5] \"4 4 2 3 5 8\" \"5 7 3 4 6 8 9 11 15\" #> [7] \"6 2 5 9\" \"7 4 8 12 13 14\" #> [9] \"8 6 4 5 7 11 12 13\" \"9 8 5 6 10 15 20 22 25 26\""},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":null,"dir":"Reference","previous_headings":"","what":"Output spatial weights for WinBUGS — nb2WB","title":"Output spatial weights for WinBUGS — nb2WB","text":"Output spatial weights WinBUGS","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Output spatial weights for WinBUGS — nb2WB","text":"","code":"nb2WB(nb) listw2WB(listw)"},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Output spatial weights for WinBUGS — nb2WB","text":"nb object class nb listw listw object example nb2listw","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Output spatial weights for WinBUGS — nb2WB","text":"list suitable convering using dput WinBUGS","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Output spatial weights for WinBUGS — nb2WB","text":"http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/geobugs12manual.pdf","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Output spatial weights for WinBUGS — nb2WB","text":"Virgilio Gomez-Rubio","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Output spatial weights for WinBUGS — nb2WB","text":"","code":"col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) x <- nb2WB(col.gal.nb) dput(x, control=NULL) #> list(c(2, 3, 1, 3, 4, 1, 2, 4, 5, 2, 3, 5, 8, 3, 4, 6, 8, 9, #> 11, 15, 5, 9, 8, 12, 13, 14, 4, 5, 7, 11, 12, 13, 5, 6, 10, 15, #> 20, 22, 25, 26, 9, 17, 20, 22, 5, 8, 12, 15, 16, 7, 8, 11, 13, #> 14, 16, 7, 8, 12, 14, 7, 12, 13, 16, 18, 19, 5, 9, 11, 16, 25, #> 26, 11, 12, 14, 15, 18, 24, 25, 10, 20, 23, 14, 16, 19, 24, 14, #> 18, 24, 9, 10, 17, 22, 23, 27, 32, 33, 35, 40, 24, 30, 34, 9, #> 10, 20, 26, 27, 28, 17, 20, 32, 16, 18, 19, 21, 25, 29, 30, 9, #> 15, 16, 24, 26, 28, 29, 9, 15, 22, 25, 28, 29, 20, 22, 28, 33, #> 22, 25, 26, 27, 29, 33, 35, 37, 38, 24, 25, 26, 28, 30, 37, 38, #> 21, 24, 29, 37, 34, 36, 20, 23, 40, 41, 20, 27, 28, 35, 21, 31, #> 36, 42, 20, 28, 33, 38, 40, 43, 44, 31, 34, 39, 42, 46, 28, 29, #> 30, 38, 43, 45, 28, 29, 35, 37, 43, 44, 36, 46, 20, 32, 35, 41, #> 47, 32, 40, 47, 34, 36, 35, 37, 38, 44, 45, 48, 35, 38, 43, 48, #> 49, 37, 43, 48, 49, 36, 39, 40, 41, 43, 44, 45, 49, 44, 45, 48 #> ), c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, #> 1), c(2, 3, 4, 4, 7, 2, 4, 6, 8, 4, 5, 6, 4, 6, 6, 7, 3, 4, 3, #> 10, 3, 6, 3, 7, 7, 6, 4, 9, 7, 4, 2, 4, 4, 4, 7, 5, 6, 6, 2, #> 5, 3, 2, 6, 5, 4, 2, 2, 4, 3)) x <- listw2WB(nb2listw(col.gal.nb)) dput(x, control=NULL) #> list(c(2, 3, 1, 3, 4, 1, 2, 4, 5, 2, 3, 5, 8, 3, 4, 6, 8, 9, #> 11, 15, 5, 9, 8, 12, 13, 14, 4, 5, 7, 11, 12, 13, 5, 6, 10, 15, #> 20, 22, 25, 26, 9, 17, 20, 22, 5, 8, 12, 15, 16, 7, 8, 11, 13, #> 14, 16, 7, 8, 12, 14, 7, 12, 13, 16, 18, 19, 5, 9, 11, 16, 25, #> 26, 11, 12, 14, 15, 18, 24, 25, 10, 20, 23, 14, 16, 19, 24, 14, #> 18, 24, 9, 10, 17, 22, 23, 27, 32, 33, 35, 40, 24, 30, 34, 9, #> 10, 20, 26, 27, 28, 17, 20, 32, 16, 18, 19, 21, 25, 29, 30, 9, #> 15, 16, 24, 26, 28, 29, 9, 15, 22, 25, 28, 29, 20, 22, 28, 33, #> 22, 25, 26, 27, 29, 33, 35, 37, 38, 24, 25, 26, 28, 30, 37, 38, #> 21, 24, 29, 37, 34, 36, 20, 23, 40, 41, 20, 27, 28, 35, 21, 31, #> 36, 42, 20, 28, 33, 38, 40, 43, 44, 31, 34, 39, 42, 46, 28, 29, #> 30, 38, 43, 45, 28, 29, 35, 37, 43, 44, 36, 46, 20, 32, 35, 41, #> 47, 32, 40, 47, 34, 36, 35, 37, 38, 44, 45, 48, 35, 38, 43, 48, #> 49, 37, 43, 48, 49, 36, 39, 40, 41, 43, 44, 45, 49, 44, 45, 48 #> ), c(0.5, 0.5, 0.333333333333333, 0.333333333333333, 0.333333333333333, #> 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.142857142857143, #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.142857142857143, #> 0.142857142857143, 0.142857142857143, 0.5, 0.5, 0.25, 0.25, 0.25, #> 0.25, 0.166666666666667, 0.166666666666667, 0.166666666666667, #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.125, #> 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.25, 0.25, #> 0.25, 0.25, 0.2, 0.2, 0.2, 0.2, 0.2, 0.166666666666667, 0.166666666666667, #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667, #> 0.25, 0.25, 0.25, 0.25, 0.166666666666667, 0.166666666666667, #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667, #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667, #> 0.166666666666667, 0.166666666666667, 0.142857142857143, 0.142857142857143, #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.142857142857143, #> 0.142857142857143, 0.333333333333333, 0.333333333333333, 0.333333333333333, #> 0.25, 0.25, 0.25, 0.25, 0.333333333333333, 0.333333333333333, #> 0.333333333333333, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, #> 0.1, 0.333333333333333, 0.333333333333333, 0.333333333333333, #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667, #> 0.166666666666667, 0.166666666666667, 0.333333333333333, 0.333333333333333, #> 0.333333333333333, 0.142857142857143, 0.142857142857143, 0.142857142857143, #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.142857142857143, #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.142857142857143, #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.166666666666667, #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667, #> 0.166666666666667, 0.25, 0.25, 0.25, 0.25, 0.111111111111111, #> 0.111111111111111, 0.111111111111111, 0.111111111111111, 0.111111111111111, #> 0.111111111111111, 0.111111111111111, 0.111111111111111, 0.111111111111111, #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.142857142857143, #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.25, #> 0.25, 0.25, 0.25, 0.5, 0.5, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, #> 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.142857142857143, 0.142857142857143, #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.142857142857143, #> 0.142857142857143, 0.2, 0.2, 0.2, 0.2, 0.2, 0.166666666666667, #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667, #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667, #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.5, #> 0.5, 0.2, 0.2, 0.2, 0.2, 0.2, 0.333333333333333, 0.333333333333333, #> 0.333333333333333, 0.5, 0.5, 0.166666666666667, 0.166666666666667, #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667, #> 0.2, 0.2, 0.2, 0.2, 0.2, 0.25, 0.25, 0.25, 0.25, 0.5, 0.5, 0.5, #> 0.5, 0.25, 0.25, 0.25, 0.25, 0.333333333333333, 0.333333333333333, #> 0.333333333333333), c(2, 3, 4, 4, 7, 2, 4, 6, 8, 4, 5, 6, 4, #> 6, 6, 7, 3, 4, 3, 10, 3, 6, 3, 7, 7, 6, 4, 9, 7, 4, 2, 4, 4, #> 4, 7, 5, 6, 6, 2, 5, 3, 2, 6, 5, 4, 2, 2, 4, 3))"},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":null,"dir":"Reference","previous_headings":"","what":"Block up neighbour list for location-less observations — nb2blocknb","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"function blocks neighbour list known spatial locations create new neighbour list multiple location-less observations know belong spatial locations, using identification tags locations key.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"","code":"nb2blocknb(nb=NULL, ID, row.names = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"nb object class nb list integer vectors containing neighbour region number ids; null, nb object neighbours created length unique(.character(ID)) ID identification tags locations location-less observations; sort(unique(.character(ID))) must identical sort(.character(attr(nb, \"region.id\"))); length row.names provided. row.names character vector observation ids added neighbours list attribute region.id, default seq(1, nrow(x)); length ID provided.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"Assume list unique locations, neighbour list can build , create input neighbour list. needs \"unfolded\", observations belonging unique location observation neighbours, observations belonging location neighbours unique location question also observation neighbours, finally removing observation (neighbour). scenario also arises say post codes available, post codes contain multiple observations, known belong specific post code, located within (given post code locations known).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"function returns object class nb list integer vectors containing neighbour observation number ids.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"","code":"# \\dontrun{ data(boston, package=\"spData\") summary(as.vector(table(boston.c$TOWN))) #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> 1.0 2.0 4.0 5.5 7.0 30.0 townaggr <- aggregate(boston.utm, list(town=boston.c$TOWN), mean) block.rel <- graph2nb(relativeneigh(as.matrix(townaggr[,2:3])), as.character(townaggr[,1]), sym=TRUE) block.rel #> Neighbour list object: #> Number of regions: 92 #> Number of nonzero links: 240 #> Percentage nonzero weights: 2.835539 #> Average number of links: 2.608696 print(is.symmetric.nb(block.rel)) #> [1] TRUE plot(block.rel, as.matrix(townaggr[,2:3])) points(boston.utm, pch=18, col=\"lightgreen\") block.nb <- nb2blocknb(block.rel, as.character(boston.c$TOWN)) block.nb #> Neighbour list object: #> Number of regions: 506 #> Number of nonzero links: 15234 #> Percentage nonzero weights: 5.949945 #> Average number of links: 30.10672 print(is.symmetric.nb(block.nb)) #> [1] TRUE plot(block.nb, boston.utm) points(boston.utm, pch=18, col=\"lightgreen\") n.comp.nb(block.nb)$nc #> [1] 1 moran.test(boston.c$CMEDV, nb2listw(boston.soi)) #> #> \tMoran I test under randomisation #> #> data: boston.c$CMEDV #> weights: nb2listw(boston.soi) #> #> Moran I statistic standard deviate = 21.786, p-value < 2.2e-16 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.690285059 -0.001980198 0.001009685 #> moran.test(boston.c$CMEDV, nb2listw(block.nb)) #> #> \tMoran I test under randomisation #> #> data: boston.c$CMEDV #> weights: nb2listw(block.nb) #> #> Moran I statistic standard deviate = 22.455, p-value < 2.2e-16 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.3122905961 -0.0019801980 0.0001958827 #> block.nb <- nb2blocknb(NULL, as.character(boston.c$TOWN)) #> Warning: neighbour object has 92 sub-graphs block.nb #> Neighbour list object: #> Number of regions: 506 #> Number of nonzero links: 4868 #> Percentage nonzero weights: 1.901295 #> Average number of links: 9.620553 #> 17 regions with no links: #> 1, 55, 56, 57, 58, 65, 196, 257, 284, 285, 286, 287, 342, 343, 348, #> 349, 354 #> 92 disjoint connected subgraphs print(is.symmetric.nb(block.nb)) #> [1] TRUE plot(block.nb, boston.utm) n.comp.nb(block.nb)$nc #> [1] 92 moran.test(boston.c$CMEDV, nb2listw(block.nb, zero.policy=TRUE), zero.policy=TRUE) #> #> \tMoran I test under randomisation #> #> data: boston.c$CMEDV #> weights: nb2listw(block.nb, zero.policy = TRUE) #> n reduced by no-neighbour observations #> #> Moran I statistic standard deviate = 21.145, p-value < 2.2e-16 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.6188830566 -0.0020491803 0.0008623116 #> # }"},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":null,"dir":"Reference","previous_headings":"","what":"Use vector files for import and export of weights — nb2lines","title":"Use vector files for import and export of weights — nb2lines","text":"Use vector files import export weights, storing spatial entity coordinates arcs, entity indices data frame.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Use vector files for import and export of weights — nb2lines","text":"","code":"nb2lines(nb, wts, coords, proj4string=NULL, as_sf=FALSE) listw2lines(listw, coords, proj4string=NULL, as_sf=FALSE) df2sn(df, i=\"i\", i_ID=\"i_ID\", j=\"j\", wt=\"wt\")"},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Use vector files for import and export of weights — nb2lines","text":"nb neighbour object class nb wts list general weights corresponding neighbours coords matrix region point coordinates, Spatial object (points polygons), sfc object (points polygons) proj4string default NULL; coords Spatial sf object, value used, otherwise value converted appropriately as_sf output object Spatial sf format, default FALSE, set TRUE coords sfc object FALSE Spatial object listw listw object spatial weights df data frame read shapefile, derived output nb2lines character name column df entity index i_ID character name column df entity region ID j character name column df entity index wt character name column df weights","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Use vector files for import and export of weights — nb2lines","text":"neighbour weights objects may retrieved converting specified columns data slot SpatialLinesDataFrame object spatial.neighbour object, converted weights list object.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Use vector files for import and export of weights — nb2lines","text":"nb2lines listw2lines return SpatialLinesDataFrame object sf object; data frame contains indices neighbour links weights. df2sn converts data retrieved reading data df back spatial.neighbour object.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Use vector files for import and export of weights — nb2lines","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Use vector files for import and export of weights — nb2lines","text":"Original idea due Gidske Leknes Andersen, Department Biology, University Bergen, Norway","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Use vector files for import and export of weights — nb2lines","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) res <- listw2lines(nb2listw(col.gal.nb), st_geometry(columbus)) summary(res) #> i j i_ID j_ID #> Min. : 1.00 Min. : 1.00 Length:230 Length:230 #> 1st Qu.:13.00 1st Qu.:13.00 Class :character Class :character #> Median :24.00 Median :24.00 Mode :character Mode :character #> Mean :24.19 Mean :24.19 #> 3rd Qu.:35.00 3rd Qu.:35.00 #> Max. :49.00 Max. :49.00 #> wt geometry #> Min. :0.1000 LINESTRING:230 #> 1st Qu.:0.1429 epsg:NA : 0 #> Median :0.1667 #> Mean :0.2130 #> 3rd Qu.:0.2500 #> Max. :0.5000 tf <- paste0(tempfile(), \".gpkg\") st_write(res, dsn=tf, driver=\"GPKG\") #> Writing layer `file2558f5fcfb4d5' to data source #> `/tmp/RtmpaA6yDM/file2558f5fcfb4d5.gpkg' using driver `GPKG' #> Writing 230 features with 5 fields and geometry type Line String. inMap <- st_read(tf) #> Reading layer `file2558f5fcfb4d5' from data source #> `/tmp/RtmpaA6yDM/file2558f5fcfb4d5.gpkg' using driver `GPKG' #> Simple feature collection with 230 features and 5 fields #> Geometry type: LINESTRING #> Dimension: XY #> Bounding box: xmin: 6.165913 ymin: 11.04088 xmax: 10.96206 ymax: 14.43766 #> Projected CRS: Undefined Cartesian SRS with unknown unit summary(inMap) #> i j i_ID j_ID #> Min. : 1.00 Min. : 1.00 Length:230 Length:230 #> 1st Qu.:13.00 1st Qu.:13.00 Class :character Class :character #> Median :24.00 Median :24.00 Mode :character Mode :character #> Mean :24.19 Mean :24.19 #> 3rd Qu.:35.00 3rd Qu.:35.00 #> Max. :49.00 Max. :49.00 #> wt geom #> Min. :0.1000 LINESTRING:230 #> 1st Qu.:0.1429 epsg:NA : 0 #> Median :0.1667 #> Mean :0.2130 #> 3rd Qu.:0.2500 #> Max. :0.5000 diffnb(sn2listw(df2sn(as.data.frame(inMap)))$neighbours, col.gal.nb) #> Warning: style is M (missing); style should be set to a valid value #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 0 #> Percentage nonzero weights: 0 #> Average number of links: 0 #> 49 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 #> 49 disjoint connected subgraphs res1 <- listw2lines(nb2listw(col.gal.nb), as(columbus, \"Spatial\")) summary(res1) #> Object of class SpatialLinesDataFrame #> Coordinates: #> min max #> x 6.221943 10.95359 #> y 11.010031 14.36908 #> Is projected: TRUE #> proj4string : [NA] #> Data attributes: #> i j i_ID j_ID #> Min. : 1.00 Min. : 1.00 Length:230 Length:230 #> 1st Qu.:13.00 1st Qu.:13.00 Class :character Class :character #> Median :24.00 Median :24.00 Mode :character Mode :character #> Mean :24.19 Mean :24.19 #> 3rd Qu.:35.00 3rd Qu.:35.00 #> Max. :49.00 Max. :49.00 #> wt #> Min. :0.1000 #> 1st Qu.:0.1429 #> Median :0.1667 #> Mean :0.2130 #> 3rd Qu.:0.2500 #> Max. :0.5000"},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial weights for neighbours lists — nb2listw","title":"Spatial weights for neighbours lists — nb2listw","text":"nb2listw function supplements neighbours list spatial weights chosen coding scheme. can..simmed helper function checks whether spatial weights object similar symmetric can transformed yield real eigenvalues Cholesky decomposition. helper function listw2U() constructs weights list object corresponding sparse matrix \\(\\frac{1}{2} ( \\mathbf{W} + \\mathbf{W}'\\).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial weights for neighbours lists — nb2listw","text":"","code":"nb2listw(neighbours, glist=NULL, style=\"W\", zero.policy=NULL) listw2U(listw)"},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial weights for neighbours lists — nb2listw","text":"neighbours object class nb glist list general weights corresponding neighbours style style can take values “W”, “B”, “C”, “U”, “minmax” “S” zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors listw listw object created example nb2listw","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Spatial weights for neighbours lists — nb2listw","text":"Starting binary neighbours list, regions either listed neighbours absent (thus set neighbours definition), function adds weights list values given coding scheme style chosen. B basic binary coding, W row standardised (sums links n), C globally standardised (sums links n), U equal C divided number neighbours (sums links unity), S variance-stabilizing coding scheme proposed Tiefelsdorf et al. 1999, p. 167-168 (sums links n). zero policy set TRUE, weights vectors zero length inserted regions without neighbour neighbours list. turn generate lag values zero, equivalent sum products zero row t(rep(0, length=length(neighbours))) %*% x, arbitraty numerical vector x length length(neighbours). spatially lagged value x zero-neighbour region zero, may (may ) sensible choice. sum glist vector one observations zero, warning message issued. consequence later operations -neighbour observations present zero.policy argument set true. “minmax” style based Kelejian Prucha (2010), divides weights minimum maximum row sums maximum column sums input weights. similar C U styles; also available Stata.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial weights for neighbours lists — nb2listw","text":"listw object following members: style one W, B, C, U, S, minmax neighbours input neighbours list weights weights neighbours chosen style, attributes set report type relationships (binary general, general form glist argument), style attributes: region.id character, neighbour object call function call zero.policy logical; value zero.policy object created","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Spatial weights for neighbours lists — nb2listw","text":"Tiefelsdorf, M., Griffith, D. ., Boots, B. 1999 variance-stabilizing coding scheme spatial link matrices, Environment Planning , 31, pp. 165–180; Kelejian, H. H., . R. Prucha. 2010. Specification estimation spatial autoregressive models autoregressive heteroskedastic disturbances. Journal Econometrics, 157: pp. 53–67.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial weights for neighbours lists — nb2listw","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial weights for neighbours lists — nb2listw","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries cards <- card(col.gal.nb) col.w <- nb2listw(col.gal.nb) plot(cards, unlist(lapply(col.w$weights, sum)),xlim=c(0,10), ylim=c(0,10), xlab=\"number of links\", ylab=\"row sums of weights\") col.b <- nb2listw(col.gal.nb, style=\"B\") points(cards, unlist(lapply(col.b$weights, sum)), col=\"red\") col.c <- nb2listw(col.gal.nb, style=\"C\") points(cards, unlist(lapply(col.c$weights, sum)), col=\"green\") col.u <- nb2listw(col.gal.nb, style=\"U\") points(cards, unlist(lapply(col.u$weights, sum)), col=\"orange\") col.s <- nb2listw(col.gal.nb, style=\"S\") points(cards, unlist(lapply(col.s$weights, sum)), col=\"blue\") legend(x=c(0, 1), y=c(7, 9), legend=c(\"W\", \"B\", \"C\", \"U\", \"S\"), bty=\"n\", col=c(\"black\", \"red\", \"green\", \"orange\", \"blue\"), pch=rep(1,5), cex=0.8, y.intersp=2.5) summary(nb2listw(col.gal.nb, style=\"minmax\")) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> Link number distribution: #> #> 2 3 4 5 6 7 8 9 10 #> 7 7 13 4 9 6 1 1 1 #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links #> #> Weights style: minmax #> Weights constants summary: #> n nn S0 S1 S2 #> minmax 49 2401 23 4.6 50.48 dlist <- nbdists(col.gal.nb, coords) dlist <- lapply(dlist, function(x) 1/x) col.w.d <- nb2listw(col.gal.nb, glist=dlist) summary(unlist(col.w$weights)) #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> 0.1000 0.1429 0.1667 0.2130 0.2500 0.5000 summary(unlist(col.w.d$weights)) #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> 0.06977 0.13114 0.17710 0.21304 0.27124 0.67178 # introducing other conditions into weights - only earlier sales count # see http://sal.uiuc.edu/pipermail/openspace/2005-October/000610.html data(baltimore, package=\"spData\") set.seed(211) dates <- sample(1:500, nrow(baltimore), replace=TRUE) nb_15nn <- knn2nb(knearneigh(cbind(baltimore$X, baltimore$Y), k=15)) glist <- vector(mode=\"list\", length=length(nb_15nn)) for (i in seq(along=nb_15nn)) glist[[i]] <- ifelse(dates[i] > dates[nb_15nn[[i]]], 1, 0) listw_15nn_dates <- nb2listw(nb_15nn, glist=glist, style=\"B\") #> Warning: zero sum general weights which(lag(listw_15nn_dates, baltimore$PRICE) == 0.0) #> [1] 1 22 29 35 66 74 80 99 117 147 155 169 195 197 200 which(sapply(glist, sum) == 0) #> [1] 1 22 29 35 66 74 80 99 117 147 155 169 195 197 200 ex <- which(sapply(glist, sum) == 0)[1] dates[ex] #> [1] 28 dates[nb_15nn[[ex]]] #> [1] 395 247 275 179 142 484 111 239 369 199 294 251 448 390 229"},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":null,"dir":"Reference","previous_headings":"","what":"Distance-based spatial weights for neighbours lists — nb2listwdist","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"nb2listwdist function supplements neighbours list spatial weights chosen types distance modelling coding scheme. offered coding schemes parallel nb2listw function, three distance-based types weights available: inverse distance weighting (IDW), double-power distance weights, exponential distance decay. can..simmed helper function checks whether spatial weights object similar symmetric can transformed yield real eigenvalues Cholesky decomposition.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"","code":"nb2listwdist(neighbours, x, type=\"idw\", style=\"raw\", alpha = 1, dmax = NULL, longlat = NULL, zero.policy=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"neighbours object class nb x sp sf, sfc object type default “idw”; intended type distance modelling, can take values “idw”, “exp”, “dpd” style default “raw”; style can take values “raw”, “W”, “B”, “C”, “U”, “minmax”, “S” alpha default 0; parameter controlling distance modelling, see “Details” dmax default NULL, maximum distance threshold required type “dpd” optional types longlat default NULL; TRUE point coordinates longitude-latitude decimal degrees, case distances measured metres; x SpatialPoints object, value taken object , overrides argument NULL; distances measured map units FALSE NULL zero.policy default NULL; use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"Starting binary neighbours list, regions either listed neighbours absent (thus set neighbours definition), function adds distance-based weights list. Three types distance weight calculations based pairwise distances \\(d_{ij}\\) possible, controlled parameter “alpha” (\\(\\alpha\\) ): $$\\textrm{idw: } w_{ij} = d_{ij}^{-\\alpha},$$ $$\\textrm{exp: } w_{ij} = \\exp(-\\alpha \\cdot d_{ij}),$$ $$\\textrm{dpd: } w_{ij} = \\left[1 - \\left(d_{ij}/d_{\\textrm{max}}\\right)^{\\alpha}\\right]^{\\alpha},$$ latter leads \\(w_{ij} = 0\\) \\(d_{ij} > d_{\\textrm{max}}\\). Note IDW weights show extreme behaviour close 0 can take value infinity. cases, infinite values replaced largest finite weight present weights list. default coding scheme “raw”, outputs raw distance-based weights without applying kind normalisation. addition, coding scheme styles also available nb2listw function can chosen. B basic binary coding, W row standardised (sums links n), C globally standardised (sums links n), U equal C divided number neighbours (sums links unity), S variance-stabilising coding scheme proposed Tiefelsdorf et al. 1999, p. 167-168 (sums links n). “minmax” style based Kelejian Prucha (2010), divides weights minimum maximum row sums maximum column sums input weights. similar C U styles; also available Stata. zero.policy set TRUE, weights vectors zero length inserted regions without neighbour neighbours list. turn generate lag values zero, equivalent sum products zero row t(rep(0, length=length(neighbours))) %*% x, arbitraty numerical vector x length length(neighbours). spatially lagged value x zero-neighbour region zero, may (may ) sensible choice.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"listw object following members: style one W, B, C, U, S, minmax type one idw, exp, dpd neighbours input neighbours list weights weights neighbours chosen style, attributes set report type relationships (binary general, general form glist argument), style ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"Tiefelsdorf, M., Griffith, D. ., Boots, B. 1999 variance-stabilizing coding scheme spatial link matrices, Environment Planning , 31, pp. 165–180; Kelejian, H. H., . R. Prucha. 2010. Specification estimation spatial autoregressive models autoregressive heteroskedastic disturbances. Journal Econometrics, 157: pp. 53–67.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"Rene Westerholt rene.westerholt@tu-dortmund.de","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"","code":"# World examples data(world, package=\"spData\") # neighbours on distance interval [0, 1000] kilometres # suppressWarnings(st_crs(world) <- \"+proj=longlat\") # for older PROJ pts <- st_centroid(st_transform(world, 3857)) #> Warning: st_centroid assumes attributes are constant over geometries nb_world <- dnearneigh(pts, 0, 1000000) #> Warning: neighbour object has 46 sub-graphs # Moran's I (life expectancy) with IDW with alpha = 2, no coding scheme world_weights <- nb2listwdist(nb_world, as(pts, \"Spatial\"), type = \"idw\", alpha = 2, zero.policy = TRUE) moran.test(world$lifeExp, world_weights, zero.policy = TRUE, na.action = na.pass) #> Warning: NAs in lagged values #> #> \tMoran I test under randomisation #> #> data: world$lifeExp #> weights: world_weights #> n reduced by no-neighbour observations #> #> Moran I statistic standard deviate = 2.7769, p-value = 0.002744 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.473883371 -0.007042254 0.029994057 #> # \\dontrun{ # Moran's I (life expectancy) with IDW with alpha = 2, no coding scheme world_weights <- nb2listwdist(nb_world, pts, type = \"idw\", alpha = 2, zero.policy = TRUE) moran.test(world$lifeExp, world_weights, zero.policy = TRUE, na.action = na.pass) #> Warning: NAs in lagged values #> #> \tMoran I test under randomisation #> #> data: world$lifeExp #> weights: world_weights #> n reduced by no-neighbour observations #> #> Moran I statistic standard deviate = 2.7769, p-value = 0.002744 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.473883371 -0.007042254 0.029994057 #> # Moran's I (life expectancy), DPD, alpha = 2, dmax = 1000 km, no coding scheme world_weights <- nb2listwdist(nb_world, pts, type = \"dpd\", dmax = 1000000, alpha = 2, zero.policy = TRUE) moran.test(world$lifeExp, world_weights, zero.policy = TRUE, na.action = na.pass) #> Warning: NAs in lagged values #> #> \tMoran I test under randomisation #> #> data: world$lifeExp #> weights: world_weights #> n reduced by no-neighbour observations #> #> Moran I statistic standard deviate = 8.8557, p-value < 2.2e-16 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.601498970 -0.007042254 0.004722063 #> # Boston examples data(boston, package=\"spData\") boston_coords <- data.frame(x = boston.utm[,1], y = boston.utm[,2]) boston.geoms <- st_as_sf(boston_coords, coords = c(\"x\", \"y\"), remove = FALSE) nb_boston <- dnearneigh(boston.geoms, 0, 3) #> Warning: neighbour object has 9 sub-graphs # Moran's I (crime) with exp weights with alpha = 2, no coding scheme boston_weights <- nb2listwdist(nb_boston, boston.geoms, type = \"exp\", alpha = 2, style=\"raw\", zero.policy = TRUE) moran.test(boston.c$CRIM, boston_weights, zero.policy = TRUE, na.action = na.pass) #> #> \tMoran I test under randomisation #> #> data: boston.c$CRIM #> weights: boston_weights #> n reduced by no-neighbour observations #> #> Moran I statistic standard deviate = 51.34, p-value < 2.2e-16 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.8845114518 -0.0019960080 0.0002981586 #> # Moran's I (crime) with idw weights with alpha = 2, coding scheme = W boston_weights <- nb2listwdist(nb_boston, boston.geoms, type = \"idw\", alpha = 2, style=\"W\", zero.policy = TRUE) moran.test(boston.c$CRIM, boston_weights, zero.policy = TRUE, na.action = na.pass) #> #> \tMoran I test under randomisation #> #> data: boston.c$CRIM #> weights: boston_weights #> n reduced by no-neighbour observations #> #> Moran I statistic standard deviate = 18.976, p-value < 2.2e-16 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.4392852330 -0.0019960080 0.0005408065 #> # }"},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial weights matrices for neighbours lists — nb2mat","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"function generates weights matrix neighbours list spatial weights chosen coding scheme.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"","code":"nb2mat(neighbours, glist=NULL, style=\"W\", zero.policy=NULL) listw2mat(listw)"},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"neighbours object class nb glist list general weights corresponding neighbours style style can take values W, B, C, S zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors listw listw object example nb2listw","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"Starting binary neighbours list, regions either listed neighbours absent (thus set neighbours definition), function creates n n weights matrix values given coding scheme style chosen. B basic binary coding, W row standardised, C globally standardised, S variance-stabilizing coding scheme proposed Tiefelsdorf et al. 1999, p. 167-168. function leaves matrix rows zero regions zero neighbours fore zero.policy TRUE. turn generate lag values zero, equivalent sum products zero row t(rep(0, length=length(neighbours))) %*% x, arbitraty numerical vector x length length(neighbours). spatially lagged value x zero-neighbour region zero, may (may ) sensible choice.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"n n matrix, n=length(neighbours)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"Tiefelsdorf, M., Griffith, D. ., Boots, B. 1999 variance-stabilizing coding scheme spatial link matrices, Environment Planning , 31, pp. 165-180.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col005 <- dnearneigh(st_coordinates(st_centroid(st_geometry(columbus), of_largest_polygon=TRUE)), 0, 0.5, as.character(columbus$NEIGNO)) #> Warning: neighbour object has 8 sub-graphs summary(col005) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 170 #> Percentage nonzero weights: 7.080383 #> Average number of links: 3.469388 #> 4 regions with no links: #> 1005, 1006, 1008, 1043 #> 8 disjoint connected subgraphs #> Link number distribution: #> #> 0 1 2 3 4 5 6 7 8 9 #> 4 11 5 8 3 9 2 2 3 2 #> 11 least connected regions: #> 1001 1007 1018 1010 1045 1044 1046 1047 1049 1048 1015 with 1 link #> 2 most connected regions: #> 1038 1036 with 9 links col005.w.mat <- nb2mat(col005, style=\"B\", zero.policy=TRUE) table(round(rowSums(col005.w.mat))) #> #> 0 1 2 3 4 5 6 7 8 9 #> 4 11 5 8 3 9 2 2 3 2"},{"path":"https://r-spatial.github.io/spdep/reference/nbcosts.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute cost of edges — nbcosts","title":"Compute cost of edges — nbcosts","text":"cost edge distance nodes. function compute distance using data.frame observations vector node.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbcosts.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute cost of edges — nbcosts","text":"","code":"nbcost(data, id, id.neigh, method = c(\"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\", \"minkowski\", \"mahalanobis\"), p = 2, cov, inverted = FALSE) nbcosts(nb, data, method = c(\"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\", \"minkowski\", \"mahalanobis\"), p = 2, cov, inverted = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/nbcosts.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute cost of edges — nbcosts","text":"nb object nb class. See poly2nb details. data matrix observations nodes. id Node index compute cost id.neigh Idex neighbours nodes node id method Character function declare distance method. method character, method must \"mahalanobis\" \"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\" \"minkowisk\". method one \"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\" \"minkowisk\", see dist details, function used compute distance. method=\"mahalanobis\", mahalanobis distance computed neighbour areas. method function, function used compute distance. p power Minkowski distance. cov covariance matrix used compute mahalanobis distance. inverted logical. 'TRUE', 'cov' supposed contain inverse covariance matrix.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbcosts.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute cost of edges — nbcosts","text":"object nbdist class. See nbdists details.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbcosts.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Compute cost of edges — nbcosts","text":"neighbours must connected graph.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbcosts.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute cost of edges — nbcosts","text":"Elias T. Krainski Renato M. Assuncao","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nbdists.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial link distance measures — nbdists","title":"Spatial link distance measures — nbdists","text":"Given list spatial neighbour links (neighbours list object type nb), function returns Euclidean distances along links list form neighbours list. longlat = TRUE, Great Circle distances used.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbdists.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial link distance measures — nbdists","text":"","code":"nbdists(nb, coords, longlat = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/nbdists.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial link distance measures — nbdists","text":"nb object class nb coords matrix point coordinates, object inheriting SpatialPoints \"sf\" \"sfc\" object; \"sf\" \"sfc\" object geometries geographical coordinates (sf::st_is_longlat(x) == TRUE sf::sf_use_s2() == TRUE), s2 used find distances https://github.com/r-spatial/s2/issues/125 longlat TRUE point coordinates longitude-latitude decimal degrees, case distances measured kilometers; coords SpatialPoints object, value taken object ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbdists.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial link distance measures — nbdists","text":"list class nbdist","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbdists.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial link distance measures — nbdists","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nbdists.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial link distance measures — nbdists","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries dlist <- nbdists(col.gal.nb, coords) dlist <- lapply(dlist, function(x) 1/x) stem(unlist(dlist)) #> #> The decimal point is at the | #> #> 1 | 1111112222223333334444444444 #> 1 | 555555556666667777777777888888888899999999999999999999 #> 2 | 00000000111111111111111122222222222222333333333333334444 #> 2 | 55555555556666666666666677777777888888999999 #> 3 | 0000111111222233334444 #> 3 | 77779999 #> 4 | 223344 #> 4 | 77 #> 5 | 001144 #> 5 | #> 6 | #> 6 | 99 #> 7 | #> 7 | 88 #>"},{"path":"https://r-spatial.github.io/spdep/reference/nblag.html","id":null,"dir":"Reference","previous_headings":"","what":"Higher order neighbours lists — nblag","title":"Higher order neighbours lists — nblag","text":"function creates higher order neighbour lists, higher order neighbours lags links graph described input neighbours list. refuse lag neighbours lists attribute self.included set TRUE. nblag_cumul cumulates neighbour lists single neighbour list (“nb” object).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nblag.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Higher order neighbours lists — nblag","text":"","code":"nblag(neighbours, maxlag) nblag_cumul(nblags)"},{"path":"https://r-spatial.github.io/spdep/reference/nblag.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Higher order neighbours lists — nblag","text":"neighbours input neighbours list class nb maxlag maximum lag constructed nblags list neighbour lists output nblag","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nblag.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Higher order neighbours lists — nblag","text":"returns list lagged neighbours lists class nb","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nblag.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Higher order neighbours lists — nblag","text":"Roger Bivand Roger.Bivand@nhh.Giovanni Millo","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nblag.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Higher order neighbours lists — nblag","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries summary(col.gal.nb, coords) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> Link number distribution: #> #> 2 3 4 5 6 7 8 9 10 #> 7 7 13 4 9 6 1 1 1 #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links col.lags <- nblag(col.gal.nb, 2) print(col.lags) #> [[1]] #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> #> [[2]] #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 406 #> Percentage nonzero weights: 16.90962 #> Average number of links: 8.285714 #> #> attr(,\"call\") #> nblag(neighbours = col.gal.nb, maxlag = 2) summary(col.lags[[2]], coords) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 406 #> Percentage nonzero weights: 16.90962 #> Average number of links: 8.285714 #> Link number distribution: #> #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 #> 1 2 5 4 2 3 5 4 2 3 7 3 4 1 1 1 1 #> 1 least connected region: #> 36 with 1 link #> 1 most connected region: #> 25 with 17 links plot(st_geometry(columbus), border=\"grey\") plot(col.gal.nb, coords, add=TRUE) title(main=\"GAL order 1 (black) and 2 (red) links\") plot(col.lags[[2]], coords, add=TRUE, col=\"red\", lty=2) cuml <- nblag_cumul(col.lags) cuml #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 636 #> Percentage nonzero weights: 26.48896 #> Average number of links: 12.97959 run <- FALSE if (require(igraph, quietly=TRUE) && require(spatialreg, quietly=TRUE)) run <- TRUE if (run) { W <- as(nb2listw(col.gal.nb), \"CsparseMatrix\") G <- graph_from_adjacency_matrix(W, mode=\"directed\", weight=\"W\") D <- diameter(G) nbs <- nblag(col.gal.nb, maxlag=D) n <- length(col.gal.nb) lmat <- lapply(nbs, nb2mat, style=\"B\", zero.policy=TRUE) mat <- matrix(0, n, n) for (i in seq(along=lmat)) mat = mat + i*lmat[[i]] G2 <- distances(G) print(all.equal(G2, mat, check.attributes=FALSE)) } #> Warning: lag 6 neighbour object has 5 sub-graphs #> Warning: lag 7 neighbour object has 20 sub-graphs #> Warning: lag 8 neighbour object has 36 sub-graphs #> Warning: lag 9 neighbour object has 44 sub-graphs #> [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":null,"dir":"Reference","previous_headings":"","what":"Set operations on neighborhood objects — nb.set.operations","title":"Set operations on neighborhood objects — nb.set.operations","text":"Performs set operations neighbors list objects union, intersection, (asymmetric!) difference complement; note 1.3-9, setdiff.nb behaves like setdiff, ordering objects compared matters - (asymmetric!) difference.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Set operations on neighborhood objects — nb.set.operations","text":"","code":"intersect.nb(nb.obj1,nb.obj2) union.nb(nb.obj1,nb.obj2) setdiff.nb(nb.obj1,nb.obj2) complement.nb(nb.obj)"},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Set operations on neighborhood objects — nb.set.operations","text":"nb.obj neighbor list created neighborhood list funtions nb.obj1 neighbor list created neighborhood list funtions nb.obj2 neighbor list created neighborhood list funtions","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Set operations on neighborhood objects — nb.set.operations","text":"functions perform set operations element neighborlist. arguments must neighbor lists created spatial objects, checked region.id attributes required identical.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Set operations on neighborhood objects — nb.set.operations","text":"new neighborlist created set operations input neighbor list(s)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Set operations on neighborhood objects — nb.set.operations","text":"Nicholas Lewin-Koh nikko@hailmail.net","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Set operations on neighborhood objects — nb.set.operations","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries col.tri.nb <- tri2nb(coords) oldpar <- par(mfrow=c(1,2)) if (require(\"dbscan\", quietly=TRUE)) { col.soi.nb <- graph2nb(soi.graph(col.tri.nb, coords)) plot(st_geometry(columbus), border=\"grey\") plot(col.soi.nb, coords, add=TRUE) title(main=\"Sphere of Influence Graph\", cex.main=0.7) plot(st_geometry(columbus), border=\"grey\") plot(complement.nb(col.soi.nb), coords, add=TRUE) title(main=\"Complement of Sphere of Influence Graph\", cex.main=0.7) } par(mfrow=c(2,2)) col2 <- droplinks(col.gal.nb, 21) #> Warning: some observations have no neighbours #> Warning: neighbour object has 3 sub-graphs plot(intersect.nb(col.gal.nb, col2), coords) #> Warning: neighbour object has 3 sub-graphs title(main=\"Intersect\", cex.main=0.7) plot(union.nb(col.gal.nb, col2), coords) title(main=\"Union\", cex.main=0.7) plot(setdiff.nb(col.gal.nb, col2), coords) #> Warning: neighbour object has 46 sub-graphs title(main=\"Set diff\", cex.main=0.7) par(oldpar)"},{"path":"https://r-spatial.github.io/spdep/reference/p.adjustSP.html","id":null,"dir":"Reference","previous_headings":"","what":"Adjust local association measures' p-values — p.adjustSP","title":"Adjust local association measures' p-values — p.adjustSP","text":"Make adjustment local association measures' p-values based number neighbours (+1) region, rather total number regions.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/p.adjustSP.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Adjust local association measures' p-values — p.adjustSP","text":"","code":"p.adjustSP(p, nb, method = \"none\")"},{"path":"https://r-spatial.github.io/spdep/reference/p.adjustSP.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Adjust local association measures' p-values — p.adjustSP","text":"p vector p-values nb list neighbours class nb method correction method defined p.adjust: \"adjustment methods include Bonferroni correction ('\"bonferroni\"') p-values multiplied number comparisons. Four less conservative corrections also included Holm (1979) ('holm'), Hochberg (1988) ('hochberg'), Hommel (1988) ('hommel') Benjamini & Hochberg (1995) ('fdr'), respectively. pass-option ('none') also included.\"","code":""},{"path":"https://r-spatial.github.io/spdep/reference/p.adjustSP.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Adjust local association measures' p-values — p.adjustSP","text":"vector corrected p-values using number neighbours + 1.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/p.adjustSP.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Adjust local association measures' p-values — p.adjustSP","text":"Danlin Yu Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/p.adjustSP.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Adjust local association measures' p-values — p.adjustSP","text":"","code":"data(afcon, package=\"spData\") oid <- order(afcon$id) resG <- as.vector(localG(afcon$totcon, nb2listw(include.self(paper.nb)))) non <- format.pval(pnorm(2*(abs(resG)), lower.tail=FALSE), 2) bon <- format.pval(p.adjustSP(pnorm(2*(abs(resG)), lower.tail=FALSE), paper.nb, \"bonferroni\"), 2) tot <- format.pval(p.adjust(pnorm(2*(abs(resG)), lower.tail=FALSE), \"bonferroni\", n=length(resG)), 2) data.frame(resG, non, bon, tot, row.names=afcon$name)[oid,] #> resG non bon tot #> THE GAMBIA -0.98383592 0.02455 0.04911 1.0000 #> MALI -1.69893391 0.00034 0.00272 0.0143 #> SENEGAL -1.46321911 0.00171 0.00857 0.0720 #> BENIN -1.30139679 0.00462 0.02312 0.1942 #> MAURITANIA -0.60496775 0.11315 0.56576 1.0000 #> NIGER -1.04877003 0.01797 0.14378 0.7549 #> IVORY COAST -1.41712454 0.00230 0.01378 0.0965 #> GUINEA -1.44888005 0.00188 0.01128 0.0789 #> BURKINA FASO -1.75085492 0.00023 0.00162 0.0097 #> LIBERIA -1.04053617 0.01871 0.07485 0.7860 #> SIERRA LEONE -0.87032623 0.04087 0.12262 1.0000 #> GHANA -1.10269327 0.01371 0.05485 0.5760 #> TOGO -0.99053008 0.02379 0.09517 0.9993 #> CAMEROON -1.13328519 0.01171 0.07025 0.4917 #> NIGERIA -1.17261672 0.00951 0.04754 0.3993 #> GABON -0.78935857 0.05720 0.17160 1.0000 #> CENTRAL AFRICAN REPUBLIC 1.17349763 0.00946 0.05678 0.3974 #> CHAD 0.46259185 0.17744 1.00000 1.0000 #> CONGO -0.20253005 0.34272 1.00000 1.0000 #> ZAIRE 2.02270432 2.6e-05 0.00026 0.0011 #> ANGOLA 1.23450728 0.00677 0.02710 0.2845 #> UGANDA 3.33600851 1.3e-11 7.6e-11 5.3e-10 #> KENYA 3.50301896 1.2e-12 7.4e-12 5.1e-11 #> TANZANIA 1.09843592 0.01401 0.12613 0.5886 #> BURUNDI 0.77417084 0.06077 0.24308 1.0000 #> RWANDA 1.45720776 0.00178 0.00891 0.0748 #> SOMALIA 1.18316273 0.00898 0.02695 0.3773 #> ETHIOPIA 2.62720027 7.4e-08 3.0e-07 3.1e-06 #> ZAMBIA 0.75273285 0.06610 0.59492 1.0000 #> ZIMBABWE -0.19956472 0.34490 1.00000 1.0000 #> MALAWI 0.21195283 0.33582 1.00000 1.0000 #> MOZAMBIQUE -0.28761679 0.28257 1.00000 1.0000 #> SOUTH AFRICA -0.86814954 0.04126 0.33004 1.0000 #> LESOTHO -0.29841469 0.27531 0.55062 1.0000 #> BOTSWANA 0.04090396 0.46740 1.00000 1.0000 #> SWAZILAND -0.65938417 0.09362 0.28087 1.0000 #> MOROCCO 0.02191606 0.48252 1.00000 1.0000 #> ALGERIA -0.36307938 0.23387 1.00000 1.0000 #> TUNISIA 0.57910139 0.12339 0.37017 1.0000 #> LIBYA 2.55272169 1.7e-07 1.2e-06 6.9e-06 #> SUDAN 4.03925235 3.3e-16 3.0e-15 1.4e-14 #> EGYPT 4.42133637 < 2e-16 < 2e-16 < 2e-16"},{"path":"https://r-spatial.github.io/spdep/reference/plot.mst.html","id":null,"dir":"Reference","previous_headings":"","what":"Plot the Minimum Spanning Tree — plot.mst","title":"Plot the Minimum Spanning Tree — plot.mst","text":"function plots MST, nodes circles edges segments.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/plot.mst.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Plot the Minimum Spanning Tree — plot.mst","text":"","code":"# S3 method for class 'mst' plot(x, coords, label.areas = NULL, cex.circles = 1, cex.labels = 1, add=FALSE, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/plot.mst.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Plot the Minimum Spanning Tree — plot.mst","text":"x Object mst class. coords two column matrix coordinates nodes. label.areas vector labels nodes cex.circles length circles plot. cex.labels length nodes labels ploted. add default FALSE, create new plot ... arguments passed plotting functions.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/plot.mst.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Plot the Minimum Spanning Tree — plot.mst","text":"Elias T. Krainski Renato M. Assuncao","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/plot.mst.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Plot the Minimum Spanning Tree — plot.mst","text":"","code":"### see example in mstree function documentation"},{"path":"https://r-spatial.github.io/spdep/reference/plot.nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Plot a neighbours list — plot.nb","title":"Plot a neighbours list — plot.nb","text":"function plot neighbours list given point coordinates represent region two dimensions; plot.listw wrapper passes neighbours component plot.nb.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/plot.nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Plot a neighbours list — plot.nb","text":"","code":"# S3 method for class 'nb' plot(x, coords, col=\"black\", points=TRUE, add=FALSE, arrows=FALSE, length=0.1, xlim=NULL, ylim=NULL, ...) # S3 method for class 'listw' plot(x, coords, col=\"black\", points=TRUE, add=FALSE, arrows=FALSE, length=0.1, xlim=NULL, ylim=NULL, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/plot.nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Plot a neighbours list — plot.nb","text":"x object class nb (plot.listw) class listw coords matrix region point coordinates, Spatial object (points polygons), sfc object (points polygons) col plotting colour points (logical) add points plot add (logical) add existing plot arrows (logical) draw arrowheads asymmetric neighbours length length plot inches arrow heads drawn asymmetric neighbours lists xlim, ylim plot window bounds ... graphical parameters par(..)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/plot.nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Plot a neighbours list — plot.nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/plot.nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Plot a neighbours list — plot.nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) plot(col.gal.nb, st_geometry(columbus)) title(main=\"GAL order 1 links with first nearest neighbours in red\", cex.main=0.6) plot(col.gal.nb, as(columbus, \"Spatial\")) title(main=\"GAL order 1 links with first nearest neighbours in red\", cex.main=0.6) coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE) col.knn <- knearneigh(coords, k=1) plot(knn2nb(col.knn), coords, add=TRUE, col=\"red\", length=0.08) #> Warning: neighbour object has 13 sub-graphs"},{"path":"https://r-spatial.github.io/spdep/reference/plot.skater.html","id":null,"dir":"Reference","previous_headings":"","what":"Plot the object of skater class — plot.skater","title":"Plot the object of skater class — plot.skater","text":"function displays results skater function. subgraphs plotted different colours.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/plot.skater.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Plot the object of skater class — plot.skater","text":"","code":"# S3 method for class 'skater' plot(x, coords, label.areas = NULL, groups.colors, cex.circles = 1, cex.labels = 1, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/plot.skater.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Plot the object of skater class — plot.skater","text":"x object skater class. coords matrix two colums coordinates nodes. label.areas vector labels nodes. groups.colors vector colors groups ou sub-graphs. cex.circles length circles represent nodes. cex.labels length labels nodes. ... arguments passed plotting funcitons.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/plot.skater.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Plot the object of skater class — plot.skater","text":"Elias T. Krainski Renato M. Assuncao","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/plot.skater.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Plot the object of skater class — plot.skater","text":"","code":"### see example in the skater function documentation"},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Construct neighbours list from polygon list — poly2nb","title":"Construct neighbours list from polygon list — poly2nb","text":"function builds neighbours list based regions contiguous boundaries, sharing one boundary point. current function part interpreted may run slowly many regions detailed boundaries, 0.2-16 fail lack memory single polygons built many border coordinates.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Construct neighbours list from polygon list — poly2nb","text":"","code":"poly2nb(pl, row.names = NULL, snap=NULL, queen=TRUE, useC=TRUE, foundInBox=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Construct neighbours list from polygon list — poly2nb","text":"pl list polygons class extending SpatialPolygons, sf sfc object containing non-empty (multi-)polygon objects row.names character vector region ids added neighbours list attribute region.id, default seq(1, nrow(x)); pl row.names, used instead default sequence. snap boundary points less snap distance apart considered indicate contiguity; used find candidate actual neighbours planar geometries, actual neighbours spherical geometries, spherical spatial indexing injects fuzzyness. set, SpatialPolygons objects, default sqrt(.Machine$double.eps), value also used sf objects coordinate reference system. sf objects defined coordinate reference system, default value 1e-7 geographical coordinates (approximately 10mm), 10mm projected coordinates metre units, converted 10mm distance units coordinates. conversion fail, snap reverts sqrt(.Machine$double.eps). queen TRUE, single shared boundary point meets contiguity condition, FALSE, one shared point required; note one shared boundary point necessarily mean shared boundary line useC default TRUE, work loop C, may set false revert R code calling two C functions n*k work loop, k average number candidate neighbours foundInBox default NULL using R code st_intersects() generate candidate neighbours (using snap= geometries spherical); NULL (legacy purposes) list length (n-1) integer vectors candidate neighbours (j > ) (created poly_findInBoxGEOS function rgeos clean polygons)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Construct neighbours list from polygon list — poly2nb","text":"neighbours list class nb. See card details “nb” objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Construct neighbours list from polygon list — poly2nb","text":"0.5-8, function includes faster bounding box indexing improvements contributed Micah Altman. cluster provided using set.ClusterOption, used finding candidate bounding box overlaps exact testing contiguity. 1.1-7, sf polygons included start end points, erroneously report queen neighbourhood rook present, see https://github.com/r-spatial/spdep/issues/50. 1.1-9 sf 1.0-0, s2 used bounding box indexing internally pl geographical coordinates. topology engine s2 differs use GEOS planar coordinates sf, output differences may expected. Since treating spherical geometries planar also questionable, clear whether spherical contiguous polygon neighbours simply follow neighbours found treating geometries planar https://github.com/r-spatial/s2/issues/125#issuecomment-864403372. However, current advice necessarily use s2 finding contiguity neighbours, least check output.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Construct neighbours list from polygon list — poly2nb","text":"Roger Bivand Roger.Bivand@nhh.contributions Micah Altman","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Construct neighbours list from polygon list — poly2nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(st_geometry(columbus))) xx <- poly2nb(as(columbus, \"Spatial\")) dxx <- diffnb(xx, col.gal.nb) #> Warning: neighbour object has 46 sub-graphs plot(st_geometry(columbus), border=\"grey\") plot(col.gal.nb, coords, add=TRUE) plot(dxx, coords, add=TRUE, col=\"red\") title(main=paste(\"Differences (red) in Columbus GAL weights (black)\", \"and polygon generated queen weights\", sep=\"\\n\"), cex.main=0.6) # poly2nb with sf sfc_MULTIPOLYGON objects sf_xx <- poly2nb(columbus) diffnb(sf_xx, xx) #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 0 #> Percentage nonzero weights: 0 #> Average number of links: 0 #> 49 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 #> 49 disjoint connected subgraphs sfc_xx <- poly2nb(st_geometry(columbus)) diffnb(sfc_xx, xx) #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 0 #> Percentage nonzero weights: 0 #> Average number of links: 0 #> 49 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 #> 49 disjoint connected subgraphs xxx <- poly2nb(as(columbus, \"Spatial\"), queen=FALSE) dxxx <- diffnb(xxx, col.gal.nb) #> Warning: neighbour object has 34 sub-graphs plot(st_geometry(columbus), border = \"grey\") plot(col.gal.nb, coords, add = TRUE) plot(dxxx, coords, add = TRUE, col = \"red\") title(main=paste(\"Differences (red) in Columbus GAL weights (black)\", \"and polygon generated rook weights\", sep=\"\\n\"), cex.main=0.6) cards <- card(xx) maxconts <- which(cards == max(cards)) if(length(maxconts) > 1) maxconts <- maxconts[1] fg <- rep(\"grey\", length(cards)) fg[maxconts] <- \"red\" fg[xx[[maxconts]]] <- \"green\" plot(st_geometry(columbus), col=fg) title(main=\"Region with largest number of contiguities\", cex.main=0.6) nc.sids <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\")[1], quiet=TRUE) system.time(xxnb <- poly2nb(nc.sids)) #> user system elapsed #> 0.065 0.000 0.066 system.time(xxnb <- poly2nb(as(nc.sids, \"Spatial\"))) #> user system elapsed #> 0.085 0.000 0.086 plot(st_geometry(nc.sids)) plot(xxnb, st_coordinates(st_centroid(nc.sids)), add=TRUE, col=\"blue\") #> Warning: st_centroid assumes attributes are constant over geometries sq <- st_polygon(list(rbind(c(0,0), c(1,0), c(1,1), c(0,1), c(0,0)))) sq2 <- sq + c(0,1) sq3 <- sq + c(1,0) sq4 <- sq + c(1,1) gm <- st_sfc(list(sq, sq2, sq3, sq4)) df <- st_as_sf(data.frame(gm, id=1:4)) plot(st_geometry(df)) text(st_coordinates(st_centroid(gm)), as.character(df$id)) unclass(poly2nb(df, queen = FALSE)) #> [[1]] #> [1] 2 3 #> #> [[2]] #> [1] 1 4 #> #> [[3]] #> [1] 1 4 #> #> [[4]] #> [1] 2 3 #> #> attr(,\"region.id\") #> [1] \"1\" \"2\" \"3\" \"4\" #> attr(,\"call\") #> poly2nb(pl = df, queen = FALSE) #> attr(,\"type\") #> [1] \"rook\" #> attr(,\"snap\") #> [1] 1.490116e-08 #> attr(,\"sym\") #> [1] TRUE #> attr(,\"ncomp\") #> attr(,\"ncomp\")$nc #> [1] 1 #> #> attr(,\"ncomp\")$comp.id #> [1] 1 1 1 1 #> col_geoms <- st_geometry(columbus) col_geoms[1] <- st_buffer(col_geoms[1], dist=-0.05) st_geometry(columbus) <- col_geoms poly2nb(columbus) #> Warning: some observations have no neighbours; #> if this seems unexpected, try increasing the snap argument. #> Warning: neighbour object has 2 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 232 #> Percentage nonzero weights: 9.662641 #> Average number of links: 4.734694 #> 1 region with no links: #> 1 #> 2 disjoint connected subgraphs"},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":null,"dir":"Reference","previous_headings":"","what":"Probability mapping for rates — probmap","title":"Probability mapping for rates — probmap","text":"function returns data frame rates counts populations risk crude rates, expected counts cases, relative risks, Poisson probabilities.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Probability mapping for rates — probmap","text":"","code":"probmap(n, x, row.names=NULL, alternative=\"less\")"},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Probability mapping for rates — probmap","text":"n numeric vector counts cases x numeric vector populations risk row.names row names passed output data frame alternative default “less”, may set “greater”","code":""},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Probability mapping for rates — probmap","text":"function returns data frame, rates may mapped class intervals chosen. class intervals used examples mostly taken referenced source.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Probability mapping for rates — probmap","text":"raw raw (crude) rates expCount expected counts cases assuming global rate relRisk relative risks: ratio observed expected counts cases multiplied 100 pmap Poisson probability map values: probablility getting “extreme” count actually observed - one-tailed, default alternative observed “less” expected","code":""},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Probability mapping for rates — probmap","text":"Bailey T, Gatrell (1995) Interactive Spatial Data Analysis, Harlow: Longman, pp. 300–303.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Probability mapping for rates — probmap","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Probability mapping for rates — probmap","text":"","code":"auckland <- st_read(system.file(\"shapes/auckland.gpkg\", package=\"spData\")[1], quiet=TRUE) res <- probmap(auckland$M77_85, 9*auckland$Und5_81) rt <- sum(auckland$M77_85)/sum(9*auckland$Und5_81) ppois_pmap <- numeric(length(auckland$Und5_81)) for (i in seq(along=ppois_pmap)) { ppois_pmap[i] <- poisson.test(auckland$M77_85[i], r=rt, T=(9*auckland$Und5_81[i]), alternative=\"less\")$p.value all.equal(ppois_pmap, res$pmap) } res$id <- 1:nrow(res) auckland$id <- res$id <- 1:nrow(res) auckland_res <- merge(auckland, res, by=\"id\") plot(auckland_res[, \"raw\"], main=\"Crude (raw) estimates\") plot(auckland_res[, \"relRisk\"], main=\"Standardised mortality ratios\") plot(auckland_res[, \"pmap\"], main=\"Poisson probabilities\", breaks=c(0, 0.05, 0.1, 0.5, 0.9, 0.95, 1))"},{"path":"https://r-spatial.github.io/spdep/reference/prunecost.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute cost of prune each edge — prunecost","title":"Compute cost of prune each edge — prunecost","text":"edge dropped, MST pruned. generate two subgraphs. , makes tree graphs tree dissimilarity values computed, one graph. dissimilarity sum sqared differences observactions nodes mean vector observations graph. dissimilarity original graph sum dissimilarity subgraphs returned.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/prunecost.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute cost of prune each edge — prunecost","text":"","code":"prunecost(edges, data, method = c(\"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\", \"minkowski\", \"mahalanobis\"), p = 2, cov, inverted = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/prunecost.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute cost of prune each edge — prunecost","text":"edges matrix 2 colums row one edge data data.frame observations nodes. method Character function declare distance method. method character, method must \"mahalanobis\" \"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\" \"minkowisk\". method one \"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\" \"minkowisk\", see dist details, function used compute distance. method=\"mahalanobis\", mahalanobis distance computed neighbour areas. method function, function used compute distance. p power Minkowski distance. cov covariance matrix used compute mahalanobis distance. inverted logical. 'TRUE', 'cov' supposed contain inverse covariance matrix.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/prunecost.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute cost of prune each edge — prunecost","text":"vector differences dissimilarity nodes dissimilarity sum subgraphs obtained pruning one edge time.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/prunecost.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute cost of prune each edge — prunecost","text":"Elias T. Krainski Renato M. Assuncao","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/prunecost.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute cost of prune each edge — prunecost","text":"","code":"d <- data.frame(a=-2:2, b=runif(5)) e <- matrix(c(1,2, 2,3, 3,4, 4,5), ncol=2, byrow=TRUE) sum(sweep(d, 2, colMeans(d))^2) #> [1] 10.35574 prunecost(e, d) #> [1] 2.138259 2.875555 2.820048 2.169740"},{"path":"https://r-spatial.github.io/spdep/reference/prunemst.html","id":null,"dir":"Reference","previous_headings":"","what":"Prune a Minimun Spanning Tree — prunemst","title":"Prune a Minimun Spanning Tree — prunemst","text":"function deletes first edge makes two subsets edges. subset Minimun Spanning Treee.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/prunemst.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Prune a Minimun Spanning Tree — prunemst","text":"","code":"prunemst(edges, only.nodes = TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/prunemst.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Prune a Minimun Spanning Tree — prunemst","text":"edges matrix two colums row one edge .nodes .nodes=FALSE, return edges nodes MST resulted. .nodes=TRUE, return two sets nodes. Defalt TRUE","code":""},{"path":"https://r-spatial.github.io/spdep/reference/prunemst.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Prune a Minimun Spanning Tree — prunemst","text":"list length two. .nodes=TRUE element vector nodes. .nodes=FALSE element list nodes edges.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/prunemst.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Prune a Minimun Spanning Tree — prunemst","text":"Elias T. Krainski Renato M. Assuncao","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/prunemst.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Prune a Minimun Spanning Tree — prunemst","text":"","code":"e <- matrix(c(2,3, 1,2, 3,4, 4,5), ncol=2, byrow=TRUE) e #> [,1] [,2] #> [1,] 2 3 #> [2,] 1 2 #> [3,] 3 4 #> [4,] 4 5 prunemst(e) #> $node1 #> [1] 2 1 #> #> $node2 #> [1] 3 4 5 #> prunemst(e, only.nodes=FALSE) #> [[1]] #> [[1]]$node #> [1] 2 1 #> #> [[1]]$edge #> [,1] [,2] #> [1,] 1 2 #> #> #> [[2]] #> [[2]]$node #> [1] 3 4 5 #> #> [[2]]$edge #> [,1] [,2] #> [1,] 3 4 #> [2,] 4 5 #> #>"},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":null,"dir":"Reference","previous_headings":"","what":"Read a GAL lattice file into a neighbours list — read.gal","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"function read.gal() reads GAL lattice file neighbours list spatial analysis. read old new style (GeoDa) GAL files. function read.geoda helper file reading comma separated value data files, calling read.csv().","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"","code":"read.gal(file, region.id=NULL, override.id=FALSE) read.geoda(file, row.names=NULL, skip=0)"},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"file name file GAL lattice data region.id region IDs specified order coerse neighbours list order numbering region.id override.id override given (NULL) region.id, collecting region.id numbering order GAL file. row.names row.names read.csv(), typically character string naming column file used skip skip number lines, read.csv()","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"Luc Anselin (2003): Spatial Analysis Laboratory, Department Agricultural Consumer Economics, University Illinois, Urbana-Champaign, now dead link: http://www.csiss.org/gispopsci/workshops/2011/PSU/readings/W15_Anselin2007.pdf; Luc Anselin (2003) GeoDa 0.9 User's Guide, pp. 80–81, Spatial Analysis Laboratory, Department Agricultural Consumer Economics, University Illinois, Urbana-Champaign, http://geodacenter.github.io/docs/geoda093.pdf; GAL - Geographical Algorithms Library, University Newcastle","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"function read.gal() returns object class nb list integer vectors containing neighbour region number ids. function read.geoda returns data frame, issues warning returned object one column.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"Example data originally downloaded now dead link: http://sal.agecon.uiuc.edu/weights/zips/us48.zip","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"","code":"us48.fipsno <- read.geoda(system.file(\"etc/weights/us48.txt\", package=\"spdep\")[1]) us48.q <- read.gal(system.file(\"etc/weights/us48_q.GAL\", package=\"spdep\")[1], us48.fipsno$Fipsno) us48.r <- read.gal(system.file(\"etc/weights/us48_rk.GAL\", package=\"spdep\")[1], us48.fipsno$Fipsno) data(state) if (as.numeric(paste(version$major, version$minor, sep=\"\")) < 19) { m50.48 <- match(us48.fipsno$\"State.name\", state.name) } else { m50.48 <- match(us48.fipsno$\"State_name\", state.name) } plot(us48.q, as.matrix(as.data.frame(state.center))[m50.48,]) plot(diffnb(us48.r, us48.q), as.matrix(as.data.frame(state.center))[m50.48,], add=TRUE, col=\"red\") #> Warning: neighbour object has 46 sub-graphs title(main=\"Differences between rook and queen criteria imported neighbours lists\")"},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Read and write spatial neighbour files — read.gwt2nb","title":"Read and write spatial neighbour files — read.gwt2nb","text":"\"gwt\" functions read write GeoDa GWT files (example file baltk4.GWT downloaded site given reference), \"dat\" functions read write Matlab sparse matrix files used James LeSage's Spatial Econometrics Toolbox (example file wmat.dat downloaded site given reference). body files headers three columns separated white space, third column must numeric locale reading platform (correct decimal separator).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Read and write spatial neighbour files — read.gwt2nb","text":"","code":"read.gwt2nb(file, region.id=NULL) write.sn2gwt(sn, file, shpfile=NULL, ind=NULL, useInd=FALSE, legacy=FALSE) read.dat2listw(file) write.sn2dat(sn, file) read.swmdbf2listw(fn, region.id=NULL, style=NULL, zero.policy=NULL) read_swm_dbf(fn) write.swmdbf(listw, file, ind, region.id = attr(listw, \"region.id\")) write_swm_dbf(listw, file, ind, region.id = attr(listw, \"region.id\")) write.sn2DBF(sn, file)"},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Read and write spatial neighbour files — read.gwt2nb","text":"file, fn name file weights data region.id character vector region IDs - ArcGIS SWM DBFs, values must character integers (numbers starting zero) listw listw object sn spatial.neighbour object shpfile character string: given Shapefile name taken GWT file dataset ind character string: region id indicator field name useInd default FALSE, TRUE, write region.id attribute ID key tags output file (use OpenGeoDa depend shapefile field named ind argument matching exported tags) legacy default FALSE; TRUE, header single field number observations style default NULL, missing, set \"M\" warning given; \"M\", passed nb2listw re-build object zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Read and write spatial neighbour files — read.gwt2nb","text":"Attempts honour region.id argument given reading GWT SWM/DBF files. region IDs given region.id= match origins destinations GWT file, error warning thrown, considered carefully. read_swm_dbf simplified interface read.swmdbf2listw -neighbour observations present, advised region.id= given read.swmdbf2listw; function read correctly minimum maximum IDs present observations neighbours without region.id= set, reading using read.swmdbf2listw fail minimum maximum ID observations neighbours region.id= given.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Read and write spatial neighbour files — read.gwt2nb","text":"read.gwt2nb returns neighbour \"nb\" object generalised weights stored list element called \"dlist\" \"GeoDa\" attribute; read.swmdbf2listw returns \"listw\" object read DBF file exported ArcGIS SWM object.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Read and write spatial neighbour files — read.gwt2nb","text":"Luc Anselin (2003) GeoDa 0.9 User's Guide, pp. 80–81, Spatial Analysis Laboratory, Department Agricultural Consumer Economics, University Illinois, Urbana-Champaign, http://geodacenter.github.io/docs/geoda093.pdf; also material formerly spatial-econometrics.com/data/contents.html","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Read and write spatial neighbour files — read.gwt2nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Read and write spatial neighbour files — read.gwt2nb","text":"","code":"data(baltimore, package=\"spData\") STATION <- baltimore$STATION gwt1 <- read.gwt2nb(system.file(\"weights/baltk4.GWT\", package=\"spData\")[1], STATION) #> Warning: 102, 115, 208 are not destinations cat(paste(\"Neighbours list symmetry;\", is.symmetric.nb(gwt1, FALSE, TRUE), \"\\n\")) #> Neighbours list symmetry; FALSE listw1 <- nb2listw(gwt1, style=\"B\", glist=attr(gwt1, \"GeoDa\")$dist) tmpGWT <- tempfile() write.sn2gwt(listw2sn(listw1), tmpGWT) gwt2 <- read.gwt2nb(tmpGWT, STATION) #> Warning: 102, 115, 208 are not destinations cat(paste(\"Neighbours list symmetry;\", is.symmetric.nb(gwt2, FALSE, TRUE), \"\\n\")) #> Neighbours list symmetry; FALSE diffnb(gwt1, gwt2) #> Warning: neighbour object has 211 sub-graphs #> Neighbour list object: #> Number of regions: 211 #> Number of nonzero links: 0 #> Percentage nonzero weights: 0 #> Average number of links: 0 #> 211 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, #> 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, #> 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, #> 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, #> 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, #> 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, #> 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, #> 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, #> 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, #> 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, #> 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, #> 206, 207, 208, 209, 210, 211 #> 211 disjoint connected subgraphs data(oldcol) tmpMAT <- tempfile() COL.W <- nb2listw(COL.nb) write.sn2dat(listw2sn(COL.W), tmpMAT) listwmat1 <- read.dat2listw(tmpMAT) #> Warning: style is M (missing); style should be set to a valid value diffnb(listwmat1$neighbours, COL.nb, verbose=TRUE) #> Warning: region.id differ; using ids of first list #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 0 #> Percentage nonzero weights: 0 #> Average number of links: 0 #> 49 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 #> 49 disjoint connected subgraphs listwmat2 <- read.dat2listw(system.file(\"etc/weights/wmat.dat\", package=\"spdep\")[1]) #> Warning: style is M (missing); style should be set to a valid value diffnb(listwmat1$neighbours, listwmat2$neighbours, verbose=TRUE) #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 0 #> Percentage nonzero weights: 0 #> Average number of links: 0 #> 49 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 #> 49 disjoint connected subgraphs run <- FALSE if (require(\"foreign\", quietly=TRUE)) run <- TRUE if (run) { nc_sf <- sf::st_read(system.file(\"gpkg/nc.gpkg\", package=\"sf\")[1]) nc_sf$UniqueID <- 1:nrow(nc_sf) fn <- system.file(\"etc/misc/nc_contiguity_unique_id.dbf\", package=\"spdep\")[1] nc1 <- read.swmdbf2listw(fn, style=\"B\") nc1 } #> Reading layer `nc.gpkg' from data source `/home/rsb/lib/r_libs/sf/gpkg/nc.gpkg' using driver `GPKG' #> Simple feature collection with 100 features and 14 fields #> Geometry type: MULTIPOLYGON #> Dimension: XY #> Bounding box: xmin: -84.32385 ymin: 33.88199 xmax: -75.45698 ymax: 36.58965 #> Geodetic CRS: NAD27 #> Warning: region.id not given, c(MYID, NID) range is 1:100 #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 100 #> Number of nonzero links: 490 #> Percentage nonzero weights: 4.9 #> Average number of links: 4.9 #> #> Weights style: B #> Weights constants summary: #> n nn S0 S1 S2 #> B 100 10000 490 980 10696 if (run) { nc1a <- read.swmdbf2listw(fn, region.id=as.character(nc_sf$UniqueID), style=\"B\") all.equal(nc1, nc1a) } #> [1] TRUE if (run) { fn <- system.file(\"etc/misc/nc_contiguity_unique_id_islands.dbf\", package=\"spdep\")[1] try(nc1i <- read.swmdbf2listw(fn, style=\"B\")) nc1i <- read.swmdbf2listw(fn, style=\"B\", zero.policy=TRUE) nc1ia <- read.swmdbf2listw(fn, region.id=as.character(nc_sf$UniqueID), style=\"B\", zero.policy=TRUE) nc1ia } #> Warning: region.id not given, c(MYID, NID) range is 1:100 #> Warning: 81 is not an origin #> Error in read.swmdbf2listw(fn, style = \"B\") : #> Error in sn2listw(df1, style = style, zero.policy = zero.policy) : #> no-neighbour observations found, set zero.policy to TRUE #> #> Warning: region.id not given, c(MYID, NID) range is 1:100 #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 100 #> Number of nonzero links: 487 #> Percentage nonzero weights: 4.87 #> Average number of links: 4.87 #> 1 region with no links: #> 81 #> Non-symmetric neighbours list #> #> Weights style: B #> Weights constants summary: #> n nn S0 S1 S2 #> B 99 9801 487 971 10632 if (run) { all.equal(nc1i, nc1ia) } #> [1] TRUE if (run) { GDAL37 <- numeric_version(unname(sf::sf_extSoftVersion()[\"GDAL\"]), strict=FALSE) (GDAL37 <- ifelse(is.na(GDAL37), FALSE, GDAL37 >= \"3.7.0\")) file <- \"etc/shapes/california.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) { cal <- st_read(zipfile) } else { td <- tempdir() bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE) target <- unzip(zipfile, files=bn, exdir=td) cal <- st_read(target) } fn <- system.file(\"etc/misc/contiguity_myid.dbf\", package=\"spdep\")[1] cal1 <- read.swmdbf2listw(fn, style=\"B\") cal1a <- read.swmdbf2listw(fn, region.id=as.character(cal$MYID), style=\"B\") all.equal(cal1, cal1a) } #> Reading layer `california' from data source #> `/tmp/Rtmp5vVziX/temp_libpath224d25059ed81/spdep/etc/shapes/california.gpkg.zip' #> using driver `GPKG' #> Simple feature collection with 58 features and 2 fields #> Geometry type: MULTIPOLYGON #> Dimension: XY #> Bounding box: xmin: -13847330 ymin: 3810869 xmax: -12704360 ymax: 5132708 #> Projected CRS: World_Mercator #> Warning: region.id not given, c(MYID, NID) range is 158:215 #> [1] TRUE if (run) { fn <- system.file(\"etc/misc/contiguity_unique_id.dbf\", package=\"spdep\")[1] cal2 <- read.swmdbf2listw(fn, style=\"B\") cal2a <- read.swmdbf2listw(fn, region.id=as.character(cal$UniqueID), style=\"B\") all.equal(cal2, cal2a) } #> Warning: region.id not given, c(MYID, NID) range is 1:58 #> [1] TRUE if (run) { fn <- system.file(\"etc/misc/contiguity_unique_id_islands.dbf\", package=\"spdep\")[1] try(cal3i <- read.swmdbf2listw(fn, style=\"B\")) cal3i <- read.swmdbf2listw(fn, style=\"B\", zero.policy=TRUE) cal3ia <- read.swmdbf2listw(fn, region.id=as.character(cal$UniqueID), style=\"B\", zero.policy=TRUE) all.equal(cal3i, cal3ia) } #> Warning: region.id not given, c(MYID, NID) range is 1:58 #> Warning: 21, 38 are not origins #> Error in read.swmdbf2listw(fn, style = \"B\") : #> Error in sn2listw(df1, style = style, zero.policy = zero.policy) : #> no-neighbour observations found, set zero.policy to TRUE #> #> Warning: region.id not given, c(MYID, NID) range is 1:58 #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> [1] TRUE if (run) { cal1a_1n_nb <- cal1a$neighbours cal1a_1n_nb <- droplinks(cal1a_1n_nb, drop=c(\"158\", \"180\", \"215\"), sym=TRUE) cal1a_1n <- nb2listw(cal1a_1n_nb, style=\"B\", zero.policy=TRUE) cal1a_1n_sn <- listw2sn(cal1a_1n) file <- tempfile(fileext=\".dbf\") write.sn2DBF(cal1a_1n_sn, file) cal1a_1n_rt <- read.swmdbf2listw(file, region.id=as.character(cal$MYID), style=\"B\", zero.policy=TRUE) all.equal(cal1a_1n$neighbours, cal1a_1n_rt$neighbours) } #> Warning: some observations have no neighbours #> Warning: neighbour object has 4 sub-graphs #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> Warning: neighbour object has 4 sub-graphs #> [1] TRUE if (run) { all.equal(cal1a_1n$weights, cal1a_1n_rt$weights, check.attributes=FALSE) } #> [1] TRUE if (run) { cal1_1n_rt <- read.swmdbf2listw(file, style=\"B\", zero.policy=TRUE) all(isTRUE(all.equal(cal1a_1n$neighbours, cal1_1n_rt$neighbours))) } #> Warning: region.id not given, c(MYID, NID) range is 159:214 #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> Warning: neighbour object has 2 sub-graphs #> [1] FALSE if (run) { all(isTRUE(all.equal(cal1a_1n$weights, cal1_1n_rt$weights))) } #> [1] FALSE"},{"path":"https://r-spatial.github.io/spdep/reference/rotation.html","id":null,"dir":"Reference","previous_headings":"","what":"Rotate a set of point by a certain angle — Rotation","title":"Rotate a set of point by a certain angle — Rotation","text":"Rotate set XY coordinates angle (radians)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/rotation.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Rotate a set of point by a certain angle — Rotation","text":"","code":"Rotation(xy, angle)"},{"path":"https://r-spatial.github.io/spdep/reference/rotation.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Rotate a set of point by a certain angle — Rotation","text":"xy 2-columns matrix data frame containing set X Y coordinates. angle Numeric. scalar giving angle points rotated. angle radians.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/rotation.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Rotate a set of point by a certain angle — Rotation","text":"2-columns matrix size xy giving rotated coordinates.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/rotation.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Rotate a set of point by a certain angle — Rotation","text":"F. Guillaume Blanchet","code":""},{"path":"https://r-spatial.github.io/spdep/reference/rotation.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Rotate a set of point by a certain angle — Rotation","text":"","code":"set.seed(1) ### Create a set of coordinates coords <- cbind(runif(20), runif(20)) ### Create a series of angles rad <- seq(0, pi, l=20) opar <- par(mfrow=c(5,4), mar=c(3,3,1,1)) for(i in rad){ coords.rot <- Rotation(coords, i) plot(coords.rot, xlab=\"\", ylab=\"\") } par(opar) ### Rotate the coordinates by an angle of 90 degrees coords.90 <- Rotation(coords, 90*pi/180) coords.90 #> [,1] [,2] #> [1,] -0.93470523 0.26550866 #> [2,] -0.21214252 0.37212390 #> [3,] -0.65167377 0.57285336 #> [4,] -0.12555510 0.90820779 #> [5,] -0.26722067 0.20168193 #> [6,] -0.38611409 0.89838968 #> [7,] -0.01339033 0.94467527 #> [8,] -0.38238796 0.66079779 #> [9,] -0.86969085 0.62911404 #> [10,] -0.34034900 0.06178627 #> [11,] -0.48208012 0.20597457 #> [12,] -0.59956583 0.17655675 #> [13,] -0.49354131 0.68702285 #> [14,] -0.18621760 0.38410372 #> [15,] -0.82737332 0.76984142 #> [16,] -0.66846674 0.49769924 #> [17,] -0.79423986 0.71761851 #> [18,] -0.10794363 0.99190609 #> [19,] -0.72371095 0.38003518 #> [20,] -0.41127443 0.77744522 plot(coords, xlim=range(rbind(coords.90,coords)[,1]), ylim=range(rbind(coords.90,coords)[,2]), asp=1) points(coords.90, pch=19)"},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":null,"dir":"Reference","previous_headings":"","what":"Options for parallel support — set.mcOption","title":"Options for parallel support — set.mcOption","text":"Provides support use parallel computation parallel package.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Options for parallel support — set.mcOption","text":"","code":"set.mcOption(value) get.mcOption() set.coresOption(value) get.coresOption() set.ClusterOption(cl) get.ClusterOption()"},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Options for parallel support — set.mcOption","text":"value valid replacement value cl cluster object created makeCluster parallel","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Options for parallel support — set.mcOption","text":"Options spdep package held environment local package namespace exported. Option values set retrieved pairs access functions, get set. mc option set default FALSE Windows systems, fork R session; default TRUE systems, may set FALSE. mc FALSE, Cluster option used: mc FALSE Cluster option NULL parallel computing done, Cluster option passed “cluster” object created parallel snow package access without passed argument. cores option set NULL default, can used store number cores use integer. cores NULL, facilities parallel package used.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Options for parallel support — set.mcOption","text":"option access functions return current settings, assignment functions usually return previous value option.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Options for parallel support — set.mcOption","text":"extended example shown documentation aple.mc, including treatment seeding RNG multicore/cluster.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Options for parallel support — set.mcOption","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Options for parallel support — set.mcOption","text":"","code":"ls(envir=spdep:::.spdepOptions) #> [1] \"cluster\" \"cores\" \"listw_is_CsparseMatrix\" #> [4] \"mc\" \"nb_subgraphs_N+E\" \"report_nb_noneighs\" #> [7] \"report_nb_subgraphs\" \"rlecuyerSeed\" \"spChkID\" #> [10] \"verbose\" \"zeroPolicy\" if (require(parallel, quietly=TRUE)) { nc <- max(2L, detectCores(logical=FALSE), na.rm = TRUE)-1L nc # set nc to 1L here if (nc > 1L) nc <- 1L #nc <- ifelse(nc > 2L, 2L, nc) coresOpt <- get.coresOption() coresOpt if (!is.na(nc)) { invisible(set.coresOption(nc)) print(exists(\"moran.mc\")) if(.Platform$OS.type == \"windows\") { # forking not permitted on Windows - start cluster print(get.mcOption()) cl <- makeCluster(get.coresOption()) print(clusterEvalQ(cl, exists(\"moran.mc\"))) set.ClusterOption(cl) clusterEvalQ(get.ClusterOption(), library(spdep)) print(clusterEvalQ(cl, exists(\"moran.mc\"))) clusterEvalQ(get.ClusterOption(), detach(package:spdep)) set.ClusterOption(NULL) print(clusterEvalQ(cl, exists(\"moran.mc\"))) stopCluster(cl) } else { mcOpt <- get.mcOption() print(mcOpt) print(mclapply(1:get.coresOption(), function(i) exists(\"moran.mc\"), mc.cores=get.coresOption())) invisible(set.mcOption(FALSE)) cl <- makeCluster(nc) print(clusterEvalQ(cl, exists(\"moran.mc\"))) set.ClusterOption(cl) clusterEvalQ(get.ClusterOption(), library(spdep)) print(clusterEvalQ(cl, exists(\"moran.mc\"))) clusterEvalQ(get.ClusterOption(), detach(package:spdep)) set.ClusterOption(NULL) print(clusterEvalQ(cl, exists(\"moran.mc\"))) stopCluster(cl) invisible(set.mcOption(mcOpt)) } invisible(set.coresOption(coresOpt)) } } #> [1] TRUE #> [1] TRUE #> [[1]] #> [1] TRUE #> #> [[1]] #> [1] FALSE #> #> [[1]] #> [1] TRUE #> #> [[1]] #> [1] FALSE #>"},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":null,"dir":"Reference","previous_headings":"","what":"Control checking of spatial object IDs — set.spChkOption","title":"Control checking of spatial object IDs — set.spChkOption","text":"Provides support checking mutual integrity spatial neighbour weights spatial data; similar mechanisms used passing global verbose zero.policy options, causing functions creating neighbour objects warn multiple subgraphs.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Control checking of spatial object IDs — set.spChkOption","text":"","code":"set.spChkOption(check) get.spChkOption() chkIDs(x, listw) spNamedVec(var, data) set.VerboseOption(check) get.VerboseOption() set.ZeroPolicyOption(check) get.ZeroPolicyOption() set.SubgraphOption(check) get.SubgraphOption() set.SubgraphCeiling(value) get.SubgraphCeiling() set.NoNeighbourOption(check) get.NoNeighbourOption() set.listw_is_CsparseMatrix_Option(check) get.listw_is_CsparseMatrix_Option()"},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Control checking of spatial object IDs — set.spChkOption","text":"check logical value, TRUE FALSE value integer value, initialised 100000L, sum numbers nodes edges neighbour graph x vector length, two-dimensional array, data frame number rows neighbours list listw listw listw object nb object inheriting \"nb\" var character string integer value column selected data two-dimensional array data frame containing var","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Control checking of spatial object IDs — set.spChkOption","text":"Analysis functions spChk argument default set NULL, call get.spChkOption() get global spatial option whether check — initialised FALSE, consequently break anything. can changed TRUE using set.spChkOption(TRUE), spChk argument can assigned analysis functions. spNamedVec() provided ensure rownames passed single columns taken two-dimensional arrays data frames.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Control checking of spatial object IDs — set.spChkOption","text":"set.spChkOption() returns old logical value, get.spChkOption() returns current logical value, chkIDs() returns logical value test lack difference. spNamedVec() returns selected column names set row names object extracted.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Control checking of spatial object IDs — set.spChkOption","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Control checking of spatial object IDs — set.spChkOption","text":"motivation mechanism provided observation spatial objects map attribute data values need linked uniquely, avoid spurious results. reordering legacy Columbus data set used earlier publications available download Spacestat website just one example common problem.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Control checking of spatial object IDs — set.spChkOption","text":"","code":"data(oldcol) rownames(COL.OLD) #> [1] \"1001\" \"1002\" \"1003\" \"1004\" \"1005\" \"1006\" \"1007\" \"1008\" \"1009\" \"1010\" #> [11] \"1011\" \"1012\" \"1013\" \"1014\" \"1015\" \"1016\" \"1017\" \"1018\" \"1019\" \"1020\" #> [21] \"1021\" \"1022\" \"1023\" \"1024\" \"1025\" \"1026\" \"1027\" \"1028\" \"1029\" \"1030\" #> [31] \"1031\" \"1032\" \"1033\" \"1034\" \"1035\" \"1036\" \"1037\" \"1038\" \"1039\" \"1040\" #> [41] \"1041\" \"1042\" \"1043\" \"1044\" \"1045\" \"1046\" \"1047\" \"1048\" \"1049\" data(columbus, package=\"spData\") rownames(columbus) #> [1] \"1005\" \"1001\" \"1006\" \"1002\" \"1007\" \"1008\" \"1004\" \"1003\" \"1018\" \"1010\" #> [11] \"1038\" \"1037\" \"1039\" \"1040\" \"1009\" \"1036\" \"1011\" \"1042\" \"1041\" \"1017\" #> [21] \"1043\" \"1019\" \"1012\" \"1035\" \"1032\" \"1020\" \"1021\" \"1031\" \"1033\" \"1034\" #> [31] \"1045\" \"1013\" \"1022\" \"1044\" \"1023\" \"1046\" \"1030\" \"1024\" \"1047\" \"1016\" #> [41] \"1014\" \"1049\" \"1029\" \"1025\" \"1028\" \"1048\" \"1015\" \"1027\" \"1026\" get.spChkOption() #> [1] FALSE oldChk <- set.spChkOption(TRUE) get.spChkOption() #> [1] TRUE chkIDs(COL.OLD, nb2listw(COL.nb)) #> [1] TRUE chkIDs(columbus, nb2listw(col.gal.nb)) #> [1] TRUE chkIDs(columbus, nb2listw(COL.nb)) #> [1] FALSE tmp <- try(moran.test(spNamedVec(\"CRIME\", COL.OLD), nb2listw(COL.nb))) tmp <- try(moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(col.gal.nb))) tmp <- try(moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(COL.nb))) #> Error in moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(COL.nb)) : #> Check of data and weights ID integrity failed set.spChkOption(FALSE) get.spChkOption() #> [1] FALSE moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(COL.nb)) #> #> \tMoran I test under randomisation #> #> data: spNamedVec(\"CRIME\", columbus) #> weights: nb2listw(COL.nb) #> #> Moran I statistic standard deviate = 3.8402, p-value = 6.147e-05 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.341628707 -0.020833333 0.008908762 #> tmp <- try(moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(COL.nb), spChk=TRUE), silent=TRUE) set.spChkOption(oldChk) get.spChkOption() #> [1] FALSE"},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"function implements SKATER procedure spatial clustering analysis. procedure essentialy begins edges set, data set number cuts. output object 'skater' class valid input .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"","code":"skater(edges, data, ncuts, crit, vec.crit, method = c(\"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\", \"minkowski\", \"mahalanobis\"), p = 2, cov, inverted = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"edges matrix 2 colums row edge data data.frame data observed nodes. ncuts number cuts crit scalar two dimensional vector criteria groups. Examples: limits group size limits population size. scalar, minimum criteria groups. vec.crit vector evaluating criteria. method Character function declare distance method. method character, method must \"mahalanobis\" \"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\" \"minkowisk\". method one \"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\" \"minkowski\", see dist details, function used compute distance. method=\"mahalanobis\", mahalanobis distance computed neighbour areas. method function, function used compute distance. p power Minkowski distance. cov covariance matrix used compute mahalanobis distance. inverted logical. 'TRUE', 'cov' supposed contain inverse covariance matrix.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"object skater class : groups vector length equal number nodes. position identifies group node edges.groups list length equal number groups element set edges .prune vector identifying groups candidates partition. candidates vector identifying groups candidates partition. ssto total dissimilarity step edge removal.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"Assuncao, R.M., Lage J.P., Reis, E.. (2002). Analise de conglomerados espaciais via arvore geradora minima. Revista Brasileira de Estatistica, 62, 1-23. Assuncao, R. M, Neves, M. C., Camara, G. Freitas, C. da C. (2006). Efficient regionalization techniques socio-economic geographical units using minimum spanning trees. International Journal Geographical Information Science Vol. 20, . 7, August 2006, 797-811","code":""},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"Renato M. Assuncao Elias T. Krainski","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"","code":"### loading data GDAL37 <- numeric_version(unname(sf::sf_extSoftVersion()[\"GDAL\"]), strict=FALSE) (GDAL37 <- ifelse(is.na(GDAL37), FALSE, GDAL37 >= \"3.7.0\")) #> [1] TRUE file <- \"etc/shapes/bhicv.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) { bh <- st_read(zipfile) } else { td <- tempdir() bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE) target <- unzip(zipfile, files=bn, exdir=td) bh <- st_read(target) } #> Reading layer `bhicv' from data source #> `/tmp/Rtmp5vVziX/temp_libpath224d25059ed81/spdep/etc/shapes/bhicv.gpkg.zip' #> using driver `GPKG' #> Simple feature collection with 98 features and 8 fields #> Geometry type: POLYGON #> Dimension: XY #> Bounding box: xmin: -45.02175 ymin: -20.93007 xmax: -42.50321 ymax: -18.08342 #> Geodetic CRS: Corrego Alegre 1970-72 ### data standardized dim(bh) #> [1] 98 9 dpad <- data.frame(scale(as.data.frame(bh)[,5:8])) ### neighboorhod list bh.nb <- poly2nb(bh) bh.nb #> Neighbour list object: #> Number of regions: 98 #> Number of nonzero links: 508 #> Percentage nonzero weights: 5.289463 #> Average number of links: 5.183673 ### calculating costs lcosts <- nbcosts(bh.nb, dpad) head(lcosts) #> [[1]] #> [1] 1.5418355 2.5253558 1.4738620 1.8462822 1.7089412 1.5613667 1.0279919 #> [8] 0.6334314 1.9029531 2.5816759 #> #> [[2]] #> [1] 1.0847913 1.7723275 0.7940341 #> #> [[3]] #> [1] 1.257984 2.634043 0.847224 1.807124 #> #> [[4]] #> [1] 1.2579836 1.0548805 0.7862035 #> #> [[5]] #> [1] 1.541835 1.295112 2.206320 #> #> [[6]] #> [1] 0.9981915 1.3801441 1.5225548 1.3606678 0.9775650 #> ### making listw nb.w <- nb2listw(bh.nb, lcosts, style=\"B\") nb.w #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 98 #> Number of nonzero links: 508 #> Percentage nonzero weights: 5.289463 #> Average number of links: 5.183673 #> #> Weights style: B #> Weights constants summary: #> n nn S0 S1 S2 #> B 98 9604 1027.424 5192.868 55983.97 ### find a minimum spanning tree mst.bh <- mstree(nb.w,5) str(mst.bh) #> 'mst' num [1:97, 1:3] 5 12 13 13 11 31 39 40 31 40 ... ### the mstree plot par(mar=c(0,0,0,0)) plot(st_geometry(bh), border=gray(.5)) pts <- st_coordinates(st_centroid(bh)) #> Warning: st_centroid assumes attributes are constant over geometries plot(mst.bh, pts, col=2, cex.lab=.6, cex.circles=0.035, fg=\"blue\", add=TRUE) ### three groups with no restriction res1 <- spdep::skater(edges=mst.bh[,1:2], data=dpad, ncuts=2) ### groups size table(res1$groups) #> #> 1 2 3 #> 18 23 57 ### the skater plot opar <- par(mar=c(0,0,0,0)) plot(res1, pts, cex.circles=0.035, cex.lab=.7) ### the skater plot, using other colors plot(res1, pts, cex.circles=0.035, cex.lab=.7, groups.colors=heat.colors(length(res1$ed))) ### the Spatial Polygons plot plot(st_geometry(bh), col=heat.colors(length(res1$edg))[res1$groups]) #par(opar) ### EXPERT OPTIONS ### more one partition res1b <- spdep::skater(res1, dpad, 1) ### length groups frequency table(res1$groups) #> #> 1 2 3 #> 18 23 57 table(res1b$groups) #> #> 1 2 3 4 #> 18 23 55 2 ### thee groups with minimum population res2 <- spdep::skater(mst.bh[,1:2], dpad, 2, 200000, bh$Pop) table(res2$groups) #> #> 1 2 3 #> 22 37 39 ### thee groups with minimun number of areas res3 <- spdep::skater(mst.bh[,1:2], dpad, 2, 3, rep(1,nrow(bh))) table(res3$groups) #> #> 1 2 3 #> 18 23 57 ### thee groups with minimun and maximun number of areas res4 <- spdep::skater(mst.bh[,1:2], dpad, 2, c(20,50), rep(1,nrow(bh))) table(res4$groups) #> #> 1 2 3 #> 50 24 24 ### if I want to get groups with 20 to 40 elements res5 <- spdep::skater(mst.bh[,1:2], dpad, 2, c(20,40), rep(1,nrow(bh))) ## DON'T MAKE DIVISIONS table(res5$groups) #> #> 1 #> 98 ### In this MST don't have groups with this restrictions ### In this case, first I do one division ### with the minimun criteria res5a <- spdep::skater(mst.bh[,1:2], dpad, 1, 20, rep(1,nrow(bh))) table(res5a$groups) #> #> 1 2 #> 75 23 ### and do more one division with the full criteria res5b <- spdep::skater(res5a, dpad, 1, c(20, 40), rep(1,nrow(bh))) table(res5b$groups) #> #> 1 2 3 #> 22 23 53 ### and do more one division with the full criteria res5c <- spdep::skater(res5b, dpad, 1, c(20, 40), rep(1,nrow(bh))) table(res5c$groups) #> #> 1 2 3 4 #> 22 23 33 20 ### It don't have another divison with this criteria res5d <- spdep::skater(res5c, dpad, 1, c(20, 40), rep(1,nrow(bh))) table(res5d$groups) #> #> 1 2 3 4 #> 22 23 33 20 # \\dontrun{ data(boston, package=\"spData\") bh.nb <- boston.soi dpad <- data.frame(scale(boston.c[,c(7:10)])) ### calculating costs system.time(lcosts <- nbcosts(bh.nb, dpad)) #> user system elapsed #> 0.071 0.000 0.074 ### making listw nb.w <- nb2listw(bh.nb, lcosts, style=\"B\") ### find a minimum spanning tree mst.bh <- mstree(nb.w,5) ### three groups with no restriction system.time(res1 <- spdep::skater(mst.bh[,1:2], dpad, 2)) #> user system elapsed #> 1.950 0.105 2.137 library(parallel) nc <- max(2L, detectCores(logical=FALSE), na.rm = TRUE)-1L # set nc to 1L here if (nc > 1L) nc <- 1L coresOpt <- get.coresOption() invisible(set.coresOption(nc)) if(!get.mcOption()) { # no-op, \"snow\" parallel calculation not available cl <- makeCluster(get.coresOption()) set.ClusterOption(cl) } ### calculating costs system.time(plcosts <- nbcosts(bh.nb, dpad)) #> user system elapsed #> 0.067 0.000 0.067 all.equal(lcosts, plcosts, check.attributes=FALSE) #> [1] TRUE ### making listw pnb.w <- nb2listw(bh.nb, plcosts, style=\"B\") ### find a minimum spanning tree pmst.bh <- mstree(pnb.w,5) ### three groups with no restriction system.time(pres1 <- spdep::skater(pmst.bh[,1:2], dpad, 2)) #> user system elapsed #> 1.916 0.092 2.019 if(!get.mcOption()) { set.ClusterOption(NULL) stopCluster(cl) } all.equal(res1, pres1, check.attributes=FALSE) #> [1] TRUE invisible(set.coresOption(coresOpt)) # }"},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial correlogram — sp.correlogram","title":"Spatial correlogram — sp.correlogram","text":"Spatial correlograms Moran's autocorrelation coefficient, print plot helper functions.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial correlogram — sp.correlogram","text":"","code":"sp.correlogram(neighbours, var, order = 1, method = \"corr\", style = \"W\", randomisation = TRUE, zero.policy = NULL, spChk=NULL) # S3 method for class 'spcor' plot(x, main, ylab, ylim, ...) # S3 method for class 'spcor' print(x, p.adj.method=\"none\", ...)"},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial correlogram — sp.correlogram","text":"neighbours object class nb var numeric vector order maximum lag order method \"corr\" correlation, \"\" Moran's , \"C\" Geary's C style style can take values W, B, C, S randomisation variance C calculated assumption randomisation, FALSE normality zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() x object sp.correlogram() class spcor p.adj.method correction method p.adjust main overall title plot ylab title y axis ylim y limits plot ... arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Spatial correlogram — sp.correlogram","text":"print function also calculates standard deviates Moran's Geary's C two-sided probability value, optionally using p.adjust correct nymber lags. plot function plots bar estimated Moran's , Geary's C value +/- twice square root variance (previous releases , twice). table includes count included observations brackets lag order. Care needs shown interpreting results remaining included observations lag order increases.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial correlogram — sp.correlogram","text":"returns list class spcor: res \"corr\" vector values; \"\", matrix estimates \"\", expectations, variances method \"\" \"corr\" cardnos list tables neighbour cardinalities lag orders used var variable name","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Spatial correlogram — sp.correlogram","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, pp. 118–122, Martin, R. L., Oeppen, J. E. 1975 identification regional forecasting models using space-time correlation functions, Transactions Institute British Geographers, 66, 95–118.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial correlogram — sp.correlogram","text":"Roger Bivand, Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial correlogram — sp.correlogram","text":"","code":"nc.sids <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\")[1], quiet=TRUE) rn <- as.character(nc.sids$FIPS) ncCC89_nb <- read.gal(system.file(\"weights/ncCC89.gal\", package=\"spData\")[1], region.id=rn) #> Warning: neighbour object has 3 sub-graphs ft.SID74 <- sqrt(1000)*(sqrt(nc.sids$SID74/nc.sids$BIR74) + sqrt((nc.sids$SID74+1)/nc.sids$BIR74)) tr.SIDS74 <- ft.SID74*sqrt(nc.sids$BIR74) cspc <- sp.correlogram(ncCC89_nb, tr.SIDS74, order=8, method=\"corr\", zero.policy=TRUE) #> Warning: lag 1 neighbour object has 3 sub-graphs #> Warning: lag 2 neighbour object has 3 sub-graphs #> Warning: lag 3 neighbour object has 3 sub-graphs #> Warning: lag 4 neighbour object has 3 sub-graphs #> Warning: lag 5 neighbour object has 3 sub-graphs #> Warning: lag 6 neighbour object has 3 sub-graphs #> Warning: lag 7 neighbour object has 3 sub-graphs #> Warning: lag 8 neighbour object has 3 sub-graphs print(cspc) #> Spatial correlogram for tr.SIDS74 #> method: Spatial autocorrelation #> 1 2 3 4 5 6 #> 0.38193491 0.47679881 0.11740653 0.09935901 0.27819159 0.30153012 #> 7 8 #> -0.05150923 0.05283813 plot(cspc) Ispc <- sp.correlogram(ncCC89_nb, tr.SIDS74, order=8, method=\"I\", zero.policy=TRUE) #> Warning: lag 1 neighbour object has 3 sub-graphs #> Warning: lag 2 neighbour object has 3 sub-graphs #> Warning: lag 3 neighbour object has 3 sub-graphs #> Warning: lag 4 neighbour object has 3 sub-graphs #> Warning: lag 5 neighbour object has 3 sub-graphs #> Warning: lag 6 neighbour object has 3 sub-graphs #> Warning: lag 7 neighbour object has 3 sub-graphs #> Warning: lag 8 neighbour object has 3 sub-graphs print(Ispc) #> Spatial correlogram for tr.SIDS74 #> method: Moran's I #> estimate expectation variance standard deviate Pr(I) two sided #> 1 (98) 0.2311685 -0.0103093 0.0055378 3.2450 0.0011747 ** #> 2 (98) 0.2246930 -0.0103093 0.0037817 3.8214 0.0001327 *** #> 3 (98) 0.0193576 -0.0103093 0.0029386 0.5473 0.5841914 #> 4 (98) 0.0042255 -0.0103093 0.0024974 0.2908 0.7711687 #> 5 (98) 0.0875548 -0.0103093 0.0022875 2.0462 0.0407386 * #> 6 (98) 0.0758362 -0.0103093 0.0021583 1.8543 0.0637011 . #> 7 (98) -0.0752243 -0.0103093 0.0022282 -1.3752 0.1690654 #> 8 (98) -0.0261063 -0.0103093 0.0025211 -0.3146 0.7530514 #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 print(Ispc, \"bonferroni\") #> Spatial correlogram for tr.SIDS74 #> method: Moran's I #> estimate expectation variance standard deviate Pr(I) two sided #> 1 (98) 0.2311685 -0.0103093 0.0055378 3.2450 0.009397 ** #> 2 (98) 0.2246930 -0.0103093 0.0037817 3.8214 0.001061 ** #> 3 (98) 0.0193576 -0.0103093 0.0029386 0.5473 1.000000 #> 4 (98) 0.0042255 -0.0103093 0.0024974 0.2908 1.000000 #> 5 (98) 0.0875548 -0.0103093 0.0022875 2.0462 0.325909 #> 6 (98) 0.0758362 -0.0103093 0.0021583 1.8543 0.509609 #> 7 (98) -0.0752243 -0.0103093 0.0022282 -1.3752 1.000000 #> 8 (98) -0.0261063 -0.0103093 0.0025211 -0.3146 1.000000 #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 plot(Ispc) Cspc <- sp.correlogram(ncCC89_nb, tr.SIDS74, order=8, method=\"C\", zero.policy=TRUE) #> Warning: lag 1 neighbour object has 3 sub-graphs #> Warning: lag 2 neighbour object has 3 sub-graphs #> Warning: lag 3 neighbour object has 3 sub-graphs #> Warning: lag 4 neighbour object has 3 sub-graphs #> Warning: lag 5 neighbour object has 3 sub-graphs #> Warning: lag 6 neighbour object has 3 sub-graphs #> Warning: lag 7 neighbour object has 3 sub-graphs #> Warning: lag 8 neighbour object has 3 sub-graphs print(Cspc) #> Spatial correlogram for tr.SIDS74 #> method: Geary's C #> estimate expectation variance standard deviate Pr(I) two sided #> 1 (98) 0.7172624 1.0000000 0.0059986 -3.6506 0.0002617 *** #> 2 (98) 0.6817819 1.0000000 0.0046785 -4.6523 3.282e-06 *** #> 3 (98) 0.9470179 1.0000000 0.0044311 -0.7959 0.4260762 #> 4 (98) 1.0016202 1.0000000 0.0041985 0.0250 0.9800516 #> 5 (98) 0.8977501 1.0000000 0.0038054 -1.6575 0.0974119 . #> 6 (98) 0.9173310 1.0000000 0.0036428 -1.3697 0.1707819 #> 7 (98) 1.0527148 1.0000000 0.0037227 0.8640 0.3875979 #> 8 (98) 1.0067939 1.0000000 0.0036482 0.1125 0.9104415 #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 print(Cspc, \"bonferroni\") #> Spatial correlogram for tr.SIDS74 #> method: Geary's C #> estimate expectation variance standard deviate Pr(I) two sided #> 1 (98) 0.7172624 1.0000000 0.0059986 -3.6506 0.002093 ** #> 2 (98) 0.6817819 1.0000000 0.0046785 -4.6523 2.626e-05 *** #> 3 (98) 0.9470179 1.0000000 0.0044311 -0.7959 1.000000 #> 4 (98) 1.0016202 1.0000000 0.0041985 0.0250 1.000000 #> 5 (98) 0.8977501 1.0000000 0.0038054 -1.6575 0.779295 #> 6 (98) 0.9173310 1.0000000 0.0036428 -1.3697 1.000000 #> 7 (98) 1.0527148 1.0000000 0.0037227 0.8640 1.000000 #> 8 (98) 1.0067939 1.0000000 0.0036482 0.1125 1.000000 #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 plot(Cspc) drop.no.neighs <- !(1:length(ncCC89_nb) %in% which(card(ncCC89_nb) == 0)) sub.ncCC89.nb <- subset(ncCC89_nb, drop.no.neighs) plot(sp.correlogram(sub.ncCC89.nb, subset(tr.SIDS74, drop.no.neighs), order=8, method=\"corr\"))"},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"permutation test spatial general cross product statistic Moran (\\(C_{ij} = z_i z_j\\)), Geary (\\(C_{ij} = (z_i - z_j)^2\\)), Sokal (\\(C_{ij} = |z_i - z_j|\\)) criteria, \\(z_i = (x_i - \\bar{x}) / \\sigma_{x}\\). plot.mc.sim helper function plot outcomes permutation test.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"","code":"sp.mantel.mc(var, listw, nsim, type = \"moran\", zero.policy = attr(listw, \"zero.policy\"), alternative = \"greater\", spChk=NULL, return_boot=FALSE) # S3 method for class 'mc.sim' plot(x, xlim, xlab, main, sub, ..., ptype=\"density\")"},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"var numeric vector length neighbours list listw listw listw object created example nb2listw nsim number permutations type \"moran\", \"geary\" \"sokal\" criteria similarity zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"two.sided\", \"less\". spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() return_boot return object class boot equivalent permutation bootstrap rather object class htest x object plotted xlim range x axis xlab title x axis main overall title plot sub sub title plot ptype either \"density\" \"hist\" ... arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"list class htest mc.sim containing following components: statistic value observed Geary's C. parameter rank observed Geary's C. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data, number simulations. p.value pseudo p-value test. res nsim simulated values statistic, final value observed statistic estimate mean variance simulated distribution.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 22-24, Haining, R. 1990 Spatial data analysis social environmental sciences, Cambridge: Cambridge University Press, p. 230–1. function checked general matrix code posted r-help list Ben Bolker 1 May 2001; another mantel() function vegan package.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"","code":"data(oldcol) sim1 <- sp.mantel.mc(COL.OLD$CRIME, nb2listw(COL.nb), nsim=99, type=\"geary\", alternative=\"two.sided\") sim1 #> #> \tMantel permutation test for geary measure #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.nb) #> number of simulations + 1: 100 #> #> statistic = 51.927, observed rank = 1, p-value = 0.02 #> alternative hypothesis: two.sided #> sample estimates: #> mean of permutations sd of permutations #> 98.852997 8.934135 #> plot(sim1) sp.mantel.mc(COL.OLD$CRIME, nb2listw(COL.nb), nsim=99, type=\"sokal\", alternative=\"two.sided\") #> #> \tMantel permutation test for sokal measure #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.nb) #> number of simulations + 1: 100 #> #> statistic = 36.695, observed rank = 1, p-value = 0.02 #> alternative hypothesis: two.sided #> sample estimates: #> mean of permutations sd of permutations #> 56.418584 3.227064 #> sp.mantel.mc(COL.OLD$CRIME, nb2listw(COL.nb), nsim=99, type=\"moran\") #> #> \tMantel permutation test for moran measure #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.nb) #> number of simulations + 1: 100 #> #> statistic = 24.526, observed rank = 100, p-value = 0.01 #> alternative hypothesis: greater #> sample estimates: #> mean of permutations sd of permutations #> -0.3401381 4.5579226 #>"},{"path":"https://r-spatial.github.io/spdep/reference/spatialdelta.html","id":null,"dir":"Reference","previous_headings":"","what":"Weighted Multivariate Spatial Autocorrelation Measures — spatialdelta","title":"Weighted Multivariate Spatial Autocorrelation Measures — spatialdelta","text":"kernel-based weighted multivariate spatial autocorrelation measure delta proposed Bavaud (2024) implemented, together support functions create spatial weights matrices symmetric binary adjacency matrices; summary display methods provided.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spatialdelta.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Weighted Multivariate Spatial Autocorrelation Measures — spatialdelta","text":"","code":"spatialdelta(dissimilarity_matrix, adjusted_spatial_weights, regional_weights=NULL, alternative = \"greater\") # S3 method for class 'spatialdelta' summary(object, ...) # S3 method for class 'summary.spatialdelta' print(x, digits=getOption(\"digits\"), ...) linearised_diffusive_weights(adjacency_matrix, regional_weights, t_choice = 2) metropolis_hastings_weights(adjacency_matrix, regional_weights) iterative_proportional_fitting_weights(adjacency_matrix, regional_weights, g=0.001, iter=1000, tol=1e-10, tol.margins=1e-10, print=FALSE) graph_distance_weights(adjacency_matrix, regional_weights, c=NULL) # S3 method for class 'adjusted_spatial_weights' as.matrix(x, ...) plot_spatialcoords(x, ...) # Default S3 method plot_spatialcoords(x, ...) # S3 method for class 'spatialdelta' plot_spatialcoords(x, cols = c(1L, 2L), mult = c(1, 1), power = 1L, fmult = NULL, names = attr(x, \"rnames\"), bg = 1, pos = 3, cex = 0.6, largest = NULL, ...) plot_moran(x, y, ...) # Default S3 method plot_moran(x, y, ...) # S3 method for class 'spatialdelta' plot_moran(x, y, fmult = NULL, names = attr(x, \"rnames\"), bg = 1, pos = 3, cex = 0.6, largest = NULL, ...) plot_spatialscree(x, ...) # Default S3 method plot_spatialscree(x, ...) # S3 method for class 'spatialdelta' plot_spatialscree(x, lwd=2, ...) factorial_coordinates(x) # Default S3 method factorial_coordinates(x) # S3 method for class 'spatialdelta' factorial_coordinates(x) plot_factorialcoords(x, ...) # Default S3 method plot_factorialcoords(x, ...) # S3 method for class 'spatialdelta' plot_factorialcoords(x, cols = c(1L, 2L), mult = c(1, 1), fmult = NULL, names = attr(x, \"rnames\"), bg = 1, pos = 3, cex = 0.6, largest = NULL, ...) plot_factorialscree(x, ...) # Default S3 method plot_factorialscree(x, ...) # S3 method for class 'spatialdelta' plot_factorialscree(x, ...) localdelta(x, ...) # Default S3 method localdelta(x, ...) # S3 method for class 'spatialdelta' localdelta(x, names = attr(x, \"rnames\"), ...) cornish_fisher(x, ...) # Default S3 method cornish_fisher(x, ...) # S3 method for class 'spatialdelta' cornish_fisher(x, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/spatialdelta.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Weighted Multivariate Spatial Autocorrelation Measures — spatialdelta","text":"dissimilarity_matrix dissimilarity_matrix square matrix dissimilarities (possibly multivariate) observations adjusted_spatial_weights adjusted_spatial_weights square matrix spatial weights returned construction functions linearised_diffusive_weights, metropolis_hastings_weights, iterative_proportional_fitting_weights, graph_distance_weights similar; named construction functions pass regional_weights spatialdelta, matrices constructed ways, argument required regional_weights default NULL, regional_weights weights reflecting contribution observation (possibly multivariate) data set, may uniform, none can zero, must sum unity; adjusted_spatial_weights \"adjusted_spatial_weights\" object created linearised_diffusive_weights, metropolis_hastings_weights, iterative_proportional_fitting_weights graph_distance_weights, regional_weights passed attribute alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"less\" \"two.sided\" object, x object, x objects returned spatialdelta class \"spatialdelta\", class \"adjusted_spatial_weights\" digits default getOption(\"digits\"), non-null value specifying minimum number significant digits printed values adjacency_matrix adjacency_matrix symmetric binary adjacency matrix t_choice default 2, inverse largest eigenvalue adjusted Laplacian adjacency matrix (t2, Bavaud 2024, page 583), otherwise 1 (t1, page 579) g default 0.001, (Bavaud 2024, page 579, 589), small quantity lift binary adjacency matrix zero iter, tol, tol.margins, print arguments passed Ipfp c default NULL, coefficient greater zero less equal -1/min(B) B matrix scalar products associated distance matrix; given, -1/min(B) used y numeric vector create Moran plot cols integer vector length 2, default c(1L, 2L), giving two columns regional factorial coordinates plot mult numeric vector length 2, default c(1, 1), scale reverse axes signs given different eigenproblem implementations power integer vector length 1, default 1; higher, use powered kernel fmult default NULL automatic scaling circle symbols expressing observation weights f plot (0.02*diff(range(X)))/diff(range(regional_weights)) X first vector coordinates; may set manually numeric value names default attr(x, \"rnames\"), coordinates annotated strings passed \"region.id\" attribute \"nb\" object used create adjusted_spatial_weights matrix \"adjacency_matrix\" object row column names bg, pos, cex, lwd arguments passed graphics functions methods largest default NULL, may integer > 0 <= region count, permitting names plotted largest circle symbols ... arguments passed functions methods","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spatialdelta.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Weighted Multivariate Spatial Autocorrelation Measures — spatialdelta","text":"general, user choose one functions constructing spatial weights symmetric binary, similar symmetric - example row-standardised - adjacency matrix. cornish_fisher method updates standard deviate p-value pair skewness excess kurtosis estimates within required domain.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spatialdelta.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Weighted Multivariate Spatial Autocorrelation Measures — spatialdelta","text":"spatialdelta returns object classes \"spatialdelta\" \"htest\". print method treats \"htest\" object. methods use additional attributes: Kx Multivariate kernel matrix eq. 16 Kw Spatial weights kernel matrix eq. 21 regional_weights Input observation weights adjusted_spatial_weights Input spatial adjusted_spatial_weightseights B symmetric matrix scalar products eq. 15 VI Spatial component delta variance Vx Multivariate component delta variance Vd0 Variance delta calculated another way eq. 38 alphamu Spatial component delta skewness alphalambda Multivariate component delta skewness gammamu Spatial component delta excess kurtosis gammalambda Multivariate component delta excess kurtosis rnames Region names passed row/column names adjusted_spatial_weights, \"region.id\" attribute \"nb\" object used create adjusted_spatial_weights matrix \"adjacency_matrix\" object linearised_diffusive_weights, metropolis_hastings_weights, iterative_proportional_fitting_weights graph_distance_weights return square spatial weights matrices (latter two return matrices created metropolis_hastings_weights igraph mipfp available); factorial_coordinates returns square factorial matrix; localdelta returns vector local deltas eq. 30.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spatialdelta.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Weighted Multivariate Spatial Autocorrelation Measures — spatialdelta","text":"Bavaud, F. (2024), Measuring Testing Multivariate Spatial Autocorrelation Weighted Setting: Kernel Approach. Geographical Analysis, 56: 573-599. doi:10.1111/gean.12390","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spatialdelta.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Weighted Multivariate Spatial Autocorrelation Measures — spatialdelta","text":"Roger Bivand, Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spatialdelta.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Weighted Multivariate Spatial Autocorrelation Measures — spatialdelta","text":"input adjacency matrix symmetric, sub-graphs islands - possible step across graph edges observation .","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/spatialdelta.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Weighted Multivariate Spatial Autocorrelation Measures — spatialdelta","text":"","code":"toy_f <- c(0.4, 0.1, 0.3, 0.2) toy_xa <- c(4, 9, 1, 1) toy_nba <- structure(list(c(2L, 3L, 4L), c(1L), c(1L, 4L), c(1L, 3L)), class=\"nb\", region.id=as.character(1:4)) toy_gla <- list(c(0.25, 0.5, 0.25), c(1), c(2/3, 1/3), c(0.5, 0.5)) toy_wa <- nb2mat(toy_nba, glist=toy_gla, style=\"W\") spatialdelta(dissimilarity_matrix=as.matrix(dist(toy_xa))^2, adjusted_spatial_weights=toy_wa, regional_weights=toy_f, alternative=\"two.sided\") #> #> \tBavaud delta normal approximation #> #> data: as.matrix(dist(toy_xa))^2 #> weights: toy_wa #> Standard deviate = 1.9799, p-value = 0.04771 #> alternative hypothesis: two.sided #> sample estimates: #> delta Expectation Variance Skewness Excess Kurtosis #> 0.13333333 -0.33333333 0.05555556 0.16162441 Inf #> toy_xb <- toy_xa toy_glb <- list(c(0.5, 0.125, 0.25, 0.125), c(0.5, 0.5), c(1/3, 0.5, 1/6), c(0.25, 0.25, 0.5)) toy_nbb <- include.self(toy_nba) toy_wb <- nb2mat(toy_nbb, glist=toy_glb, style=\"W\") spatialdelta(dissimilarity_matrix=as.matrix(dist(toy_xb))^2, adjusted_spatial_weights=toy_wb, regional_weights=toy_f, alternative=\"two.sided\") #> #> \tBavaud delta normal approximation #> #> data: as.matrix(dist(toy_xb))^2 #> weights: toy_wb #> Standard deviate = 1.9799, p-value = 0.04771 #> alternative hypothesis: two.sided #> sample estimates: #> delta Expectation Variance Skewness Excess Kurtosis #> 0.56666667 0.33333333 0.01388889 0.16162441 Inf #> toy_xc <- c(3, 3, 1, 1) toy_nbc <- structure(list(c(3L, 4L), c(3L, 4L), c(1L, 2L), c(1L, 2L)), class=\"nb\", region.id=as.character(1:4)) toy_glc <- list(c(0.6, 0.4), c(0.6, 0.4), c(0.8, 0.2), c(0.8, 0.2)) toy_wc <- nb2mat(toy_nbc, glist=toy_glc, style=\"W\") spatialdelta(dissimilarity_matrix=as.matrix(dist(toy_xc))^2, adjusted_spatial_weights=toy_wc, regional_weights=toy_f, alternative=\"two.sided\") #> #> \tBavaud delta normal approximation #> #> data: as.matrix(dist(toy_xc))^2 #> weights: toy_wc #> Standard deviate = -2.2361, p-value = 0.02535 #> alternative hypothesis: two.sided #> sample estimates: #> delta Expectation Variance Skewness Excess Kurtosis #> -1.00000000 -0.33333333 0.08888889 -0.63887656 Inf #> # \\donttest{ if (require(Guerry, quietly=TRUE)) { data(gfrance85) gfrance85 <- st_as_sf(gfrance85) moral <- scale(st_drop_geometry(gfrance85)[, 7:12]) Dmoral <- as.matrix(dist(moral))^2 fG <- gfrance85$Pop1831/sum(gfrance85$Pop1831) gnb <- poly2nb(gfrance85, row.names=gfrance85$Department) frG <- nb2mat(gnb, style=\"B\") ldwG <- linearised_diffusive_weights(adjacency_matrix=frG, regional_weights=fG) mhwG <- metropolis_hastings_weights(adjacency_matrix=frG, regional_weights=fG) ifwG <- iterative_proportional_fitting_weights(adjacency_matrix=frG, regional_weights=fG) gdwG <- graph_distance_weights(adjacency_matrix=frG, regional_weights=fG) (moral_ldw <- spatialdelta(dissimilarity_matrix=Dmoral, adjusted_spatial_weights=ldwG)) (cornish_fisher(moral_ldw)) moral_mhw <- spatialdelta(dissimilarity_matrix=Dmoral, adjusted_spatial_weights=mhwG) moral_ifw <- spatialdelta(dissimilarity_matrix=Dmoral, adjusted_spatial_weights=ifwG) moral_gdw <- spatialdelta(dissimilarity_matrix=Dmoral, adjusted_spatial_weights=gdwG) opar <- par(mfrow=c(2, 2)) plot_spatialcoords(moral_ldw, cols=c(2,1), mult=c(-1, -1), main=\"Linearised Diffusive\", asp=1) plot_spatialcoords(moral_mhw, cols=c(2,1), mult=c(1, 1), main=\"Metropolis-Hastings\", asp=1) plot_spatialcoords(moral_ifw, cols=c(2,1), mult=c(1, 1), main=\"Iterative fitting\", asp=1) plot_spatialcoords(moral_gdw, cols=c(2,1), mult=c(1, 1), main=\"Graph distance\", asp=1) par(opar) opar <- par(mfrow=c(2, 2)) plot_spatialscree(moral_ldw, main=\"linearised diffusive\") plot_spatialscree(moral_mhw, main=\"Metropolis-Hastings\") plot_spatialscree(moral_ifw, main=\"iterative fitting\") plot_spatialscree(moral_gdw, main=\"graph distance\") par(opar) Crime_pers <- scale(gfrance85$Crime_pers) funif <- rep(1/length(Crime_pers), length(Crime_pers)) lw <- nb2listw(gnb, style=\"W\") Crime_pers_delta <- spatialdelta(dissimilarity_matrix=as.matrix(dist(Crime_pers))^2, adjusted_spatial_weights=listw2mat(lw), regional_weights=funif) Crime_pers_delta$estimate[\"delta\"] locdelta <- localdelta(Crime_pers_delta) moran.test(Crime_pers, lw, randomisation=FALSE)$estimate[\"Moran I statistic\"] locmoran <- localmoran(c(Crime_pers), lw)[,1] all.equal(locmoran, locdelta) all.equal(unname(moral_ldw$estimate[\"delta\"]), # Eq. 30 p. 588 sum(fG * localdelta(moral_ldw))) all.equal(unname(moral_mhw$estimate[\"delta\"]), # Eq. 30 p. 588 sum(fG * localdelta(moral_mhw))) all.equal(unname(moral_ifw$estimate[\"delta\"]), # Eq. 30 p. 588 sum(fG * localdelta(moral_ifw))) all.equal(unname(moral_gdw$estimate[\"delta\"]), # Eq. 30 p. 588 sum(fG * localdelta(moral_gdw))) } #> [1] TRUE # }"},{"path":"https://r-spatial.github.io/spdep/reference/spdep-defunct.html","id":null,"dir":"Reference","previous_headings":"","what":"Defunct Functions in Package spdep — spdep-defunct","title":"Defunct Functions in Package spdep — spdep-defunct","text":"functions defunct release 1.2-1. functions moved spatialreg package.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spdep-defunct.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Defunct Functions in Package spdep — spdep-defunct","text":"","code":"aple.plot() localAple() aple.mc() aple() lextrB() lextrW() lextrS() griffith_sone() subgraph_eigenw() mom_calc() mom_calc_int2() stsls() # S3 method for class 'stsls' impacts() GMerrorsar() # S3 method for class 'gmsar' summary() gstsls() # S3 method for class 'gmsar' impacts() # S3 method for class 'gmsar' Hausman.test() lagmess() ME() SpatialFiltering() LR.sarlm() # S3 method for class 'sarlm' logLik() LR1.sarlm() Wald1.sarlm() # S3 method for class 'sarlm' Hausman.test() as.spam.listw() as_dgRMatrix_listw() as_dsTMatrix_listw() as_dsCMatrix_I() as_dsCMatrix_IrW() Jacobian_W() powerWeights() # S3 method for class 'lagImpact' plot() # S3 method for class 'lagImpact' print() # S3 method for class 'lagImpact' summary() # S3 method for class 'lagImpact' HPDinterval() intImpacts() can.be.simmed() eigenw() similar.listw() do_ldet() jacobianSetup() cheb_setup() mcdet_setup() eigen_setup() eigen_pre_setup() spam_setup() spam_update_setup() Matrix_setup() Matrix_J_setup() LU_setup() LU_prepermutate_setup() moments_setup() SE_classic_setup() SE_whichMin_setup() SE_interp_setup() MCMCsamp() # S3 method for class 'spautolm' MCMCsamp() # S3 method for class 'sarlm' MCMCsamp() spautolm() # S3 method for class 'spautolm' summary() spBreg_sac() # S3 method for class 'MCMC_sar_g' impacts() # S3 method for class 'MCMC_sem_g' impacts() # S3 method for class 'MCMC_sac_g' impacts() spBreg_err() spBreg_lag() # S3 method for class 'SLX' predict() lmSLX() # S3 method for class 'SLX' impacts() create_WX() # S3 method for class 'sarlm' anova() bptest.sarlm() errorsarlm() # S3 method for class 'sarlm' impacts() lagsarlm() # S3 method for class 'sarlm' predict() # S3 method for class 'sarlm.pred' print() # S3 method for class 'sarlm.pred' as.data.frame() # S3 method for class 'sarlm' residuals() # S3 method for class 'sarlm' deviance() # S3 method for class 'sarlm' coef() # S3 method for class 'sarlm' vcov() # S3 method for class 'sarlm' fitted() sacsarlm() # S3 method for class 'sarlm' summary() # S3 method for class 'sarlm' print() # S3 method for class 'summary.sarlm' print() trW()"},{"path":"https://r-spatial.github.io/spdep/reference/spdep-defunct.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Defunct Functions in Package spdep — spdep-defunct","text":"Model-fitting functions functions supporting model fitting moved spatialreg package.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/spdep.html","id":null,"dir":"Reference","previous_headings":"","what":"Return package version number — spdep","title":"Return package version number — spdep","text":"function retreives package version build information","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spdep.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Return package version number — spdep","text":"","code":"spdep(build = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/spdep.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Return package version number — spdep","text":"build TRUE, also returns build information","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spdep.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Return package version number — spdep","text":"character vector one two elements","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spdep.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Return package version number — spdep","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":null,"dir":"Reference","previous_headings":"","what":"Provides constants for spatial weights matrices — spweights.constants","title":"Provides constants for spatial weights matrices — spweights.constants","text":"function calculates constants needed tests spatial autocorrelation general weights matrices represented listw objects. Note: spdep 0.3-32, values S1 S2 returned correctly underlying symmetric asymmetric neighbour lists, 0.3-32, S1 S2 wrong listw objects based asymmetric neighbour lists, k-nearest neighbours (thanks Luc Anselin finding bug).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Provides constants for spatial weights matrices — spweights.constants","text":"","code":"spweights.constants(listw, zero.policy=attr(listw, \"zero.policy\"), adjust.n=TRUE) Szero(listw)"},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Provides constants for spatial weights matrices — spweights.constants","text":"listw listw object example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE ignore zones without neighbours, FALSE fail encountered adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Provides constants for spatial weights matrices — spweights.constants","text":"n number zones n1 n - 1 n2 n - 2 n3 n - 3 nn n * n S0 global sum weights S1 S1 sum weights S2 S2 sum weights","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Provides constants for spatial weights matrices — spweights.constants","text":"Haining, R. 1990 Spatial data analysis social environmental sciences, Cambridge University Press, p. 233; Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 19, 21.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Provides constants for spatial weights matrices — spweights.constants","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Provides constants for spatial weights matrices — spweights.constants","text":"","code":"data(oldcol) B <- spweights.constants(nb2listw(COL.nb, style=\"B\")) W <- spweights.constants(nb2listw(COL.nb, style=\"W\")) C <- spweights.constants(nb2listw(COL.nb, style=\"C\")) S <- spweights.constants(nb2listw(COL.nb, style=\"S\")) U <- spweights.constants(nb2listw(COL.nb, style=\"U\")) print(data.frame(rbind(unlist(B), unlist(W), unlist(C), unlist(S), unlist(U)), row.names=c(\"B\", \"W\", \"C\", \"S\", \"U\"))) #> n n1 n2 n3 nn S0 S1 S2 #> B 49 48 47 46 2401 232 464.00000000 5.136000e+03 #> W 49 48 47 46 2401 49 23.29434146 2.048729e+02 #> C 49 48 47 46 2401 49 20.69827586 2.291085e+02 #> S 49 48 47 46 2401 49 21.25561347 2.134568e+02 #> U 49 48 47 46 2401 1 0.00862069 9.542212e-02"},{"path":"https://r-spatial.github.io/spdep/reference/ssw.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute the sum of dissimilarity — ssw","title":"Compute the sum of dissimilarity — ssw","text":"function computes sum dissimilarity observation mean (scalar vector) observations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/ssw.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute the sum of dissimilarity — ssw","text":"","code":"ssw(data, id, method = c(\"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\", \"minkowski\", \"mahalanobis\"), p = 2, cov, inverted = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/ssw.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute the sum of dissimilarity — ssw","text":"data matrix observations nodes. id Node index compute cost method Character function declare distance method. method character, method must \"mahalanobis\" \"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\" \"minkowisk\". method one \"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\" \"minkowisk\", see dist details, function used compute distance. method=\"mahalanobis\", mahalanobis distance computed neighbour areas. method function, function used compute distance. p power Minkowski distance. cov covariance matrix used compute mahalanobis distance. inverted logical. 'TRUE', 'cov' supposed contain inverse covariance matrix.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/ssw.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute the sum of dissimilarity — ssw","text":"numeric, sum dissimilarity observations id data mean (scalar vector) observations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/ssw.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute the sum of dissimilarity — ssw","text":"Elias T. Krainski Renato M. Assuncao","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/ssw.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute the sum of dissimilarity — ssw","text":"","code":"data(USArrests) n <- nrow(USArrests) ssw(USArrests, 1:n) #> [1] 3701.394 ssw(USArrests, 1:(n/2)) #> [1] 1910.214 ssw(USArrests, (n/2+1):n) #> [1] 1625.882 ssw(USArrests, 1:(n/2)) + ssw(USArrests, (n/2+1):n) #> [1] 3536.096"},{"path":"https://r-spatial.github.io/spdep/reference/subset.listw.html","id":null,"dir":"Reference","previous_headings":"","what":"Subset a spatial weights list — subset.listw","title":"Subset a spatial weights list — subset.listw","text":"function subsets spatial weights list, retaining objects subset argument vector TRUE. present subset non-general weights lists (created nb2listw glist=NULL).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/subset.listw.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Subset a spatial weights list — subset.listw","text":"","code":"# S3 method for class 'listw' subset(x, subset, zero.policy = attr(x, \"zero.policy\"), ...)"},{"path":"https://r-spatial.github.io/spdep/reference/subset.listw.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Subset a spatial weights list — subset.listw","text":"x object class listw subset logical expression zero.policy default attr(x, \"zero.policy\") set x created, attribute set, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors - passed nb2listw ... generic function pass-","code":""},{"path":"https://r-spatial.github.io/spdep/reference/subset.listw.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Subset a spatial weights list — subset.listw","text":"function returns object class listw component style input object, component neighbours list integer vectors containing neighbour region number ids (compacted run 1:number regions subset), component weights weights computed neighbours using style. -neighbour observations created subsetting zero.policy input weights object FALSE, set TRUE warning issued.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/subset.listw.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Subset a spatial weights list — subset.listw","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/subset.listw.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Subset a spatial weights list — subset.listw","text":"","code":"col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) to.be.dropped <- c(31, 34, 36, 39, 42, 46) pre <- nb2listw(col.gal.nb) print(pre) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> #> Weights style: W #> Weights constants summary: #> n nn S0 S1 S2 #> W 49 2401 49 23.48489 204.6687 post <- subset(pre, !(1:length(col.gal.nb) %in% to.be.dropped)) print(post) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 43 #> Number of nonzero links: 212 #> Percentage nonzero weights: 11.46566 #> Average number of links: 4.930233 #> #> Weights style: W #> Weights constants summary: #> n nn S0 S1 S2 #> W 43 1849 43 19.26584 178.4604 columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) nb <- poly2nb(columbus) lw <- nb2listw(nb, style=\"W\") attr(lw, \"zero.policy\") #> [1] FALSE (lwa <- subset(lw, 1:nrow(columbus) != c(21))) #> Warning: subsetting caused increase in subgraph count #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 48 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.982639 #> Average number of links: 4.791667 #> 2 disjoint connected subgraphs #> #> Weights style: W #> Weights constants summary: #> n nn S0 S1 S2 #> W 48 2304 48 22.46811 199.4398 attr(lwa, \"zero.policy\") #> [1] FALSE (lwb <- subset(lw, !(1:nrow(columbus) %in% c(21, 36, 39)))) #> Warning: subsetting caused increase in subgraph count #> Warning: subsetting created no-neighbour observations, zero.policy set TRUE #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 46 #> Number of nonzero links: 216 #> Percentage nonzero weights: 10.20794 #> Average number of links: 4.695652 #> 1 region with no links: #> 46 #> 3 disjoint connected subgraphs #> #> Weights style: W #> Weights constants summary: #> n nn S0 S1 S2 #> W 45 2025 45 22.857 187.4843 attr(lwb, \"zero.policy\") #> [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/reference/subset.nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Subset a neighbours list — subset.nb","title":"Subset a neighbours list — subset.nb","text":"function subsets neighbors list, retaining objects subset argument vector TRUE.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/subset.nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Subset a neighbours list — subset.nb","text":"","code":"# S3 method for class 'nb' subset(x, subset, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/subset.nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Subset a neighbours list — subset.nb","text":"x object class nb subset logical expression ... generic function pass-","code":""},{"path":"https://r-spatial.github.io/spdep/reference/subset.nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Subset a neighbours list — subset.nb","text":"function returns object class nb list integer vectors containing neighbour region number ids (compacted run 1:number regions subset).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/subset.nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Subset a neighbours list — subset.nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/subset.nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Subset a neighbours list — subset.nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries plot(col.gal.nb, coords) to.be.dropped <- c(31, 34, 36, 39, 42, 46) text(coords[to.be.dropped,1], coords[to.be.dropped,2], labels=to.be.dropped, pos=2, offset=0.3) sub.col.gal.nb <- subset(col.gal.nb, !(1:length(col.gal.nb) %in% to.be.dropped)) plot(sub.col.gal.nb, coords[-to.be.dropped,], col=\"red\", add=TRUE) which(!(attr(col.gal.nb, \"region.id\") %in% attr(sub.col.gal.nb, \"region.id\"))) #> [1] 31 34 36 39 42 46"},{"path":"https://r-spatial.github.io/spdep/reference/summary.nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Print and summary function for neighbours and weights lists — summary.nb","title":"Print and summary function for neighbours and weights lists — summary.nb","text":"function prints summary measures links neighbours list. matrix coordinates given well, summary descriptive measures link lengths also printed. Print summary functions also available \"listw\" weights list objects, also reporting constants (S0, S1, S2) used inference global spatial autocorrelation statistics Moran's , Geary's C, join-count tests Getis-Ord G.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/summary.nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Print and summary function for neighbours and weights lists — summary.nb","text":"","code":"# S3 method for class 'nb' summary(object, coords=NULL, longlat = NULL, scale = 1, ...) # S3 method for class 'nb' print(x, ...) # S3 method for class 'listw' summary(object, coords, longlat, zero.policy = attr(object, \"zero.policy\"), scale = 1, adjust.n=TRUE, ...) # S3 method for class 'listw' print(x, zero.policy = attr(x, \"zero.policy\"), ...)"},{"path":"https://r-spatial.github.io/spdep/reference/summary.nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Print and summary function for neighbours and weights lists — summary.nb","text":"object object class nb coords matrix region point coordinates SpatialPoints object sfc points object longlat TRUE point coordinates longitude-latitude decimal degrees, case distances measured kilometers; coords SpatialPoints object, value taken object ... additional arguments affecting output produced x object class nb zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; FALSE stop error empty neighbour sets scale passed stem() control plot length adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations spweights.constants adjusted","code":""},{"path":"https://r-spatial.github.io/spdep/reference/summary.nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Print and summary function for neighbours and weights lists — summary.nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/summary.nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Print and summary function for neighbours and weights lists — summary.nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE) col.gal.nb #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 summary(col.gal.nb, coords) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> Link number distribution: #> #> 2 3 4 5 6 7 8 9 10 #> 7 7 13 4 9 6 1 1 1 #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links col.listw <- nb2listw(col.gal.nb, style=\"W\") col.listw #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> #> Weights style: W #> Weights constants summary: #> n nn S0 S1 S2 #> W 49 2401 49 23.48489 204.6687 summary(col.listw) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> Link number distribution: #> #> 2 3 4 5 6 7 8 9 10 #> 7 7 13 4 9 6 1 1 1 #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links #> #> Weights style: W #> Weights constants summary: #> n nn S0 S1 S2 #> W 49 2401 49 23.48489 204.6687 col_geoms <- st_geometry(columbus) col_geoms[21] <- st_buffer(col_geoms[21], dist=-0.05) st_geometry(columbus) <- col_geoms nb <- poly2nb(columbus) #> Warning: some observations have no neighbours; #> if this seems unexpected, try increasing the snap argument. #> Warning: neighbour object has 3 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. summary(nb) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> 1 region with no links: #> 21 #> 3 disjoint connected subgraphs #> Link number distribution: #> #> 0 2 3 4 5 6 7 8 9 10 #> 1 5 9 12 4 10 2 4 1 1 #> 5 least connected regions: #> 1 6 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links try(nb2listw(nb, style=\"W\")) #> Error in nb2listw(nb, style = \"W\") : #> Empty neighbour sets found (zero.policy: FALSE) summary(nb2listw(nb, style=\"W\", zero.policy=TRUE)) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> 1 region with no links: #> 21 #> 3 disjoint connected subgraphs #> Link number distribution: #> #> 0 2 3 4 5 6 7 8 9 10 #> 1 5 9 12 4 10 2 4 1 1 #> 5 least connected regions: #> 1 6 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links #> #> Weights style: W #> Weights constants summary: #> n nn S0 S1 S2 #> W 48 2304 48 22.46811 199.4398 summary(nb2listw(nb, style=\"W\", zero.policy=TRUE), adjust.n=FALSE) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> 1 region with no links: #> 21 #> 3 disjoint connected subgraphs #> Link number distribution: #> #> 0 2 3 4 5 6 7 8 9 10 #> 1 5 9 12 4 10 2 4 1 1 #> 5 least connected regions: #> 1 6 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links #> #> Weights style: W #> Weights constants summary: #> n nn S0 S1 S2 #> W 49 2401 48 22.46811 199.4398"},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":null,"dir":"Reference","previous_headings":"","what":"Test a neighbours list for symmetry — is.symmetric.nb","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"Checks neighbours list symmetry/transitivity (neighbour j, j neighbour ). holds distance contiguity based neighbours, k-nearest neighbours. helper function sym.attr.nb() calls .symmetric.nb() set sym attribute needed, make.sym.nb makes non-symmetric list symmetric adding neighbors. .symmetric.glist checks list general weights corresponding neighbours symmetry symmetric neighbours.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"","code":"is.symmetric.nb(nb, verbose = NULL, force = FALSE) sym.attr.nb(nb) make.sym.nb(nb) old.make.sym.nb(nb) is.symmetric.glist(nb, glist)"},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"nb object class nb list integer vectors containing neighbour region number ids. verbose default NULL, use global option value; TRUE prints non-matching pairs force respect neighbours list sym attribute test anyway glist list general weights corresponding neighbours","code":""},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"TRUE symmetric, FALSE ; .symmetric.glist returns value attribute, \"d\", indicating failed symmetry largest failing value.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"new version make.sym.nb Bjarke Christensen now included. older version renamed old.make.sym.nb, comparison constitutes nice demonstration vectorising speedup using sapply lapply rather loops. -neighbour observations present, old.make.sym.nb used.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries ind <- row.names(as(columbus, \"Spatial\")) print(is.symmetric.nb(col.gal.nb, verbose=TRUE, force=TRUE)) #> [1] TRUE k4 <- knn2nb(knearneigh(coords, k=4), row.names=ind) k4 <- sym.attr.nb(k4) print(is.symmetric.nb(k4)) #> [1] FALSE k4.sym <- make.sym.nb(k4) print(is.symmetric.nb(k4.sym)) #> [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"function creates object class nb (defined library spdep) containing connexion diagram. edges sites based tolerance angle maximum distance. angle directional; direction always bottow top screen.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"","code":"tolerance.nb(coords, unit.angle = \"degrees\", max.dist, tolerance, rot.angle, plot.sites=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"coords matrix data frame containing X Y coordinates study sites. unit.angle Character. measurement units angles defined: either \"degrees\" (default) \"radians\". max.dist Numeric. maximum distance edge linking two sites together. tolerance Numeric. tolerance angle site can influence another site. angle measured vertically bottom top pictures rotation points. rot.angle Numeric, optional. angle set coordinates rotated creating connexion diagram. set coordinates rotated counterclockwise. Negative values produce clockwise rotation. plot.sites Logical (TRUE, FALSE) determining site plotted graphic window. graph allows one make sure points rotated correct direction.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"Even though function creates connexion diagram based tolerance angle going bottom top screen, resulting object symmetric, meaning site influences another vice versa. final object represent directional connexion network.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"function returns object class nb list integer vectors corresponding neighbour region numbers.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"warning","dir":"Reference","previous_headings":"","what":"Warning","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"function design handle large number rows coords. use function set coordinates 1500 entries memory intensive.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"F. Guillaume Blanchet","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"","code":"set.seed(1) ex.data<-cbind(runif(50),rexp(50)) ### Construct object of class nb with a tolerance angle of 30 degrees ### and a maximum distance of 2 m. nb.ex<-tolerance.nb(ex.data, unit.angle = \"degrees\", max.dist=1, tolerance = 30) #> Warning: neighbour object has 3 sub-graphs ### Construct object of class nb with a tolerance angle of 30 degrees ### and a maximum distance of 2 m. The coordinates are rotated at an angle ### of 45 degrees counterclockwise. nb.ex2<-tolerance.nb(ex.data, unit.angle = \"degrees\", max.dist=1, tolerance = 30, rot.angle = 45) #> Warning: neighbour object has 4 sub-graphs ### Construct object of class nb with a tolerance angle of pi/8 radians ### and a maximum distance of 1.5 m. The coordinates are rotated at ### an angle of pi/4 radians clockwise. nb.ex3<-tolerance.nb(ex.data, unit.angle = \"radians\", max.dist=1.5, tolerance = pi/8, rot.angle = -pi*2/3) #> Warning: neighbour object has 5 sub-graphs par(mfrow=c(1,3)) plot(nb.ex,ex.data,asp=1) plot(nb.ex2,ex.data,asp=1) plot(nb.ex3,ex.data,asp=1)"},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Neighbours list from tri object — tri2nb","title":"Neighbours list from tri object — tri2nb","text":"function uses deldir package convert matrix two-dimensional coordinates neighbours list class nb list integer vectors containing neighbour region number ids.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Neighbours list from tri object — tri2nb","text":"","code":"tri2nb(coords, row.names = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Neighbours list from tri object — tri2nb","text":"coords matrix, data.frame tibble point coordinates two columns, SpatialPoints object sfc points object row.names character vector region ids added neighbours list attribute region.id, default seq(1, nrow(x))","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Neighbours list from tri object — tri2nb","text":"coordinates duplicated, function used. coordinates grid, need ordered first three collinear, first triangle can constructed. can achieved randomising order coordinates (possibly several times), re-ordering order data match new order neighbour list - fix used, remember re-order row.names argument well coordinates! Please also note triangulation grid points give arbitrary diagonal neighbours, may sensible outcome, dnearneigh() may serve better tri2nb() used.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Neighbours list from tri object — tri2nb","text":"function returns object class nb list integer vectors containing neighbour region number ids.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Neighbours list from tri object — tri2nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Neighbours list from tri object — tri2nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE) ind <- row.names(columbus) suppressPackageStartupMessages(require(deldir)) col.tri.nb <- tri2nb(coords, row.names=ind) plot(st_geometry(columbus), border=\"grey\") plot(col.tri.nb, coords, add=TRUE) title(main=\"Raw triangulation links\", cex.main=0.6) x <- seq(0,1,0.1) y <- seq(0,2,0.2) xy <- expand.grid(x, y) try(xy.nb <- tri2nb(xy)) seed <- 1234 xid <- sample(1:nrow(xy)) xy.nb <- tri2nb(xy[xid,]) plot(xy.nb, xy[xid,]) # example of reading points with readr::read_csv() yielding a tibble load(system.file(\"etc/misc/coords.rda\", package=\"spdep\")) class(coords) #> [1] \"spec_tbl_df\" \"tbl_df\" \"tbl\" \"data.frame\" nb <- tri2nb(coords) plot(nb, coords)"},{"path":"https://r-spatial.github.io/spdep/reference/write.nb.gal.html","id":null,"dir":"Reference","previous_headings":"","what":"Write a neighbours list as a GAL lattice file — write.nb.gal","title":"Write a neighbours list as a GAL lattice file — write.nb.gal","text":"Write neighbours list GAL lattice file, may also use newer GeoDa header format","code":""},{"path":"https://r-spatial.github.io/spdep/reference/write.nb.gal.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Write a neighbours list as a GAL lattice file — write.nb.gal","text":"","code":"write.nb.gal(nb, file, oldstyle=TRUE, shpfile=NULL, ind=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/write.nb.gal.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Write a neighbours list as a GAL lattice file — write.nb.gal","text":"nb object class nb list integer vectors containing neighbour region number ids. file name file GAL lattice data oldstyle TRUE, first line file contains number spatial units, FALSE, uses newer GeoDa style shpfile Shapefile name taken GAL file dataset ind region id indicator variable name","code":""},{"path":"https://r-spatial.github.io/spdep/reference/write.nb.gal.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Write a neighbours list as a GAL lattice file — write.nb.gal","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/write.nb.gal.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Write a neighbours list as a GAL lattice file — write.nb.gal","text":"","code":"col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) GALfile <- tempfile(\"GAL\") write.nb.gal(col.gal.nb, GALfile) col.queen <- read.gal(GALfile) summary(diffnb(col.queen, col.gal.nb)) #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 0 #> Percentage nonzero weights: 0 #> Average number of links: 0 #> 49 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 #> 49 disjoint connected subgraphs #> Link number distribution: #> #> 0 #> 49"},{"path":[]},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-1-3-13-2025-06-10","dir":"Changelog","previous_headings":"","what":"Version 1-3-13 (2025-06-10)","title":"Version 1-3-13 (2025-06-10)","text":"Adds Bavaud’s multivariate spatialdelta support functions methods Add note changes output tests error autocorrelation contrast codings set non-default values","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-11-2025-04-24","dir":"Changelog","previous_headings":"","what":"Version 1.3-11 (2025-04-24)","title":"Version 1.3-11 (2025-04-24)","text":"CRAN release: 2025-04-24 introduce warnings factors (categorical variables) Durbin models (SD.RStests) remove |> vignette avoid R >= 4.1 dependency https://stat.ethz.ch/pipermail/r-devel/2025-January/083768.html update reference Koley (2024) man/SD.RStests.Rd add warnings Durbin terms including categorical variables SD.RStests","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-10-2025-01-20","dir":"Changelog","previous_headings":"","what":"Version 1.3-10 (2025-01-20)","title":"Version 1.3-10 (2025-01-20)","text":"CRAN release: 2025-01-20 R_NO_REMAP problem R < 4.4.1 fixed replacing COPY_TO_USER_STRING Rf_mkChar, include/Rdefines.h revision 86416 set COPY_TO_USER_STRING mkChar defined Rf_mkChar R_NO_REMAP defined, #176, thanks Edzer Pebesma disambiguate skater examples satisfy pkgdown, used rgeoda::skater; patches examples satisfy pkgdown use inherits skater","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-9-2025-01-16","dir":"Changelog","previous_headings":"","what":"Version 1.3-9 (2025-01-16)","title":"Version 1.3-9 (2025-01-16)","text":"CRAN release: 2025-01-16 revisit diffnb set operations like union.nb setdiff.nb following #175; diffnb largely rewritten longer generate deformed output; set operations modified match base functions actions convert error Rf_error, length Rf_length etc. accommodate R_NO_REMAP, see https://github.com/r-spatial/spdep/commit/b61f6b17be09383c94b45e912f9213735aa62212 R 4.5 re-instate rgeoda references","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-8-2024-12-02","dir":"Changelog","previous_headings":"","what":"Version 1.3-8 (2024-12-02)","title":"Version 1.3-8 (2024-12-02)","text":"CRAN release: 2024-12-02 Remove remaining spData ESRI shapefile use","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-7-2024-11-25","dir":"Changelog","previous_headings":"","what":"Version 1.3-7 (2024-11-25)","title":"Version 1.3-7 (2024-11-25)","text":"CRAN release: 2024-11-25 (temporarily) remove rgeoda references successfully re-submitted CRAN add write.swmdbf #171 complement #163 modify defaults licd_multi","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-6-2024-09-13","dir":"Changelog","previous_headings":"","what":"Version 1.3-6 (2024-09-13)","title":"Version 1.3-6 (2024-09-13)","text":"CRAN release: 2024-09-13 adding vignette describing recent changes poly2nb #162, subgraph -neighbour (island) handling adding prototype LICD ESDA function licd_multi hotspot method add read.swmdbf2listw #163 reading DBF files exported ArcGIS representing SWM objects; note problems observation IDs known, see help file #162 add option -neighbour checking poly2nb - default report whether -neighbour observations present #162 change default snap= argument poly2nb 10mm Condition forthcoming tmap 4 #160 handle n.comp.nb delay print.nb elsewhere total number neighbours large","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-5-2024-06-10","dir":"Changelog","previous_headings":"","what":"Version 1.3-5 (2024-06-10)","title":"Version 1.3-5 (2024-06-10)","text":"CRAN release: 2024-06-10 #157 migrate ESRI Shapefile GPKG files; convert bhicv.shp GPKG #155 Throw error hotspot despatched object without \"quadr\" attribute #154 turn s2 vignette","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-4-2024-05-31","dir":"Changelog","previous_headings":"","what":"Version 1.3-4 (2024-05-31)","title":"Version 1.3-4 (2024-05-31)","text":"CRAN release: 2024-05-31 add scale argument geary.test, geary.mc geary #151, appropriate tests Introduce error knearneigh k less largest count identical points; encountered, increase k remove spurious warning knearneigh longlat geometries fix https://github.com/edzer/sdsr/issues/121, wrong assignment old test names lmRStests fix #144 plot.nb nb2lines","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-3-2024-02-07","dir":"Changelog","previous_headings":"","what":"Version 1.3-3 (2024-02-07)","title":"Version 1.3-3 (2024-02-07)","text":"CRAN release: 2024-02-07 change lm.LMtests lm.RStests re-name Lagrange multiplier Rao’s score; add GNM_ prefix test names input object inherits SlX created spatialreg::lmSLX (Koley, forthcoming) add SD.RStests implementation Rao’s score tests spatial Durbin models (Koley Bera, 2024) SDEM models (Koley, forthcoming) #143 row.names pass-poly2nb corrected, harmonised row.names pass-also nbdists dnearneigh #139 add na.action argument geary.test, geary.mc globalG.test add style sn2listw use tri2nb","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-1-2023-11-23","dir":"Changelog","previous_headings":"","what":"Version 1.3-1 (2023-11-23)","title":"Version 1.3-1 (2023-11-23)","text":"CRAN release: 2023-11-23 functions creating nb objects now warn object sub-graph count > 1 get.SubgraphOption TRUE (default FALSE): complement.nb, diffnb, dnearneigh, droplinks, edit.nb, graph2nb, knn2nb, nb2blocknb, nblag, nblag_cumul, poly2nb, read.gal, read.gwt2nb, setdiff.nb, tolerance.nb, tri2nb, union.nb summary.nb, print.nb, summary.listw print.listw now report subgraph count n.comp.nb one subset.nb now reports subgraph count neighbour object increases subsetting adding zero.policy attribute functions creating listw objects: nb2listw, sn2listw, mat2listw, nb2listwdist. Default zero.policy= argument updated use attr(., \"zero.policy\") summary.listw, print.listw, moran, moran.test, moran.mc, moran.plot, geary.mc, geary, geary.test, globalG.test, joincount.test, joincount.mc, joincount.multi, localC, localC_perm, localmoran, localmoran_perm, localG, localG_perm, lee, lee.test, lee.mc, lm.morantest, lm.LMtests, sp.mantel.mc, listw2star, lag.listw, lm.morantest, lm.LMtests, subset.listw, EBImoran.mc, LOSH, LOSH.mc, LOSH.cs, lm.morantest.exactand lm.morantest.sad confusing error message moran.plot() -neighbour cases, zero.policy=FALSE replace rgrass7 rgrass vignette fix #133 (edit.nb affected attaching sp)","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-8-2023-02-28","dir":"Changelog","previous_headings":"","what":"Version 1.2-8 (2023-02-28)","title":"Version 1.2-8 (2023-02-28)","text":"CRAN release: 2023-02-28 mat2listw() warning style= argument given, M\" given https://github.com/r-spatial/spatialreg/issues/24, https://github.com/r-spatial/spatialreg/issues/23. remaining users run_perm() - localC(), localmoran_bv() local_joincount_uni() get no_repeat_in_row= arguments. Address 2) #124; localG_perm() localmoran_perm() get no_repeat_in_row= arguments use conditional permutation without replacement sample vectors; default implementation uses sampling replacement, acceptable across simulation draws, arguably less acceptable within draws. Feedback valued. Address 1) #124; localG_perm() localG() now return analytical standard deviates. standard deviates simulated distributions now returned attr(., \"internals\")[,\"StdDev.Gi\"] localG_perm(), p-values, etc. move sp Depends Imports, reduce visual impression sp objects required spdep; sf objects now preferred, sp objects can used , although users may need attach sp expliciitly. fix #121 #123; correcting returned values localG_perm() estimating G-star measure (fix self x values weights) address #120, moving documentation listw2U() ?lm.morantest ?nb2listw addressing #119 interpretation moran_bv() results adding #116, René Westerholt fix #113, low R version grDevices::hcl.colors() addressing #111 Josiah Parry PRs René Westerholt, ending #109, local GS measure","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-7-2022-10-01","dir":"Changelog","previous_headings":"","what":"Version 1.2-7 (2022-10-01)","title":"Version 1.2-7 (2022-10-01)","text":"CRAN release: 2022-10-01 #103 refactoring local joincount test Josiah Parry add hotspot methods localmoran (analytical, permutation, Saddlepoint exact), localC (univariate multivariate) localG (analytical permutation) #95 add \"two.sided\" lee.mc(), sp.mantel.mc(), EBImoran.mc(), joincount.mc(), geary.mc() #92, #93, #94, #96, #97 contributions prototype bivariate Moran, local bivariate Moran local joincount bivariate joincount tests Josiah Parry #91 tolerance.nb() update F. Guillaume Blanchet updating coercion Matrix 1.4-2 fix ncpus issue dontrun examples remove suggested packages rgdal, rgeos, maptools","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-5-2022-08-11","dir":"Changelog","previous_headings":"","what":"Version 1.2-5 (2022-08-11)","title":"Version 1.2-5 (2022-08-11)","text":"CRAN release: 2022-08-11 permit use data.frame tibble matrix functions creating neighbour objects 2D points (preferred use object inheriting `\"SpatialPoints\" \"sfc\") fix #87 wrong logic infinite weights nb2listwdist() https://github.com/r-spatial/s2/pull/174 speeds dnearneigh() geographical coordinates without using s2::s2_closest_edges(). Adapting vignettes absence rgdal maptools","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-4-2022-04-18","dir":"Changelog","previous_headings":"","what":"Version 1.2-4 (2022-04-18)","title":"Version 1.2-4 (2022-04-18)","text":"CRAN release: 2022-04-18 added remove.self(), thanks Josiah Parry #83. unescape underscores help pages.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-3-2022-03-29","dir":"Changelog","previous_headings":"","what":"Version 1.2-3 (2022-03-29)","title":"Version 1.2-3 (2022-03-29)","text":"CRAN release: 2022-03-29 replace deprecated S-compatibility macros DOUBLE_ #81 improved dnearneigh() help page. #79 remove \"htest\" class LOSH.mc() output object. Added GA SI article citations.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-2-2022-01-28","dir":"Changelog","previous_headings":"","what":"Version 1.2-2 (2022-01-28)","title":"Version 1.2-2 (2022-01-28)","text":"CRAN release: 2022-01-28 Replace rainbow() hcl.colors(..., \"Set 2\") plot.skater(). Add link R-sig-geo thread EBlocal() NaN estimates many counts zero help page. Revise add documentation object returned localC_perm() #68 #72 #73 #74 #75 #76 localmoran.sad(), localmoran.exact() localmoran.exact.alt() now use multiple compute nodes needed; Omega used, multiple cores may need memory #77 s2 > 1.0.7, use indexed distances dnearneigh() https://github.com/r-spatial/s2/pull/162.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-1-2022-01-05","dir":"Changelog","previous_headings":"","what":"Version 1.2-1 (2022-01-05)","title":"Version 1.2-1 (2022-01-05)","text":"CRAN release: 2022-01-04 Switching deprecated functions moved spatialreg defunct.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-13-2021-12-14","dir":"Changelog","previous_headings":"","what":"Version 1.1-13 (2021-12-14)","title":"Version 1.1-13 (2021-12-14)","text":"CRAN release: 2021-12-14 Recent changes poly2nb() reduced recently (1.1-8) removed use snap= finding candidate neighbours; many thanks Matilda Brown clear well-documented issue #65 Add local Geary’s C #66 thanks Josiah Parry, discussion work #68 localmoran_perm() returns look-folded rank p-values","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-12-2021-11-09","dir":"Changelog","previous_headings":"","what":"Version 1.1-12 (2021-11-09)","title":"Version 1.1-12 (2021-11-09)","text":"CRAN release: 2021-11-09 poly2nb(), reverted removal legacy interpreted overlapping envelope code sp objects coerced sf without rgeos. Add Fortran character handling USE_FC_LEN_T WRE §6.6.1. Checks OK forthcoming deldir 1.0-0. Fixes #62 clarifying dnearneigh() help page","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-11-2021-09-07","dir":"Changelog","previous_headings":"","what":"Version 1.1-11 (2021-09-07)","title":"Version 1.1-11 (2021-09-07)","text":"CRAN release: 2021-09-07 knearneigh() nbdists(); added prototype adaptation s2 unprojected coordinates, used sf_use_s2() TRUE became default sf 1.0.0 https://github.com/r-spatial/s2/issues/125. activated default. dnearneigh() can choose prototype s2 approach sf_use_s2() TRUE use_s2=TRUE unprojected coordinates; https://github.com/r-spatial/s2/issues/125 seems distance thresholds present use brute-force rather spatial indexing. Use activated default. poly2nb() now uses sf::st_intersects() find candidate neighbours unless findInBounds= NULL. spatial indexing, fast scales well large data sets. sf_use_s2() TRUE, sf::st_intersects() passes geometries s2::s2_intersects_matrix(), also uses spatial indexing fast, scaling well large data sets. localmoran() localmoran_perm() return cluster quadrants attribute three splits, zeros, means medians variable interest spatial lag. localmoran_perm() returns skewness kurtosis permutation samples.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-8-2021-05-23","dir":"Changelog","previous_headings":"","what":"Version 1.1-8 (2021-05-23)","title":"Version 1.1-8 (2021-05-23)","text":"CRAN release: 2021-05-23 #55 related #20 cycling order setting grids provoked re-design interface cell2nb(), passing \"GridTopology\" \"SpatialGrid\" objects unnamed first x= argument. Coerce \"RasterLayer\" similar raster, terra stars objects sp class objects first need . working renewing arguments cell2nb(), useful add tinytest support, now present function may extended functions creating \"nb\" objects. #58 contributed Jeff Sauer Levi Wolf (https://doi.org/10.31219/osf.io/ugkhp) providing conditional standard deviates local Moran’s Error assignment matrix detected CRAN check SIDS vignette, section median polish","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-7-2021-04-03","dir":"Changelog","previous_headings":"","what":"Version 1.1-7 (2021-04-03)","title":"Version 1.1-7 (2021-04-03)","text":"CRAN release: 2021-04-03 Changes continuous integration vignettes. Error poly2nb(, queen=FALSE) sf grids (double counting closed polygon start/end points), https://github.com/r-spatial/spdep/issues/50, thanks Christopher Kenny. Adding local Moran local G conditional permutation: localmoran_perm() localG_perm(). Adding nb2listwdist() contributed René Westerholt. Adding use sf GEOS find polygon contiguity candidates poly2nb() geometry count >= 500 - uses intersections polygon envelopes. #38, #53 removing RANN, adding dbscan suggestions fast dnearneigh() knearneigh() via use_kd_tree= argument fast planar neighbour set finding 2D 3D. Affects soi.graph() , used RANN. #54 avoid partial matching glist= handling. Disambiguating spdep spatialreg model output object class names prior making spdep model fitting functions defunct.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-5-2020-06-29","dir":"Changelog","previous_headings":"","what":"Version 1.1-5 (2020-06-29)","title":"Version 1.1-5 (2020-06-29)","text":"CRAN release: 2020-06-29 Replacing broken geoda URLs, moving knitr rmarkdown, work-around missing weights files spData.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-3-2019-09-18","dir":"Changelog","previous_headings":"","what":"Version 1.1-3 (2019-09-18)","title":"Version 1.1-3 (2019-09-18)","text":"CRAN release: 2019-09-18 small maintenance update accommodate forthcoming change spData (dataset used example spdep spData changing name; name involved putting “x”, “y” “xyz” global environment lazy loading dataset).","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-2-2019-04-05","dir":"Changelog","previous_headings":"","what":"Version 1.1-2 (2019-04-05)","title":"Version 1.1-2 (2019-04-05)","text":"CRAN release: 2019-04-05 Follow-version spdep functions methods transferred spatialreg package marked deprecated, still exported spdep. Reverse dependencies passing released version still pass version.","code":""}] +[{"path":"https://r-spatial.github.io/spdep/articles/CO69.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"“The Problem of Spatial Autocorrelation:” forty years on","text":"Cliff Ord (1969), published forty years ago, marked turning point treatment spatial autocorrelation quantitative geography. provided framework needed applied researcher attempt implementation different system, possibly using different programming language. spirit, examine spatial weights represented implementations may reproduced, tabulated results paper may reproduced, may extended cover simulation. One major assertions Cliff Ord (1969) statistic advances measurement spatial autocorrelation respect Moran (1950) Geary (1954) general specification spatial weights used. general form implications preparation weights , calculation measures. look spatial weights first, moving consider measures presented paper subsequent developments. , put together data set matching used Cliff Ord (1969). provide tabulated data counties Irish Republic, omit Dublin analyses. shapefile included package, kindly made available Michael Tiefelsdorf, used starting point: read SpatialPolygonsDataFrame — classes used handling spatial data fully described Roger S. Bivand, Pebesma, Gómez-Rubio (2008). need add data tabulated paper Table 2,1 p. 40, form text file added rainfall values Table 9, p. 49: Since assigned county names feature identifiers reading shapefiles, extra data, combine objects: Finally, need drop Dublin county omitted analyses conducted Cliff Ord (1969): double-check data, let us calculate sample Beta coefficients, using formulae given paper sample moments: differ somewhat ways skewness kurtosis computed modern statistical software, see example Joanes Gill (1998). However, purposes, let us reproduce Table 3, p. 42: Using tabulated value \\(23.6\\) percentage agricultural holdings 50 1950 Waterford, skewness kurtosis reproduced, comparison irishdata dataset , turns value rather \\(26.6\\), yields tabulated skewness kurtosis values. going , variables considered presented Table \\[vars\\]. Description variables Geary data set.","code":"library(spdep) eire <- as(sf::st_read(system.file(\"shapes/eire.gpkg\", package=\"spData\")[1]), \"Spatial\") row.names(eire) <- as.character(eire$names) #proj4string(eire) <- CRS(\"+proj=utm +zone=30 +ellps=airy +units=km\") class(eire) ## [1] \"SpatialPolygonsDataFrame\" ## attr(,\"package\") ## [1] \"sp\" names(eire) ## [1] \"A\" \"towns\" \"pale\" \"size\" \"ROADACC\" \"OWNCONS\" \"POPCHG\" ## [8] \"RETSALE\" \"INCOME\" \"names\" fn <- system.file(\"etc/misc/geary_eire.txt\", package=\"spdep\")[1] ge <- read.table(fn, header=TRUE) names(ge) ## [1] \"serlet\" \"county\" \"pagval2_10\" \"pagval10_50\" ## [5] \"pagval50p\" \"cowspacre\" \"ocattlepacre\" \"pigspacre\" ## [9] \"sheeppacre\" \"townvillp\" \"carspcap\" \"radiopcap\" ## [13] \"retailpcap\" \"psinglem30_34\" \"rainfall\" row.names(ge) <- as.character(ge$county) all.equal(row.names(ge), row.names(eire)) ## [1] TRUE eire_ge <- cbind(eire, ge) eire_ge1 <- eire_ge[!(row.names(eire_ge) %in% \"Dublin\"),] length(row.names(eire_ge1)) ## [1] 25 skewness <- function(z) {z <- scale(z, scale=FALSE); ((sum(z^3)/length(z))^2)/((sum(z^2)/length(z))^3)} kurtosis <- function(z) {z <- scale(z, scale=FALSE); (sum(z^4)/length(z))/((sum(z^2)/length(z))^2)} print(sapply(as(eire_ge1, \"data.frame\")[13:24], skewness), digits=3) ## pagval2_10 pagval10_50 pagval50p cowspacre ocattlepacre ## 1.675429 1.294978 0.000382 1.682094 0.086267 ## pigspacre sheeppacre townvillp carspcap radiopcap ## 1.138387 1.842362 0.472748 0.011111 0.342805 ## retailpcap psinglem30_34 ## 0.002765 0.068169 print(sapply(as(eire_ge1, \"data.frame\")[13:24], kurtosis), digits=4) ## pagval2_10 pagval10_50 pagval50p cowspacre ocattlepacre ## 3.790 4.331 1.508 4.294 2.985 ## pigspacre sheeppacre townvillp carspcap radiopcap ## 3.754 4.527 2.619 1.865 2.730 ## retailpcap psinglem30_34 ## 2.188 2.034 print(sapply(as(eire_ge1, \"data.frame\")[c(13,16,18,19)], function(x) skewness(log(x))), digits=3) ## pagval2_10 cowspacre pigspacre sheeppacre ## 0.68801 0.17875 0.00767 0.04184 print(sapply(as(eire_ge1, \"data.frame\")[c(13,16,18,19)], function(x) kurtosis(log(x))), digits=4) ## pagval2_10 cowspacre pigspacre sheeppacre ## 2.883 2.799 2.212 2.421"},{"path":"https://r-spatial.github.io/spdep/articles/CO69.html","id":"spatial-weights","dir":"Articles","previous_headings":"","what":"Spatial weights","title":"“The Problem of Spatial Autocorrelation:” forty years on","text":"basis comparison, first read unstandardised weighting matrix given Table A1, p. 54, paper, reading file corrected misprint giving O rather D neighbour V: file, counties represented serial letters, ordering conversion integer index representation required reach representation similar SpatialStats module spatial neighbours: done , can change representation listw object, assigning appropriate style (generalised binary) unstandardised values: Note values S0, S1, S2 correspond closely given page 42 paper, \\(0.84688672\\), \\(0.01869986\\) \\(0.12267319\\). discrepancies appear due rounding printed table weights. contiguous neighbours represented object match found using poly2nb. However, see reproduced contiguities smaller link count: missing link Clare Kerry, perhaps Tarbert–Killimer ferry, counties contiguous, Figure \\[plot\\_nb\\] shows: County boundaries contiguities attempt also made reproduce generalised weights 25 Irish counties reported Cliff Ord (1969), Dublin omitted. Reproducing inverse distance component \\(d_{ij}^{-1}\\) generalised weights \\(d_{ij}^{-1} \\beta_{(j)}\\) eased statement Cliff Ord (1973, 55) points chosen represent counties “geographic centres,” different centroids yielded applying chosen computational geometry function. distance metric given, may kilometers miles — tried, results sensitive difference applies equally across weights; miles used . Computing proportion shared distance measure \\(\\beta_{(j)}\\) harder, requires availability full topology input polygons. Roger S. Bivand, Pebesma, Gómez-Rubio (2008, 244) show employ vect2neigh function (written Markus Neteler) package using GRASS GIS vector handling create full topology spaghetti vector data extract border segment lengths; similar approach also mentioned using ArcGIS coverages purpose. GRASS used create topology, next proportion shared distance measure calculated. compare, need remove Tarbert–Killimer ferry link manually, view summary original weights, well correlation coefficient reconstructed weights. Naturally, unless boundary coordinates used identical original analysis, presumably measured hand, small differences occur. Even though differences general weights, identical contiguities, small, consequences measure spatial autocorrelation substantial, use fifth variable, cattle per 1000 acres crops pasture (1952), see reconstructed weights seem “reveal” autocorrelation original weights.","code":"fn <- system.file(\"etc/misc/unstand_sn.txt\", package=\"spdep\")[1] unstand <- read.table(fn, header=TRUE) summary(unstand) ## from to weight ## Length:110 Length:110 Min. :0.000600 ## Class :character Class :character 1st Qu.:0.003225 ## Mode :character Mode :character Median :0.007550 ## Mean :0.007705 ## 3rd Qu.:0.010225 ## Max. :0.032400 class(unstand) <- c(\"spatial.neighbour\", class(unstand)) of <- ordered(unstand$from) attr(unstand, \"region.id\") <- levels(of) unstand$from <- as.integer(of) unstand$to <- as.integer(ordered(unstand$to)) attr(unstand, \"n\") <- length(unique(unstand$from)) lw_unstand <- sn2listw(unstand) lw_unstand$style <- \"B\" lw_unstand ## Characteristics of weights list object: ## Neighbour list object: ## Number of regions: 25 ## Number of nonzero links: 110 ## Percentage nonzero weights: 17.6 ## Average number of links: 4.4 ## ## Weights style: B ## Weights constants summary: ## n nn S0 S1 S2 ## B 25 625 0.8476 0.01871808 0.1229232 nb <- poly2nb(eire_ge1) nb ## Neighbour list object: ## Number of regions: 25 ## Number of nonzero links: 108 ## Percentage nonzero weights: 17.28 ## Average number of links: 4.32 xx <- diffnb(nb, lw_unstand$neighbours, legacy=TRUE, verbose=TRUE) ## Neighbour difference for region id: Clare in relation to id: Kerry ## Neighbour difference for region id: Kerry in relation to id: Clare plot(eire_ge1, border=\"grey60\") plot(nb, coordinates(eire_ge1), add=TRUE, pch=\".\", lwd=2) plot(xx, coordinates(eire_ge1), add=TRUE, pch=\".\", lwd=2, col=3) library(terra) v_eire_ge1 <-vect(eire_ge1) SG <- rasterize(v_eire_ge1, rast(nrows=70, ncols=50, extent=ext(v_eire_ge1)), field=\"county\") library(rgrass) grass_home <- \"/home/rsb/topics/grass/g820/grass82\" initGRASS(grass_home, home=tempdir(), SG=SG, override=TRUE) write_VECT(v_eire_ge1, \"eire\", flags=c(\"o\", \"overwrite\")) res <- vect2neigh(\"eire\", ID=\"serlet\") res$length <- res$length*1000 attr(res, \"external\") <- attr(res, \"external\")*1000 attr(res, \"total\") <- attr(res, \"total\")*1000 grass_borders <- sn2listw(res) raw_borders <- grass_borders$weights int_tot <- attr(res, \"total\") - attr(res, \"external\") prop_borders <- lapply(1:length(int_tot), function(i) raw_borders[[i]]/int_tot[i]) dlist <- nbdists(grass_borders$neighbours, coordinates(eire_ge1)) inv_dlist <- lapply(dlist, function(x) 1/(x/1.609344)) combo_km <- lapply(1:length(inv_dlist), function(i) inv_dlist[[i]]*prop_borders[[i]]) combo_km_lw <- nb2listw(grass_borders$neighbours, glist=combo_km, style=\"B\") summary(combo_km_lw) ## Characteristics of weights list object: ## Neighbour list object: ## Number of regions: 25 ## Number of nonzero links: 108 ## Percentage nonzero weights: 17.28 ## Average number of links: 4.32 ## Link number distribution: ## ## 1 2 3 4 5 6 7 8 ## 1 2 5 5 8 1 2 1 ## 1 least connected region: ## E with 1 link ## 1 most connected region: ## V with 8 links ## ## Weights style: B ## Weights constants summary: ## n nn S0 S1.5 S2 ## B 25 625 0.9083144 0.02191845 0.1427746 red_lw_unstand <- lw_unstand Clare <- which(attr(lw_unstand, \"region.id\") == \"C\") Kerry <- which(attr(lw_unstand, \"region.id\") == \"H\") Kerry_in_Clare <- which(lw_unstand$neighbours[[Clare]] == Kerry) Clare_in_Kerry <- which(lw_unstand$neighbours[[Kerry]] == Clare) red_lw_unstand$neighbours[[Clare]] <- red_lw_unstand$neighbours[[Clare]][-Kerry_in_Clare] red_lw_unstand$neighbours[[Kerry]] <- red_lw_unstand$neighbours[[Kerry]][-Clare_in_Kerry] red_lw_unstand$weights[[Clare]] <- red_lw_unstand$weights[[Clare]][-Kerry_in_Clare] red_lw_unstand$weights[[Kerry]] <- red_lw_unstand$weights[[Kerry]][-Clare_in_Kerry] summary(red_lw_unstand) ## Characteristics of weights list object: ## Neighbour list object: ## Number of regions: 25 ## Number of nonzero links: 108 ## Percentage nonzero weights: 17.28 ## Average number of links: 4.32 ## Link number distribution: ## ## 1 2 3 4 5 6 7 8 ## 1 2 5 5 8 1 2 1 ## 1 least connected region: ## E with 1 link ## 1 most connected region: ## V with 8 links ## ## Weights style: B ## Weights constants summary: ## n nn S0 S1 S2 ## B 25 625 0.8437 0.01870287 0.1222501 cor(unlist(red_lw_unstand$weights), unlist(combo_km_lw$weights)) ## [1] 0.969543 flatten <- function(x, digits=3, statistic=\"I\") { res <- c(format(x$estimate, digits=digits), format(x$statistic, digits=digits), format.pval(x$p.value, digits=digits)) res <- matrix(res, ncol=length(res)) colnames(res) <- paste(c(\"\", \"E\", \"V\", \"SD_\", \"P_\"), \"I\", sep=\"\") rownames(res) <- deparse(substitute(x)) res } `reconstructed weights` <- moran.test(eire_ge1$ocattlepacre, combo_km_lw) `original weights` <- moran.test(eire_ge1$ocattlepacre, red_lw_unstand) print(rbind(flatten(`reconstructed weights`), flatten(`original weights`)), quote=FALSE) ## I EI VI SD_I P_I ## reconstructed weights 0.3203 -0.0417 0.0225 2.41 0.00792 ## original weights 0.2779 -0.0417 0.0223 2.14 0.0161"},{"path":"https://r-spatial.github.io/spdep/articles/CO69.html","id":"measures-of-spatial-autocorrelation","dir":"Articles","previous_headings":"","what":"Measures of spatial autocorrelation","title":"“The Problem of Spatial Autocorrelation:” forty years on","text":"targets reproduction Tables 4 5 Cliff Ord (1969, 43–44), first containing standard deviates normality randomisation original Moran measure binary weights, original Geary measure binary weights, proposed measure unstandardised general weights, proposed measure row-standardised general weights. addition, four variables log-transformed basis skewness kurtosis results presented . carry transformation variables, generate additional binary row-standardised general spatial weights objects — note weights constants row-standardised general weights agree given p. 42 paper, allowing small differences due rounding weights values displayed paper (p. 54): standard representation measures : \\[= \\frac{n}{\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}} \\frac{\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}(x_i-\\bar{x})(x_j-\\bar{x})}{\\sum_{=1}^{n}(x_i - \\bar{x})^2}\\] Moran’s \\(\\) — paper termed proposed statistic, Geary’s \\(C\\): \\[C = \\frac{(n-1)}{2\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}} \\frac{\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}(x_i-x_j)^2}{\\sum_{=1}^{n}(x_i - \\bar{x})^2}\\] \\(x_i, =1, \\ldots, n\\) \\(n\\) observations numeric variable interest, \\(w_{ij}\\) spatial weights. order reproduce standard deviates given paper, sufficient apply moran.test variables three different spatial weights objects, two different values randomisation= argument. addition, geary.test applied single spatial weights objects, two different values randomisation= argument. order conduct 8 different tests 16 variables, use lapply list variables specified order, sapply list output objects name generate table row column order original (save copy six columns comparison bootstrap results ): values standard deviates agree Table 4 original paper, exception proposed statistic standardised weights normality untransformed variables. can see happened substituting weights constants standardised weights unstandardised weights: Next, let us look Table 5 original paper. tabulate values measures , , since expectation constant measure, square root variance measure randomisation — extracting values calculated : values follows, match original exception initial version Moran’s \\(\\) first two columns. write function implementing equations 3 4: \\[= \\frac{\\sum_{=1}^{n}\\sum_{j=+1}^{n}w_{ij}(x_i-\\bar{x})(x_j-\\bar{x})}{\\sum_{=1}^{n}(x_i - \\bar{x})^2}\\] crucially inner summation \\(+1 \\ldots n\\), \\(1 \\ldots n\\), can reproduce values measure shown original Table 5: variance term given equation 7 original paper case normality, randomisation; reference p. 28 equation 38 p. 26 permit reproduction values second column Table 5. variance equation given equation 1.35 Cliff Ord (1973, 9) either, time possible say tabulated values computed. Note since standard deviances reproduced correctly, can reproduced second column values using measure expectance, just matter establishing formula used, far proved possible.","code":"eire_ge1$ln_pagval2_10 <- log(eire_ge1$pagval2_10) eire_ge1$ln_cowspacre <- log(eire_ge1$cowspacre) eire_ge1$ln_pigspacre <- log(eire_ge1$pigspacre) eire_ge1$ln_sheeppacre <- log(eire_ge1$sheeppacre) vars <- c(\"pagval2_10\", \"ln_pagval2_10\", \"pagval10_50\", \"pagval50p\", \"cowspacre\", \"ln_cowspacre\", \"ocattlepacre\", \"pigspacre\", \"ln_pigspacre\", \"sheeppacre\", \"ln_sheeppacre\", \"townvillp\", \"carspcap\", \"radiopcap\", \"retailpcap\", \"psinglem30_34\") nb_B <- nb2listw(lw_unstand$neighbours, style=\"B\") nb_B ## Characteristics of weights list object: ## Neighbour list object: ## Number of regions: 25 ## Number of nonzero links: 110 ## Percentage nonzero weights: 17.6 ## Average number of links: 4.4 ## ## Weights style: B ## Weights constants summary: ## n nn S0 S1 S2 ## B 25 625 110 220 2176 lw_std <- nb2listw(lw_unstand$neighbours, glist=lw_unstand$weights, style=\"W\") lw_std ## Characteristics of weights list object: ## Neighbour list object: ## Number of regions: 25 ## Number of nonzero links: 110 ## Percentage nonzero weights: 17.6 ## Average number of links: 4.4 ## ## Weights style: W ## Weights constants summary: ## n nn S0 S1 S2 ## W 25 625 25 15.84089 103.6197 system.time({ MoranN <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=nb_B, randomisation=FALSE)) MoranR <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=nb_B, randomisation=TRUE)) GearyN <- lapply(vars, function(x) geary.test(eire_ge1[[x]], listw=nb_B, randomisation=FALSE)) GearyR <- lapply(vars, function(x) geary.test(eire_ge1[[x]], listw=nb_B, randomisation=TRUE)) Prop_unstdN <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=lw_unstand, randomisation=FALSE)) Prop_unstdR <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=lw_unstand, randomisation=TRUE)) Prop_stdN <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=lw_std, randomisation=FALSE)) Prop_stdR <- lapply(vars, function(x) moran.test(eire_ge1[[x]], listw=lw_std, randomisation=TRUE)) }) ## user system elapsed ## 0.03 0.00 0.11 res <- sapply(c(\"MoranN\", \"MoranR\", \"GearyN\", \"GearyR\", \"Prop_unstdN\", \"Prop_unstdR\", \"Prop_stdN\", \"Prop_stdR\"), function(x) sapply(get(x), \"[[\", \"statistic\")) rownames(res) <- vars ores <- res[,c(1,2,5:8)] print(formatC(res, format=\"f\", digits=4), quote=FALSE) ## MoranN MoranR GearyN GearyR Prop_unstdN Prop_unstdR Prop_stdN Prop_stdR ## pagval2_10 3.7851 3.8779 4.3142 3.9016 3.3307 3.4159 3.9276 4.0292 ## ln_pagval2_10 4.0965 4.1074 4.0841 4.0343 3.5795 3.5894 4.1278 4.1393 ## pagval10_50 1.0899 1.1316 2.7511 2.3760 1.3348 1.3882 1.5127 1.5738 ## pagval50p 5.2011 5.0555 4.0178 4.7194 4.6604 4.5247 4.8823 4.7387 ## cowspacre 5.1969 5.3907 4.3531 3.7709 4.1379 4.2991 4.7274 4.9135 ## ln_cowspacre 5.2420 5.2455 3.9211 3.9085 4.2007 4.2037 4.6532 4.6566 ## ocattlepacre 0.5565 0.5593 -0.1707 -0.1668 2.1366 2.1478 1.9219 1.9320 ## pigspacre 2.4807 2.5393 2.2928 2.0802 2.8312 2.9010 3.1908 3.2703 ## ln_pigspacre 2.3015 2.2724 2.0520 2.1893 2.5171 2.4839 2.8460 2.8081 ## sheeppacre 1.0188 1.0630 0.8689 0.7387 1.7398 1.8187 1.4792 1.5470 ## ln_sheeppacre 1.2930 1.2827 1.5156 1.5767 2.3708 2.3511 2.0374 2.0203 ## townvillp 2.2759 2.2681 2.5475 2.5902 1.2148 1.2104 1.6275 1.6216 ## carspcap 4.4927 4.4015 3.2247 3.5992 3.8897 3.8075 4.1826 4.0934 ## radiopcap 0.3156 0.3153 1.2294 1.2348 0.5915 0.5909 0.7857 0.7849 ## retailpcap 3.4985 3.4524 3.1303 3.3497 2.9291 2.8888 3.0346 2.9926 ## psinglem30_34 2.7349 2.6895 2.3382 2.5519 2.7541 2.7065 2.7078 2.6605 wc_unstd <- spweights.constants(lw_unstand) wrong_N_sqVI <- sqrt((wc_unstd$nn*wc_unstd$S1 - wc_unstd$n*wc_unstd$S2 + 3*wc_unstd$S0*wc_unstd$S0)/((wc_unstd$nn-1)*wc_unstd$S0*wc_unstd$S0)-((-1/(wc_unstd$n-1))^2)) raw_data <- grep(\"^ln_\", vars, invert=TRUE) I <- sapply(Prop_stdN, function(x) x$estimate[1])[raw_data] EI <- sapply(Prop_stdN, function(x) x$estimate[2])[raw_data] res <- (I - EI)/wrong_N_sqVI names(res) <- vars[raw_data] print(formatC(res, format=\"f\", digits=4), quote=FALSE) ## pagval2_10 pagval10_50 pagval50p cowspacre ocattlepacre pigspacre ## 3.8836 1.4957 4.8276 4.6744 1.9003 3.1550 ## sheeppacre townvillp carspcap radiopcap retailpcap psinglem30_34 ## 1.4627 1.6093 4.1357 0.7769 3.0006 2.6774 res <- lapply(c(\"MoranR\", \"GearyR\", \"Prop_unstdR\", \"Prop_stdR\"), function(x) sapply(get(x), function(y) c(y$estimate[1], sqrt(y$estimate[3])))) res <- t(do.call(\"rbind\", res)) colnames(res) <- c(\"I\", \"sigma_I\", \"C\", \"sigma_C\", \"unstd_r\", \"sigma_r\", \"std_r\", \"sigma_r\") rownames(res) <- vars print(formatC(res, format=\"f\", digits=4), quote=FALSE) ## I sigma_I C sigma_C unstd_r sigma_r std_r sigma_r ## pagval2_10 0.4074 0.1158 0.3477 0.1672 0.4559 0.1456 0.5384 0.1440 ## ln_pagval2_10 0.4444 0.1183 0.3825 0.1531 0.4930 0.1490 0.5680 0.1473 ## pagval10_50 0.0877 0.1143 0.5840 0.1751 0.1577 0.1436 0.1818 0.1420 ## pagval50p 0.5754 0.1221 0.3925 0.1287 0.6545 0.1539 0.6795 0.1522 ## cowspacre 0.5749 0.1144 0.3418 0.1745 0.5764 0.1438 0.6566 0.1421 ## ln_cowspacre 0.5803 0.1186 0.4071 0.1517 0.5858 0.1493 0.6456 0.1476 ## ocattlepacre 0.0244 0.1181 1.0258 0.1547 0.2775 0.1486 0.2422 0.1469 ## pigspacre 0.2527 0.1159 0.6533 0.1667 0.3812 0.1458 0.4296 0.1441 ## ln_pigspacre 0.2314 0.1202 0.6897 0.1417 0.3343 0.1514 0.3787 0.1497 ## sheeppacre 0.0792 0.1137 0.8686 0.1778 0.2182 0.1429 0.1768 0.1412 ## ln_sheeppacre 0.1117 0.1196 0.7708 0.1453 0.3125 0.1506 0.2593 0.1489 ## townvillp 0.2284 0.1191 0.6148 0.1487 0.1398 0.1499 0.1987 0.1482 ## carspcap 0.4914 0.1211 0.5124 0.1355 0.5394 0.1526 0.5761 0.1509 ## radiopcap -0.0042 0.1188 0.8141 0.1505 0.0467 0.1495 0.0744 0.1478 ## retailpcap 0.3734 0.1202 0.5267 0.1413 0.3959 0.1515 0.4066 0.1498 ## psinglem30_34 0.2828 0.1207 0.6465 0.1385 0.3697 0.1520 0.3583 0.1503 oMoranf <- function(x, nb) { z <- scale(x, scale=FALSE) n <- length(z) glist <- lapply(1:n, function(i) {ii <- nb[[i]]; ifelse(ii > i, 1, 0)}) lw <- nb2listw(nb, glist=glist, style=\"B\") wz <- lag(lw, z) I <- (sum(z*wz)/sum(z*z)) I } res <- sapply(vars, function(x) oMoranf(eire_ge1[[x]], nb=lw_unstand$neighbours)) print(formatC(res, format=\"f\", digits=4), quote=FALSE) ## pagval2_10 ln_pagval2_10 pagval10_50 pagval50p cowspacre ln_cowspacre ## 0.8964 0.9776 0.1928 1.2660 1.2649 1.2766 ## ocattlepacre pigspacre ln_pigspacre sheeppacre ln_sheeppacre townvillp ## 0.0536 0.5559 0.5091 0.1743 0.2458 0.5024 ## carspcap radiopcap retailpcap psinglem30_34 ## 1.0811 -0.0093 0.8215 0.6222"},{"path":"https://r-spatial.github.io/spdep/articles/CO69.html","id":"simulating-measures-of-spatial-autocorrelation","dir":"Articles","previous_headings":"","what":"Simulating measures of spatial autocorrelation","title":"“The Problem of Spatial Autocorrelation:” forty years on","text":"Cliff Ord (1969) conduct simulation experiments, although sequels , notably Cliff Ord (1973), among many others. Simulation studies necessarily demanding computationally, especially spatially autocorrelated variables created, Cliff Ord (1973, 146–53). book, also report use permutation tests, also known Monte Carlo Hope hypothesis testing procedures (Cliff Ord 1973, 50–52). procedures provided way examine distribution statistic interest exchanging random observed values observations, comparing simulated distribution null hypothesis spatial patterning observed value statistic question. First let us define function MoranI.boot just return value Moran’s \\(\\) variable var permutation index , function Nsim generate random samples variable interest assuming Normality. make easier process variables turn, encapsulate calls boot wrapper functions f_bperm f_bpara. Running 4999 simulations 16 three different weights specifications parametric permutation bootstrap takes quite lot time. collate results compare analytical standard deviates Normality randomisation, see fact differences large, expressed median absolute difference tables. can also see inferences based one-sided \\(\\alpha=0.05\\) cut-analytical bootstrap approaches. indicates can, general, rely analytical standard deviates, bootstrap methods help assumptions underlying measures met. assumptions affect shape distribution measure tails; one possibility use Saddlepoint approximation find equivalent analytical bootstrap-based standard deviate inference (Tiefelsdorf 2002). Saddlepoint approximation requires eigenvalues weights matrix iterative root-finding global Moran’s \\(\\), local Moran’s \\(I_i\\), analytical forms known. Even computational burden, Saddlepoint approximation global Moran’s \\(\\) runs quite quickly. First need fit null linear models (including intercept) variables, apply lm.morantest.sad fitted model objects: Although analytical standard deviates (Normality) larger reached using Saddlepoint approximation measured median absolute deviation, differences lead different inferences chosen cut-. reflects fact shape distribution sensitive small \\(n\\), moderate \\(n\\) global Moran’s \\(\\), effects seen tails. consequences local Moran’s \\(I_i\\) much stronger, clique neighbours observation typically small. perhaps interest differences much smaller case general weights unstandardised binary weights. addition choose use exact distribution Moran’s \\(\\), described Tiefelsdorf (2000); implementation covered R. S. Bivand, Müller, Reder (2009). global case also needs eigenvalues weights matrix, solution numerical integration function, cases, timings quite acceptable. output comparable Saddlepoint approximation, inferences drawn chosen cut-analytical standard deviates calculated Normality. Li, Calder, Cressie (2007) take challenge Cliff Ord (1969, 31), try give statistic bounded fixed range. APLE measure intended approximate spatial dependence parameter simultaneous autoregressive model better Moran’s \\(\\), re-scales measure function eigenvalues spatial weights matrix. APLE requires use row standardised weights. order save time, use two internal functions spatialreg:::preAple spatialreg:::inAple, since definition spatial weights, eigenvalue calculations need made. notation using ::: operator says function named operator found namespace package named operator. APLE values repeat pattern already seen — variables, measured autocorrelation similar irrespective spatial weights definition, others, change definition binary general make difference.","code":"MoranI.boot <- function(var, i, ...) { var <- var[i] return(moran(x=var, ...)$I) } Nsim <- function(d, mle) { n <- length(d) rnorm(n, mle$mean, mle$sd) } f_bperm <- function(x, nsim, listw) { boot(x, statistic=MoranI.boot, R=nsim, sim=\"permutation\", listw=listw, n=length(x), S0=Szero(listw)) } f_bpara <- function(x, nsim, listw) { boot(x, statistic=MoranI.boot, R=nsim, sim=\"parametric\", ran.gen=Nsim, mle=list(mean=mean(x), sd=sd(x)), listw=listw, n=length(x), S0=Szero(listw)) } nsim <- 4999 set.seed(1234) system.time({ MoranNb <- lapply(vars, function(x) f_bpara(x=eire_ge1[[x]], nsim=nsim, listw=nb_B)) MoranRb <- lapply(vars, function(x) f_bperm(x=eire_ge1[[x]], nsim=nsim, listw=nb_B)) Prop_unstdNb <- lapply(vars, function(x) f_bpara(x=eire_ge1[[x]], nsim=nsim, listw=lw_unstand)) Prop_unstdRb <- lapply(vars, function(x) f_bperm(x=eire_ge1[[x]], nsim=nsim, listw=lw_unstand)) Prop_stdNb <- lapply(vars, function(x) f_bpara(x=eire_ge1[[x]], nsim=nsim, listw=lw_std)) Prop_stdRb <- lapply(vars, function(x) f_bperm(x=eire_ge1[[x]], nsim=nsim, listw=lw_std)) }) res <- lapply(c(\"MoranNb\", \"MoranRb\", \"Prop_unstdNb\", \"Prop_unstdRb\", \"Prop_stdNb\", \"Prop_stdRb\"), function(x) sapply(get(x), function(y) (y$t0 - mean(y$t))/sd(y$t))) res <- t(do.call(\"rbind\", res)) colnames(res) <- c(\"MoranNb\", \"MoranRb\", \"Prop_unstdNb\", \"Prop_unstdRb\", \"Prop_stdNb\", \"Prop_stdRb\") rownames(res) <- vars print(formatC(res, format=\"f\", digits=4), quote=FALSE) ## pagval2_10 ln_pagval2_10 pagval10_50 pagval50p cowspacre ln_cowspacre ## 0.8964 0.9776 0.1928 1.2660 1.2649 1.2766 ## ocattlepacre pigspacre ln_pigspacre sheeppacre ln_sheeppacre townvillp ## 0.0536 0.5559 0.5091 0.1743 0.2458 0.5024 ## carspcap radiopcap retailpcap psinglem30_34 ## 1.0811 -0.0093 0.8215 0.6222 oores <- ores - res apply(oores, 2, mad) ## MoranN MoranR Prop_unstdN Prop_unstdR Prop_stdN Prop_stdR ## 1.6470091 1.6241614 0.7681895 0.7170636 1.2615083 1.2723149 alpha_0.05 <- qnorm(0.05, lower.tail=FALSE) all((res >= alpha_0.05) == (ores >= alpha_0.05)) ## [1] FALSE lm_objs <- lapply(vars, function(x) lm(formula(paste(x, \"~1\")), data=eire_ge1)) system.time({ MoranSad <- lapply(lm_objs, function(x) lm.morantest.sad(x, listw=nb_B)) Prop_unstdSad <- lapply(lm_objs, function(x) lm.morantest.sad(x, listw=lw_unstand)) Prop_stdSad <- lapply(lm_objs, function(x) lm.morantest.sad(x, listw=lw_std)) }) ## user system elapsed ## 0.05 0.02 0.08 res <- sapply(c(\"MoranSad\", \"Prop_unstdSad\", \"Prop_stdSad\"), function(x) sapply(get(x), \"[[\", \"statistic\")) rownames(res) <- vars print(formatC(res, format=\"f\", digits=4), quote=FALSE) ## MoranSad Prop_unstdSad Prop_stdSad ## pagval2_10 3.2903 3.1711 3.8283 ## ln_pagval2_10 3.5346 3.3982 4.0441 ## pagval10_50 1.0883 1.3219 1.4791 ## pagval50p 4.4402 4.4258 4.9377 ## cowspacre 4.4366 3.9164 4.7406 ## ln_cowspacre 4.4758 3.9760 4.6493 ## ocattlepacre 0.6030 2.0748 1.8642 ## pigspacre 2.2611 2.7154 3.0775 ## ln_pigspacre 2.1158 2.4271 2.7417 ## sheeppacre 1.0250 1.7040 1.4476 ## ln_sheeppacre 1.2669 2.2921 1.9731 ## townvillp 2.0949 1.2079 1.5872 ## carspcap 3.8500 3.6840 4.1044 ## radiopcap 0.3750 0.6094 0.7906 ## retailpcap 3.0663 2.8049 2.9245 ## psinglem30_34 2.4649 2.6449 2.6089 oores <- res - ores[,c(1,3,5)] apply(oores, 2, mad) ## MoranSad Prop_unstdSad Prop_stdSad ## 0.37142684 0.10779060 0.05650183 all((res >= alpha_0.05) == (ores[,c(1,3,5)] >= alpha_0.05)) ## [1] TRUE system.time({ MoranEx <- lapply(lm_objs, function(x) lm.morantest.exact(x, listw=nb_B)) Prop_unstdEx <- lapply(lm_objs, function(x) lm.morantest.exact(x, listw=lw_unstand)) Prop_stdEx <- lapply(lm_objs, function(x) lm.morantest.exact(x, listw=lw_std)) }) ## user system elapsed ## 0.05 0.01 0.15 res <- sapply(c(\"MoranEx\", \"Prop_unstdEx\", \"Prop_stdEx\"), function(x) sapply(get(x), \"[[\", \"statistic\")) rownames(res) <- vars print(formatC(res, format=\"f\", digits=4), quote=FALSE) ## MoranEx Prop_unstdEx Prop_stdEx ## pagval2_10 3.2895 3.1660 3.8261 ## ln_pagval2_10 3.5384 3.3979 4.0430 ## pagval10_50 1.0798 1.3131 1.4745 ## pagval50p 4.4568 4.4430 4.9446 ## cowspacre 4.4532 3.9268 4.7453 ## ln_cowspacre 4.4928 3.9875 4.6531 ## ocattlepacre 0.5967 2.0611 1.8596 ## pigspacre 2.2486 2.7033 3.0740 ## ln_pigspacre 2.1031 2.4131 2.7380 ## sheeppacre 1.0168 1.6924 1.4430 ## ln_sheeppacre 1.2575 2.2779 1.9685 ## townvillp 2.0822 1.1999 1.5826 ## carspcap 3.8593 3.6899 4.1037 ## radiopcap 0.3696 0.6054 0.7873 ## retailpcap 3.0616 2.7938 2.9210 ## psinglem30_34 2.4533 2.6321 2.6050 oores <- res - ores[,c(1,3,5)] apply(oores, 2, mad) ## MoranEx Prop_unstdEx Prop_stdEx ## 0.37187539 0.09751723 0.05419300 all((res >= alpha_0.05) == (ores[,c(1,3,5)] >= alpha_0.05)) ## [1] TRUE vars_scaled <- lapply(vars, function(x) scale(eire_ge1[[x]], scale=FALSE)) nb_W <- nb2listw(lw_unstand$neighbours, style=\"W\") pre <- spatialreg:::preAple(0, listw=nb_W) MoranAPLE <- sapply(vars_scaled, function(x) spatialreg:::inAple(x, pre)) pre <- spatialreg:::preAple(0, listw=lw_std, override_similarity_check=TRUE) Prop_stdAPLE <- sapply(vars_scaled, function(x) spatialreg:::inAple(x, pre)) res <- cbind(MoranAPLE, Prop_stdAPLE) colnames(res) <- c(\"APLE W\", \"APLE Gstd\") rownames(res) <- vars print(formatC(res, format=\"f\", digits=4), quote=FALSE)"},{"path":"https://r-spatial.github.io/spdep/articles/CO69.html","id":"odds-and-ends-ldots","dir":"Articles","previous_headings":"","what":"Odds and ends \\(\\ldots\\)","title":"“The Problem of Spatial Autocorrelation:” forty years on","text":"differences found case variables inference using original binary weights, general weights proposed Cliff Ord (1969) necessarily related weights thenselves. Figures \\[plot\\_wts\\] \\[plot\\_map\\] show values weights sparse matrix form, sums weights county sums identical design. case binary weights, matrix entries equal, sums -weight counties many neighbours. General weights -weight counties close , neighbours, share larger boundary proportions (asymmetric relationship). impact using boundary proportions, boundary county exterior subtracted, thus boosting weights edge counties neighbours, even . Standardised general weights -weight -weight counties neighbours, chiefly edges study area. small data set, \\(n=25\\), possible edge configuration effects relatively strong, may impact inference different ways. issue egde effects really satisfactorily resolved, kept mind analyses data sets size shape.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"creating-neighbours","dir":"Articles","previous_headings":"","what":"Creating Neighbours","title":"Creating Neighbours","text":"vignette formed pp. 239–251 first edition Bivand, R. S., Pebesma, E. Gómez-Rubio V. (2008) Applied Spatial Data Analysis R, Springer-Verlag, New York. retired second edition (2013) accommodate material topics, made available form understanding publishers.","code":""},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"introduction","dir":"Articles","previous_headings":"Creating Neighbours","what":"Introduction","title":"Creating Neighbours","text":"Creating spatial weights necessary step using areal data, perhaps just check remaining spatial patterning residuals. first step define relationships observations given non-zero weight, choose neighbour criterion used; second assign weights identified neighbour links. 281 census tract data set eight central New York State counties featured prominently (Waller Gotway 2004) used many examples, supplemented tract boundaries derived TIGER 1992 distributed SEDAC/CIESIN. boundaries projected geographical coordinates UTM zone~18. file identical boundaries used original source, close may re-distributed, unlike version used book. Starting census tract queen contiguities, touching polygons neighbours, used (Waller Gotway 2004) provided DBF file website, GAL format file created read R. sake simplicity showing create neighbour objects, work subset map consisting census tracts within Syracuse, although principles apply full data set. retrieve part neighbour list Syracuse using subset method.","code":"library(spdep) ## Loading required package: spData ## To access larger datasets in this package, install the spDataLarge ## package with: `install.packages('spDataLarge', ## repos='https://nowosad.github.io/drat/', type='source')` ## Loading required package: sf ## Linking to GEOS 3.13.0, GDAL 3.10.1, PROJ 9.5.1; sf_use_s2() is TRUE if (packageVersion(\"spData\") >= \"2.3.2\") { NY8a <- sf::st_read(system.file(\"shapes/NY8_utm18.gpkg\", package=\"spData\")) } else { NY8a <- sf::st_read(system.file(\"shapes/NY8_bna_utm18.gpkg\", package=\"spData\")) sf::st_crs(NY8a) <- \"EPSG:32618\" NY8a$Cases <- NY8a$TRACTCAS } ## Reading layer `NY8_utm18' from data source ## `C:\\Users\\rzomor2\\AppData\\Local\\R\\win-library\\4.4\\spData\\shapes\\NY8_utm18.gpkg' ## using driver `GPKG' ## Simple feature collection with 281 features and 17 fields ## Geometry type: POLYGON ## Dimension: XY ## Bounding box: xmin: 358241.9 ymin: 4649755 xmax: 480393.1 ymax: 4808545 ## Projected CRS: WGS 84 / UTM zone 18N NY8 <- as(NY8a, \"Spatial\") NY_nb <- read.gal(system.file(\"weights/NY_nb.gal\", package=\"spData\"), region.id=as.character(as.integer(row.names(NY8))-1L)) Syracuse <- NY8[!is.na(NY8$AREANAME) & NY8$AREANAME == \"Syracuse city\",] Sy0_nb <- subset(NY_nb, !is.na(NY8$AREANAME) & NY8$AREANAME == \"Syracuse city\") summary(Sy0_nb) ## Neighbour list object: ## Number of regions: 63 ## Number of nonzero links: 346 ## Percentage nonzero weights: 8.717561 ## Average number of links: 5.492063 ## Link number distribution: ## ## 1 2 3 4 5 6 7 8 9 ## 1 1 5 9 14 17 9 6 1 ## 1 least connected region: ## 164 with 1 link ## 1 most connected region: ## 136 with 9 links"},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"creating-contiguity-neighbours","dir":"Articles","previous_headings":"Creating Neighbours","what":"Creating Contiguity Neighbours","title":"Creating Neighbours","text":"can create copy neighbours object polygon contiguities using poly2nb() function spdep. takes object extending SpatialPolygons class first argument, using heuristics identifies polygons sharing boundary points neighbours. also snap= argument, allow shared boundary points short distance one another. can see, creating contiguity neighbours Syracuse object reproduces neighbours (Waller Gotway 2004). Careful examination next figure shows, however, graph neighbours planar, since neighbour links cross . default, contiguity condition met least one point boundary one polygon within snap distance least one point neighbour. relationship given argument queen=TRUE analogy movements chessboard. three polygons meet single point, meet contiguity condition, giving rise crossed links. queen=FALSE, least two boundary points must within snap distance , conventional name `rook’ relationship. figure shows crossed line differences arise polygons touch single point, compared stricter rook criterion. : Queen-style census tract contiguities, Syracuse; b: Rook-style contiguity differences shown thicker orange lines access GIS GRASS ArcGIS, can export SpatialPolygonsDataFrame object use topology engine GIS find contiguities graph polygon edges - shared edge yield output rook relationship. procedure , however, depend topology set polygons clean, holds subset, full eight-county data set. infrequently, small artefacts, slivers boundary lines intersect diverge distances seen plots, require intervention keep geometries data correctly associated. geometrical artefacts present, topology clean, unambiguous shared polygon boundaries found cases; artefacts typically arise data collected one purpose combined data used another purpose. Topologies usually cleaned GIS snapping' vertices closer threshold distance together, removing artefacts -- example, snapping across river channel correct boundary median line input polygons stop channel banks side. Thepoly2nb()function asnap` argument, may also used input data possess geometrical artefacts. Similar approaches may also used read ArcGIS coverage data tallying left neighbour right neighbour arc indices polygons data set, using either RArcInfo rgdal. Syracuse case, exclaves islands' belonging data set, sharing boundary points within snap distance. number polygons moderate, missing neighbour links may added interactively using theedit()method fornb` objects, displaying polygon background. method may used removing links , although contiguity exists, may considered void, across mountain range.","code":"class(Syracuse) ## [1] \"SpatialPolygonsDataFrame\" ## attr(,\"package\") ## [1] \"sp\" Sy1_nb <- poly2nb(Syracuse) isTRUE(all.equal(Sy0_nb, Sy1_nb, check.attributes=FALSE)) ## [1] TRUE Sy2_nb <- poly2nb(Syracuse, queen=FALSE) isTRUE(all.equal(Sy0_nb, Sy2_nb, check.attributes=FALSE)) ## [1] FALSE oopar <- par(mfrow=c(1,2), mar=c(3,3,1,1)+0.1) plot(Syracuse, border=\"grey60\") plot(Sy0_nb, coordinates(Syracuse), add=TRUE, pch=19, cex=0.6) text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"a)\", cex=0.8) plot(Syracuse, border=\"grey60\") plot(Sy0_nb, coordinates(Syracuse), add=TRUE, pch=19, cex=0.6) plot(diffnb(Sy0_nb, Sy2_nb, verbose=FALSE), coordinates(Syracuse), add=TRUE, pch=\".\", cex=0.6, lwd=2, col=\"orange\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"b)\", cex=0.8) par(oopar) library(rgrass) v <- terra::vect(sf::st_as_sf(Syracuse)) SG <- terra::rast(terra::ext(v), crs=terra::crs(v)) pr <- initGRASS(\"/home/rsb/topics/grass/g840/grass84\", tempdir(), SG=SG, override=TRUE) write_VECT(v, \"SY0\", flags=c(\"o\", \"overwrite\")) contig <- vect2neigh(\"SY0\") Sy3_nb <- sn2listw(contig, style=\"B\")$neighbours isTRUE(all.equal(Sy3_nb, Sy2_nb, check.attributes=FALSE)) ## [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"creating-graph-based-neighbours","dir":"Articles","previous_headings":"Creating Neighbours","what":"Creating Graph-Based Neighbours","title":"Creating Neighbours","text":"Continuing irregularly located areal entities, possible choose point represent polygon-support entities. often polygon centroid, average coordinates dimension, takes proper care weight component triangles polygon area. also possible use points, data available, construct, example population-weighted centroids. representative points available, criteria neighbourhood can extended just contiguity include graph measures, distance thresholds, \\(k\\)-nearest neighbours. direct graph representation neighbours make Delaunay triangulation points, shown first panel figure. neighbour relationships defined triangulation, extends outwards convex hull points planar. Note graph-based representations construct interpoint relationships based Euclidean distance, option use Great Circle distances geographical coordinates. joins distant points around convex hull, may worthwhile thin triangulation Sphere Influence (SOI) graph, removing links relatively long. Points SOI neighbours circles centred points, radius equal points’ nearest neighbour distances, intersect two places (Avis Horton 1985). Functions graph-based neighbours kindly contributed Nicholas Lewin-Koh. : Delauney triangulation neighbours; b: Sphere influence neighbours (available); c: Gabriel graph neighbours; d: Relative graph neighbours Delaunay triangulation neighbours SOI neighbours symmetric design – \\(\\) neighbour \\(j\\), \\(j\\) neighbour \\(\\). Gabriel graph also subgraph Delaunay triangulation, retaining different set neighbours (Matula Sokal 1980). , however, guarantee symmetry; applies Relative graph neighbours (Toussaint 1980). graph2nb() function takes sym argument insert links restore symmetry, graphs longer exactly fulfil neighbour criteria. graph-based neighbour schemes always ensure points least one neighbour. Subgraphs full triangulation may also one graph trimming. functions .symmetric.nb() can used check symmetry, argument force=TRUE symmetry attribute overridden, n.comp.nb() reports number graph components ~components points belong (enforcing symmetry, algorithm assumes graph directed). one graph component, matrix representation spatial weights can become block-diagonal observations appropriately sorted.","code":"coords <- coordinates(Syracuse) IDs <- row.names(as(Syracuse, \"data.frame\")) #FIXME library(tripack) Sy4_nb <- tri2nb(coords, row.names=IDs) if (require(dbscan, quietly=TRUE)) { Sy5_nb <- graph2nb(soi.graph(Sy4_nb, coords), row.names=IDs) } else Sy5_nb <- NULL Sy6_nb <- graph2nb(gabrielneigh(coords), row.names=IDs) Sy7_nb <- graph2nb(relativeneigh(coords), row.names=IDs) oopar <- par(mfrow=c(2,2), mar=c(1,1,1,1)+0.1) plot(Syracuse, border=\"grey60\") plot(Sy4_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"a)\", cex=0.8) plot(Syracuse, border=\"grey60\") if (!is.null(Sy5_nb)) { plot(Sy5_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"b)\", cex=0.8) } plot(Syracuse, border=\"grey60\") plot(Sy6_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"c)\", cex=0.8) plot(Syracuse, border=\"grey60\") plot(Sy7_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"d)\", cex=0.8) par(oopar) nb_l <- list(Triangulation=Sy4_nb, Gabriel=Sy6_nb, Relative=Sy7_nb) if (!is.null(Sy5_nb)) nb_l <- c(nb_l, list(SOI=Sy5_nb)) sapply(nb_l, function(x) is.symmetric.nb(x, verbose=FALSE, force=TRUE)) ## Triangulation Gabriel Relative ## TRUE FALSE FALSE sapply(nb_l, function(x) n.comp.nb(x)$nc) ## Triangulation Gabriel Relative ## 1 1 1"},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"distance-based-neighbours","dir":"Articles","previous_headings":"Creating Neighbours","what":"Distance-Based Neighbours","title":"Creating Neighbours","text":"alternative method choose \\(k\\) nearest points neighbours – adapts across study area, taking account differences densities areal entities. Naturally, overwhelming majority cases, leads asymmetric neighbours, ensure areas \\(k\\) neighbours. knearneigh() function returns intermediate form converted nb object knn2nb(); knearneigh() can also take longlat= argument handle geographical coordinates. : \\(k=1\\) neighbours; b: \\(k=2\\) neighbours; c: \\(k=4\\) neighbours figure shows neighbour relationships \\(k= 1, 2, 4\\), many components \\(k=1\\). need , \\(k\\)-nearest neighbour objects can made symmetrical using make.sym.nb() function. \\(k=1\\) object also useful finding minimum distance areas distance-based neighbour. Using nbdists() function, can calculate list vectors distances corresponding neighbour object, first nearest neighbours. greatest value minimum distance needed make sure areas linked least one neighbour. dnearneigh() function used find neighbours interpoint distance, arguments d1 d2 setting lower upper distance bounds; can also take longlat argument handle geographical coordinates. : Neighbours within 1,158m; b: neighbours within 1,545m; c: neighbours within 2,317m figure shows numbers distance-based neighbours increase moderate increases distance. Moving \\(0.75\\) times minimum -included distance, -included distance, \\(1.5\\) times minimum -included distance, numbers links grow rapidly. major problem first nearest neighbour distances study area much larger others, since avoid -neighbour areal entities, distance criterion need set many areas many neighbours. Distance-based neighbours: frequencies numbers neighbours census tract figure shows counts sizes sets neighbours three different distance limits. Syracuse, census tracts similar areas, try use distance-based neighbour criterion eight-county study area, smallest distance securing least one neighbour every areal entity 38km. areal entities approximately regularly spaced, using distance-based neighbours necessarily problem. Provided care taken handle side effects “weighting” areas analysis, using lists neighbours -neighbour areas necessarily problem either, certainly raise questions. Different disciplines handle definition neighbours ways convention; particular, seems ecologists frequently use distance bands. many distance bands used, approach variogram, although underlying understanding spatial autocorrelation seems contagion rather continuous.","code":"Sy8_nb <- knn2nb(knearneigh(coords, k=1), row.names=IDs) ## Warning in knn2nb(knearneigh(coords, k = 1), row.names = IDs): neighbour object ## has 15 sub-graphs Sy9_nb <- knn2nb(knearneigh(coords, k=2), row.names=IDs) Sy10_nb <- knn2nb(knearneigh(coords, k=4), row.names=IDs) nb_l <- list(k1=Sy8_nb, k2=Sy9_nb, k4=Sy10_nb) sapply(nb_l, function(x) is.symmetric.nb(x, verbose=FALSE, force=TRUE)) ## k1 k2 k4 ## FALSE FALSE FALSE sapply(nb_l, function(x) n.comp.nb(x)$nc) ## k1 k2 k4 ## 15 1 1 oopar <- par(mfrow=c(1,3), mar=c(1,1,1,1)+0.1) plot(Syracuse, border=\"grey60\") plot(Sy8_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"a)\", cex=0.8) plot(Syracuse, border=\"grey60\") plot(Sy9_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"b)\", cex=0.8) plot(Syracuse, border=\"grey60\") plot(Sy10_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"c)\", cex=0.8) par(oopar) dsts <- unlist(nbdists(Sy8_nb, coords)) summary(dsts) ## Min. 1st Qu. Median Mean 3rd Qu. Max. ## 395.7 587.3 700.1 760.4 906.1 1544.6 max_1nn <- max(dsts) max_1nn ## [1] 1544.615 Sy11_nb <- dnearneigh(coords, d1=0, d2=0.75*max_1nn, row.names=IDs) ## Warning in dnearneigh(coords, d1 = 0, d2 = 0.75 * max_1nn, row.names = IDs): ## neighbour object has 4 sub-graphs Sy12_nb <- dnearneigh(coords, d1=0, d2=1*max_1nn, row.names=IDs) Sy13_nb <- dnearneigh(coords, d1=0, d2=1.5*max_1nn, row.names=IDs) nb_l <- list(d1=Sy11_nb, d2=Sy12_nb, d3=Sy13_nb) sapply(nb_l, function(x) is.symmetric.nb(x, verbose=FALSE, force=TRUE)) ## d1 d2 d3 ## TRUE TRUE TRUE sapply(nb_l, function(x) n.comp.nb(x)$nc) ## d1 d2 d3 ## 4 1 1 oopar <- par(mfrow=c(1,3), mar=c(1,1,1,1)+0.1) plot(Syracuse, border=\"grey60\") plot(Sy11_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"a)\", cex=0.8) plot(Syracuse, border=\"grey60\") plot(Sy12_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"b)\", cex=0.8) plot(Syracuse, border=\"grey60\") plot(Sy13_nb, coords, add=TRUE, pch=\".\") text(bbox(Syracuse)[1,1], bbox(Syracuse)[2,2], labels=\"c)\", cex=0.8) par(oopar) dS <- c(0.75, 1, 1.5)*max_1nn res <- sapply(nb_l, function(x) table(card(x))) mx <- max(card(Sy13_nb)) res1 <- matrix(0, ncol=(mx+1), nrow=3) rownames(res1) <- names(res) colnames(res1) <- as.character(0:mx) res1[1, names(res$d1)] <- res$d1 res1[2, names(res$d2)] <- res$d2 res1[3, names(res$d3)] <- res$d3 library(RColorBrewer) pal <- grey.colors(3, 0.95, 0.55, 2.2) # RSB quietening greys barplot(res1, col=pal, beside=TRUE, legend.text=FALSE, xlab=\"numbers of neighbours\", ylab=\"tracts\") legend(\"topright\", legend=format(dS, digits=1), fill=pal, bty=\"n\", cex=0.8, title=\"max. distance\") dsts0 <- unlist(nbdists(NY_nb, coordinates(NY8))) summary(dsts0) ## Min. 1st Qu. Median Mean 3rd Qu. Max. ## 82.7 1505.0 3378.7 5865.8 8954.3 38438.1"},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"higher-order-neighbours","dir":"Articles","previous_headings":"Creating Neighbours","what":"Higher-Order Neighbours","title":"Creating Neighbours","text":"Distance bands can generated using sequence d1 d2 argument values dnearneigh() function needed construct spatial autocorrelogram understood ecology. conventions, correlograms constructed taking input list neighbours first-order sets, stepping across graph second-, third-, higher-order neighbours based number links traversed, permitting cycles, risk making \\(\\) neighbour \\(\\) (O’Sullivan Unwin 2003). nblag() function takes existing neighbour list returns list lists, first maxlag= order neighbours. shows wave connectedness graph spreads third order, receding eighth order, dying away ninth order - tracts nine steps graph. distance bands graph step order approaches spreading neighbourhoods can used examine shape relationship intensities space, like variogram, can used attempting look effects scale.","code":"Sy0_nb_lags <- nblag(Sy0_nb, maxlag=9) ## Warning in nblag(Sy0_nb, maxlag = 9): lag 6 neighbour object has 7 sub-graphs ## Warning in nblag(Sy0_nb, maxlag = 9): lag 7 neighbour object has 22 sub-graphs ## Warning in nblag(Sy0_nb, maxlag = 9): lag 8 neighbour object has 52 sub-graphs ## Warning in nblag(Sy0_nb, maxlag = 9): lag 9 neighbour object has 63 sub-graphs names(Sy0_nb_lags) <- c(\"first\", \"second\", \"third\", \"fourth\", \"fifth\", \"sixth\", \"seventh\", \"eighth\", \"ninth\") res <- sapply(Sy0_nb_lags, function(x) table(card(x))) mx <- max(unlist(sapply(Sy0_nb_lags, function(x) card(x)))) nn <- length(Sy0_nb_lags) res1 <- matrix(0, ncol=(mx+1), nrow=nn) rownames(res1) <- names(res) colnames(res1) <- as.character(0:mx) for (i in 1:nn) res1[i, names(res[[i]])] <- res[[i]] res1 ## 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 ## first 0 1 1 5 9 14 17 9 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ## second 0 0 0 0 2 2 0 6 6 11 11 4 3 7 4 6 1 0 0 0 0 0 0 0 0 ## third 0 0 0 0 0 0 0 1 3 5 5 7 14 6 8 3 3 0 1 1 1 3 1 0 1 ## fourth 0 0 0 0 0 0 0 0 1 3 5 7 16 16 5 3 3 2 0 1 1 0 0 0 0 ## fifth 0 0 0 1 1 3 1 1 3 7 13 12 8 9 3 1 0 0 0 0 0 0 0 0 0 ## sixth 6 3 0 2 8 2 5 5 4 8 9 5 5 1 0 0 0 0 0 0 0 0 0 0 0 ## seventh 21 7 4 5 9 7 3 5 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ## eighth 49 6 5 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ## ninth 63 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0"},{"path":"https://r-spatial.github.io/spdep/articles/nb.html","id":"grid-neighbours","dir":"Articles","previous_headings":"Creating Neighbours","what":"Grid Neighbours","title":"Creating Neighbours","text":"data known arranged regular, rectangular grid, cell2nb() function can used construct neighbour lists, including torus. useful simulations, , since areal entities equal numbers neighbours, edges, structure graph neutral can achieved. Neighbours can either type rook queen. regular, rectangular grid complete, can use knowledge cell size stored grid topology create appropriate list neighbours, using tightly bounded distance criterion. Neighbour lists kind commonly found ecological assays, studies species richness national continental scale. also settings, moderately large \\(n\\), \\(n=3\\),103, use sparse, list based representation shows strength. Handling \\(281 \\times 281\\) matrix eight-county census tracts feasible, easy \\(63 \\times 63\\) matrix Syracuse census tracts, demanding 3,\\(103 \\times 3\\),103 matrix.","code":"cell2nb(7, 7, type=\"rook\", torus=TRUE) ## Neighbour list object: ## Number of regions: 49 ## Number of nonzero links: 196 ## Percentage nonzero weights: 8.163265 ## Average number of links: 4 cell2nb(7, 7, type=\"rook\", torus=FALSE) ## Neighbour list object: ## Number of regions: 49 ## Number of nonzero links: 168 ## Percentage nonzero weights: 6.997085 ## Average number of links: 3.428571 data(meuse.grid) coordinates(meuse.grid) <- c(\"x\", \"y\") gridded(meuse.grid) <- TRUE dst <- max(slot(slot(meuse.grid, \"grid\"), \"cellsize\")) mg_nb <- dnearneigh(coordinates(meuse.grid), 0, dst) mg_nb ## Neighbour list object: ## Number of regions: 3103 ## Number of nonzero links: 12022 ## Percentage nonzero weights: 0.1248571 ## Average number of links: 3.874315 table(card(mg_nb)) ## ## 1 2 3 4 ## 1 133 121 2848"},{"path":[]},{"path":[]},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"introduction","dir":"Articles","previous_headings":"Creating Neighbours using sf objects","what":"Introduction","title":"Creating Neighbours using sf objects","text":"vignette tracks legacy nb vignette, based part first (2008) edition ASDAR. adds hints code nb vignette use sf vector representation instead sp vector representation create neighbour objects. .","code":""},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"summary","dir":"Articles","previous_headings":"Creating Neighbours using sf objects","what":"Summary","title":"Creating Neighbours using sf objects","text":"summary results : general, need reproduce results using \"Spatial\" objects spdep, coerce sf objects sp objects constructing neighbour objects (particularly polygon centroids used point representation). However, new work, use \"sf\" objects read using sf. spdep 1.1-7, number steps taken choose efficient approaches especially larger data sets, using functions sf approximate nearest neighbour (ANN) implementation dbscan rather RANN.","code":""},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"data-set","dir":"Articles","previous_headings":"Creating Neighbours using sf objects","what":"Data set","title":"Creating Neighbours using sf objects","text":"’ll use whole NY 8 county set boundaries, challenge implementations just Syracuse subset. description input geometries ADSAR : New York leukemia: used documented extensively Waller Gotway (2004) data formerly made available Chap. 9 http://web1.sph.emory.edu/users/lwaller/ch9index.htm; data import process described help file NY_data spData; geometries downloaded CIESIN server formerly sedac.ciesin.columbia.edu/data/set/acrp-boundary-1992/data-download, now possibly earthdata.nasa.gov/data/catalog/sedac-ciesin-sedac-acrp-1992-bf-1.00, file /pub/census/usa/tiger/ny/bna_st/t8_36.zip, extensively edited; zip archive NY_data.zip shapefiles GAL format neighbours list book website. , zipfile now new location requiring login. object listw_NY directly imported nyadjwts.dbf Waller & Gotway (2004) chapter 9 website. version New York 8 counties geometries used ASDAR included shapefile spdep converted original BNA file using external utility program convert MapInfo format converted using GDAL 1.4.1 (OGR BNA driver available; entered OGR 1.5.0, release end 2007), contains invalid geometries. found mid-2007 included villages /excluded -umbilical cords boundary enclosing tract, underlying BNA file first converted MapInfo (holes exist ). use GPKG file created follows (rgdal also used output; GDAL prior GDAL 3.3 built GEOS, BNA vector driver use geometry tests: BNA driver supports reading polygons holes lakes. determines hole lake geometrical analysis (inclusion, non-intersection tests) ignores completely notion polygon winding (whether polygon edges described clockwise counter-clockwise). GDAL must built GEOS enabled make geometry test work.):","code":"library(sf) sf_bna <- st_read(\"t8_36.bna\", stringsAsFactors=FALSE) table(st_is_valid(sf_bna)) sf_bna$AREAKEY <- gsub(\"\\\\.\", \"\", sf_bna$Primary.ID) data(NY_data, package=\"spData\") key <- as.character(nydata$AREAKEY) sf_bna1 <- sf_bna[match(key, sf_bna$AREAKEY), c(\"AREAKEY\")] sf_bna2 <- merge(sf_bna1, nydata, by=\"AREAKEY\") sf_bna2_utm18 <- st_transform(sf_bna2, \"+proj=utm +zone=18 +datum=NAD27\") st_write(sf_bna2_utm18, \"NY8_bna_utm18.gpkg\")"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"nb-and-listw-objects-copied-from-the-nb_igraph-vignette","dir":"Articles","previous_headings":"Creating Neighbours using sf objects","what":"nb and listw objects (copied from the nb_igraph vignette)","title":"Creating Neighbours using sf objects","text":"Since spdep package created, spatial weights objects constructed lists three components attributes, old-style class listw objects. first component listw object nb object, list n integer vectors, least character vector region.id attribute n unique values (like row.names data.frame object); n number spatial entities. Component list contains integer identifiers neighbours sorted vector duplication values 1:n; neighbours, component vector length 1 value 0L. nb object may contain attribute indicating whether symmetric , whether neighbour j implies j neighbour . neighbour definitions symmetric construction, contiguities distance thresholds, others asymmetric, k-nearest neighbours. nb object redundantly stores -j j-links. second component listw object list n numeric vectors, length corresponding non-zero vectors nbobject. give values spatial weights -j neighbour pair. often case neighbours symmetric construction, weights , example weights row-standardised dividing row input weights count neighbours cardinality neighbour set . nb2listwfunction, also possible pass general weights, inverse distances, shares boundary lengths . third component listw object records style weights character code, \"B\" binary weights taking values zero one (one recorded), \"W\" row-standardised weights, . order subset listw objects, knowledge style may necessary.","code":""},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"comparison-of-sp-and-sf-approaches","dir":"Articles","previous_headings":"Creating Neighbours using sf objects","what":"Comparison of sp and sf approaches","title":"Creating Neighbours using sf objects","text":"First housekeeping setup permit vignette built packages missing --date: Let us read GPKG file valid geometries ‘sf’ ‘sp’ objects:","code":"if (!suppressPackageStartupMessages(require(sf, quietly=TRUE))) { message(\"install the sf package\") dothis <- FALSE } if (dothis) sf_extSoftVersion() ## GEOS GDAL proj.4 GDAL_with_GEOS USE_PROJ_H ## \"3.13.0\" \"3.10.1\" \"9.5.1\" \"true\" \"true\" ## PROJ ## \"9.5.1\" NY8_sf <- st_read(system.file(\"shapes/NY8_bna_utm18.gpkg\", package=\"spData\"), quiet=TRUE) table(st_is_valid(NY8_sf)) ## ## TRUE ## 281"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"contiguity-neighbours-for-polygon-support","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Comparison of sp and sf approaches","what":"Contiguity neighbours for polygon support","title":"Creating Neighbours using sf objects","text":"first generate queen contiguity nb object using legacy spdep approach. first either uses pre-computed list vectors probable neighbours finds intersecting bounding boxes internally. points boundaries set polygons making observation checked distance less snap points set polygons making observation included set candidate neighbours. contiguity symmetric, j contiguities tested. queen contiguity found soon one point matches, rook contiguity soon two points match: Using spatial indices check intersection polygons much faster legacy method poly2nb. spdep 1.1-7, use made GEOS sf find candidate neighbours foundInBox=NULL, default value. contiguity symmetric definition, foundInBox= requires intersections higher indices, leading slight overhead remove duplicates, st_intersects() reports j ans j relationships. st_intersects() report whether neighbours queen rook, step needed distinguish two cases. spdep::poly2nb uses two heuristics, first find candidate neighbours intersecting polygons (st_intersects()), second use symmetry relationship halve number remaining tests. means performance linear n, overhead identifying candidates, back-filling symmetric neighbours. , spdep::poly2nb() stops searching queen contiguity soon first neighbour point found within snap distance (identical, tested first); second neighbour point indicates rook contiguities. details alternatives spherical geometries, see section @ref(spher-poly2nb) .","code":"suppressPackageStartupMessages(library(spdep)) reps <- 10 eps <- sqrt(.Machine$double.eps) system.time(for(i in 1:reps) NY8_sf_1_nb <- poly2nb(NY8_sf, queen=TRUE, snap=eps))/reps ## user system elapsed ## 0.047 0.008 0.120 NY8_sf_1_nb ## Neighbour list object: ## Number of regions: 281 ## Number of nonzero links: 1632 ## Percentage nonzero weights: 2.066843 ## Average number of links: 5.807829"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"contiguity-neighbours-from-invalid-polygons","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Comparison of sp and sf approaches","what":"Contiguity neighbours from invalid polygons","title":"Creating Neighbours using sf objects","text":"Next, explore possible source differences neighbour object reproduction, using original version tract boundaries used ASDAR, invalid geometries mentioned earlier (NY8_utm18.gpkg created original ESRI Shapefile used ASDAR): can see number differences neighbour sets derived fully valid geometries older partly invalid set: Using st_make_valid() make geometries valid: also see geometry type geometry column changes: checking \"sfg\" objects, two now objects different topological dimensions. can remedied using st_collection_extract() get polygon objects: However, making geometries valid, change geometries, new sets neighbours still differ made valid geometries ways imposing validity: neighbour sets old boundaries without imposing validity:","code":"if (packageVersion(\"spData\") >= \"2.3.2\") { NY8_sf_old <- sf::st_read(system.file(\"shapes/NY8_utm18.gpkg\", package=\"spData\")) } else { NY8_sf_old <- sf::st_read(system.file(\"shapes/NY8_utm18.shp\", package=\"spData\")) } ## Reading layer `NY8_utm18' from data source ## `C:\\Users\\rzomor2\\AppData\\Local\\R\\win-library\\4.4\\spData\\shapes\\NY8_utm18.gpkg' ## using driver `GPKG' ## Simple feature collection with 281 features and 17 fields ## Geometry type: POLYGON ## Dimension: XY ## Bounding box: xmin: 358241.9 ymin: 4649755 xmax: 480393.1 ymax: 4808545 ## Projected CRS: WGS 84 / UTM zone 18N table(st_is_valid(NY8_sf_old)) ## ## FALSE TRUE ## 5 276 try(NY8_sf_old_1_nb <- poly2nb(NY8_sf_old), silent = TRUE) all.equal(NY8_sf_old_1_nb, NY8_sf_1_nb, check.attributes=FALSE) ## [1] \"Component 57: Numeric: lengths (4, 5) differ\" ## [2] \"Component 58: Numeric: lengths (5, 6) differ\" ## [3] \"Component 66: Numeric: lengths (7, 11) differ\" ## [4] \"Component 73: Numeric: lengths (4, 5) differ\" ## [5] \"Component 260: Numeric: lengths (8, 9) differ\" NY8_sf_old_val <- st_make_valid(NY8_sf_old, dist=0) table(st_is_valid(NY8_sf_old_val)) ## ## TRUE ## 281 class(st_geometry(NY8_sf_old)) ## [1] \"sfc_POLYGON\" \"sfc\" class(st_geometry(NY8_sf_old_val)) ## [1] \"sfc_GEOMETRY\" \"sfc\" table(sapply(st_geometry(NY8_sf_old_val), function(x) class(x)[[2]])) ## ## MULTIPOLYGON POLYGON ## 3 278 NY8_sf_old_val <- st_collection_extract(NY8_sf_old_val, \"POLYGON\") table(sapply(st_geometry(NY8_sf_old_val), function(x) class(x)[[2]])) ## ## MULTIPOLYGON ## 281 try(NY8_sf_old_1_nb_val <- poly2nb(NY8_sf_old_val), silent = TRUE) all.equal(NY8_sf_old_1_nb_val, NY8_sf_1_nb, check.attributes=FALSE) ## [1] \"Component 57: Numeric: lengths (4, 5) differ\" ## [2] \"Component 58: Numeric: lengths (5, 6) differ\" ## [3] \"Component 66: Numeric: lengths (7, 11) differ\" ## [4] \"Component 73: Numeric: lengths (4, 5) differ\" ## [5] \"Component 260: Numeric: lengths (8, 9) differ\" all.equal(NY8_sf_old_1_nb_val, NY8_sf_old_1_nb, check.attributes=FALSE) ## [1] TRUE"},{"path":[]},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"finding-points-for-polygon-objects","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Planar point-based neighbours","what":"Finding points for polygon objects","title":"Creating Neighbours using sf objects","text":"knearneigh() dnearneigh() require point support, decisions must taken place point areal object. can use st_centroid() get centroids, using of_largest_polygon=TRUE argument make sure centroid largest polygon id observation made one external ring: st_point_on_surface() guarantees point fall surface member polygon: indeed taking centre largest inscribed circle (function returns radius line segment, choose central point, point circle): need check whether coordinates planar :","code":"NY8_ct_sf <- st_centroid(st_geometry(NY8_sf), of_largest_polygon=TRUE) NY8_pos_sf <- st_point_on_surface(st_geometry(NY8_sf)) if (unname(sf_extSoftVersion()[\"GEOS\"] >= \"3.9.0\")) NY8_cic_sf <- st_cast(st_inscribed_circle(st_geometry(NY8_sf), nQuadSegs=0), \"POINT\")[(1:(2*nrow(NY8_sf)) %% 2) != 0] st_is_longlat(NY8_ct_sf) ## [1] FALSE"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"graph-based-neighbours","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Planar point-based neighbours","what":"Graph-based neighbours","title":"Creating Neighbours using sf objects","text":", can check graph-based neighbours (planar coordinates ):","code":"suppressPackageStartupMessages(require(deldir)) NY84_nb <- tri2nb(NY8_ct_sf) if (require(dbscan, quietly=TRUE)) { NY85_nb <- graph2nb(soi.graph(NY84_nb, NY8_ct_sf)) } else NY85_nb <- NULL NY86_nb <- graph2nb(gabrielneigh(NY8_ct_sf)) NY87_nb <- graph2nb(relativeneigh(NY8_ct_sf))"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"k-nearest-neighbours","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Planar point-based neighbours","what":"K-nearest neighbours","title":"Creating Neighbours using sf objects","text":"K-nearest neighbours use coordinate matrices, can handle Great Circle distances, demonstrated , data set used planar, case dbscan::kNN() 2D 3D building kd-tree used: Legacy code may used omitting kd-tree:","code":"system.time(for (i in 1:reps) suppressWarnings(NY88_nb_sf <- knn2nb(knearneigh(NY8_ct_sf, k=1))))/reps ## user system elapsed ## 0.029 0.000 0.050 system.time(for (i in 1:reps) suppressWarnings(NY89_nb_sf <- knn2nb(knearneigh(NY8_ct_sf, k=1, use_kd_tree=FALSE))))/reps ## user system elapsed ## 0.017 0.002 0.044"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"distance-neighbours","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Planar point-based neighbours","what":"Distance neighbours","title":"Creating Neighbours using sf objects","text":"Distance neighbours need threshold - nbdists shows maximum distance first nearest neighbour: dnearneigh can also handle Great Circle distances, demonstrated , data set used planar: default, function uses dbscan::frNN() build kd-tree 2D 3D used find distance neighbours. small n, argument use_kd_tree=FALSE may speed computation little reverting legacy code building kd-tree first, general differences small user notice:","code":"dsts <- unlist(nbdists(NY88_nb_sf, NY8_ct_sf)) summary(dsts) ## Min. 1st Qu. Median Mean 3rd Qu. Max. ## 82.85 912.85 1801.11 3441.04 4461.26 17033.11 max_1nn <- max(dsts) system.time(for (i in 1:reps) suppressWarnings(NY810_nb <- dnearneigh(NY8_ct_sf, d1=0, d2=0.75*max_1nn)))/reps ## user system elapsed ## 0.008 0.000 0.033 system.time(for (i in 1:reps) suppressWarnings(NY811_nb <- dnearneigh(NY8_ct_sf, d1=0, d2=0.75*max_1nn, use_kd_tree=FALSE)))/reps ## user system elapsed ## 0.017 0.006 0.033"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"spherical-point-based-neighbours","dir":"Articles","previous_headings":"Creating Neighbours using sf objects","what":"Spherical point-based neighbours","title":"Creating Neighbours using sf objects","text":"Spherical point-based neighbours may found using Great Circle distances. used many years, switch sf 1.0-0 use s2 default opened new opportunities spatial indexing sphere may help.","code":"pts_ll <- st_transform(NY8_ct_sf, \"OGC:CRS84\") st_is_longlat(pts_ll) ## [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"k-nearest-neighbours-1","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Spherical point-based neighbours","what":"K-nearest neighbours","title":"Creating Neighbours using sf objects","text":"input geometries geographical coordinates, sf_use_s2() TRUE, knearneigh() use spatially indexed points s2::s2_closest_edges() (see https://github.com/r-spatial/s2/issues/125#issuecomment-860107442) performs well also larger data sets: smaller data set, legacy approach without spatial indexing adequate, slows number observations increases: WGS84 ellipsoid Great Circle distances differ little s2 spherical distances, yielding output diverges two tract centroids:","code":"(old_use_s2 <- sf_use_s2()) ## [1] TRUE sf_use_s2(TRUE) system.time(for (i in 1:reps) pts_ll1_nb <- knn2nb(knearneigh(pts_ll, k=6)))/reps ## user system elapsed ## 0.023 0.000 0.051 sf_use_s2(FALSE) ## Spherical geometry (s2) switched off system.time(for (i in 1:reps) pts_ll2_nb <- knn2nb(knearneigh(pts_ll, k=6)))/reps ## user system elapsed ## 0.020 0.001 0.046 all.equal(pts_ll1_nb, pts_ll2_nb, check.attributes=FALSE) ## [1] \"Component 52: Mean relative difference: 1.466667\" ## [2] \"Component 124: Mean relative difference: 0.0251046\" pts_ll1_nb[[52]] ## [1] 15 38 48 49 50 53 pts_ll2_nb[[52]] ## [1] 37 38 48 49 50 53 pts_ll1_nb[[124]] ## [1] 117 122 123 125 133 134 pts_ll2_nb[[124]] ## [1] 116 117 123 125 133 134 sf_use_s2(old_use_s2) ## Spherical geometry (s2) switched on"},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"distance-neighbours-1","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Spherical point-based neighbours","what":"Distance neighbours","title":"Creating Neighbours using sf objects","text":"Distance neighbours problematic. nbdists() works well s2 spherical coordinates, none tried adaptations dnearneigh() work adequately yet. argument use_s2= set TRUE s2 > 1.0-7, using s2::s2_closest_edges() legacy brute-force approach, calculating distances j copying j symmetry. distance metric alway \"km\". permit s2 methods run, without arguments set, s2 > 1.0-7, s2::s2_dwithin_matrix() run: Alternatively, spherical distances can used dwithin=FALSE s2::s2_closest_edges(); although running similar time, s2::s2_closest_edges() depends additional k= argument, , mis-set, may miss valid neighbours: Using s2::s2_closest_edges() respects d1 > 0 without requiring second pass R, faster s2::s2_dwithin_matrix(): Using s2::s2_dwithin_matrix() requires second pass, one lower bound, another upper bound, set difference operation find neighbours distance band: Setting use_s2=FALSE falls back legacy version, uses symmetry reduce time: Minor differences may occur legacy ellipsoid s2 spherical approaches:","code":"max_1nn_ll <- max(unlist(nbdists(knn2nb(knearneigh(pts_ll, k=1)), pts_ll))) ## Warning in knn2nb(knearneigh(pts_ll, k = 1)): neighbour object has 62 ## sub-graphs args(dnearneigh) ## function (x, d1, d2, row.names = NULL, longlat = NULL, bounds = c(\"GE\", ## \"LE\"), use_kd_tree = TRUE, symtest = FALSE, use_s2 = packageVersion(\"s2\") > ## \"1.0.7\", k = 200, dwithin = TRUE) ## NULL if (packageVersion(\"s2\") > \"1.0.7\") { system.time(for (i in 1:(reps/5)) suppressWarnings(pts_ll3_nb <- dnearneigh(pts_ll, d1=0, d2=0.75*max_1nn_ll)))/(reps/5) } ## user system elapsed ## 0.015 0.000 0.065 system.time(for (i in 1:(reps/5)) suppressWarnings(pts_ll5_nb <- dnearneigh(pts_ll, d1=0, d2=0.75*max_1nn_ll, dwithin=FALSE)))/(reps/5) ## user system elapsed ## 0.010 0.000 0.025 if (packageVersion(\"s2\") > \"1.0.7\") all.equal(pts_ll3_nb, pts_ll5_nb, check.attributes=FALSE) ## [1] TRUE if (packageVersion(\"s2\") > \"1.0.7\") { system.time(for (i in 1:(reps/5)) suppressWarnings(pts_ll3a_nb <- dnearneigh(pts_ll, d1=5, d2=0.75*max_1nn_ll, dwithin=FALSE)))/(reps/5) } ## user system elapsed ## 0.035 0.000 0.030 if (packageVersion(\"s2\") > \"1.0.7\") { system.time(for (i in 1:(reps/5)) suppressWarnings(pts_ll5a_nb <- dnearneigh(pts_ll, d1=5, d2=0.75*max_1nn_ll)))/(reps/5) } ## user system elapsed ## 0.055 0.000 0.085 if (packageVersion(\"s2\") > \"1.0.7\") all.equal(pts_ll3a_nb, pts_ll5a_nb, check.attributes=FALSE) ## [1] TRUE system.time(for (i in 1:reps) suppressWarnings(pts_ll6_nb <- dnearneigh(pts_ll, d1=0, d2=0.75*max_1nn_ll, use_s2=FALSE)))/reps ## user system elapsed ## 0.014 0.000 0.022 all.equal(pts_ll5_nb, pts_ll6_nb, check.attributes=FALSE) ## [1] \"Component 20: Numeric: lengths (6, 5) differ\" ## [2] \"Component 28: Numeric: lengths (7, 6) differ\" ## [3] \"Component 112: Numeric: lengths (109, 108) differ\" ## [4] \"Component 116: Numeric: lengths (109, 108) differ\" ## [5] \"Component 122: Numeric: lengths (105, 106) differ\" ## [6] \"Component 123: Numeric: lengths (108, 107) differ\" ## [7] \"Component 130: Numeric: lengths (108, 109) differ\" ## [8] \"Component 134: Numeric: lengths (106, 105) differ\" ## [9] \"Component 158: Numeric: lengths (101, 102) differ\" ## [10] \"Component 165: Numeric: lengths (101, 102) differ\" ## [11] \"Component 168: Numeric: lengths (101, 102) differ\" ## [12] \"Component 179: Numeric: lengths (89, 90) differ\" ## [13] \"Component 180: Numeric: lengths (96, 97) differ\" ## [14] \"Component 188: Numeric: lengths (46, 47) differ\" ## [15] \"Component 189: Numeric: lengths (55, 56) differ\" ## [16] \"Component 196: Numeric: lengths (47, 46) differ\" ## [17] \"Component 210: Numeric: lengths (106, 104) differ\" ## [18] \"Component 226: Numeric: lengths (88, 87) differ\" ## [19] \"Component 229: Numeric: lengths (55, 53) differ\" ## [20] \"Component 235: Numeric: lengths (40, 39) differ\" ## [21] \"Component 237: Numeric: lengths (14, 15) differ\" ## [22] \"Component 245: Numeric: lengths (16, 15) differ\" system.time(for (i in 1:reps) suppressWarnings(pts_ll6a_nb <- dnearneigh(pts_ll, d1=5, d2=0.75*max_1nn_ll, use_s2=FALSE)))/reps ## user system elapsed ## 0.007 0.001 0.019 if (packageVersion(\"s2\") > \"1.0.7\") all.equal(pts_ll5a_nb, pts_ll6a_nb, check.attributes=FALSE) ## [1] \"Component 20: Numeric: lengths (6, 5) differ\" ## [2] \"Component 28: Numeric: lengths (7, 6) differ\" ## [3] \"Component 112: Numeric: lengths (62, 61) differ\" ## [4] \"Component 113: Numeric: lengths (62, 63) differ\" ## [5] \"Component 116: Numeric: lengths (56, 55) differ\" ## [6] \"Component 119: Numeric: lengths (68, 69) differ\" ## [7] \"Component 122: Numeric: lengths (43, 44) differ\" ## [8] \"Component 123: Numeric: lengths (50, 49) differ\" ## [9] \"Component 128: Numeric: lengths (65, 64) differ\" ## [10] \"Component 130: Numeric: lengths (61, 63) differ\" ## [11] \"Component 132: Numeric: lengths (45, 46) differ\" ## [12] \"Component 134: Numeric: lengths (46, 45) differ\" ## [13] \"Component 136: Numeric: lengths (61, 62) differ\" ## [14] \"Component 147: Numeric: lengths (50, 51) differ\" ## [15] \"Component 154: Numeric: lengths (56, 57) differ\" ## [16] \"Component 158: Numeric: lengths (49, 50) differ\" ## [17] \"Component 165: Mean relative difference: 0.02823018\" ## [18] \"Component 168: Numeric: lengths (54, 56) differ\" ## [19] \"Component 179: Numeric: lengths (77, 78) differ\" ## [20] \"Component 180: Numeric: lengths (85, 86) differ\" ## [21] \"Component 188: Numeric: lengths (39, 40) differ\" ## [22] \"Component 189: Numeric: lengths (48, 49) differ\" ## [23] \"Component 196: Numeric: lengths (45, 44) differ\" ## [24] \"Component 210: Numeric: lengths (68, 66) differ\" ## [25] \"Component 226: Numeric: lengths (82, 81) differ\" ## [26] \"Component 229: Numeric: lengths (48, 46) differ\" ## [27] \"Component 235: Numeric: lengths (38, 37) differ\" ## [28] \"Component 237: Numeric: lengths (14, 15) differ\" ## [29] \"Component 245: Numeric: lengths (15, 14) differ\""},{"path":"https://r-spatial.github.io/spdep/articles/nb_sf.html","id":"spher-poly2nb","dir":"Articles","previous_headings":"Creating Neighbours using sf objects > Spherical point-based neighbours","what":"Contiguity neighbours for spherical polygon support","title":"Creating Neighbours using sf objects","text":"also turns sf functions used find contiguity neighbours, s2 spatial indexing functionality accessed finding candidate neighbours intersecting geometries. timings little slower st_intersects() hands geometry predicates s2_intersects_matrix(), results , spatial indexing used, scales well larger data sets:","code":"NY8_sf_ll <- st_transform(NY8_sf, \"OGC:CRS84\") st_is_longlat(NY8_sf_ll) ## [1] TRUE sf_use_s2(TRUE) system.time(for (i in 1:reps) NY8_sf_1_nb_ll <- poly2nb(NY8_sf_ll, queen=TRUE, snap=eps))/reps ## user system elapsed ## 0.085 0.011 0.179 all.equal(NY8_sf_1_nb, NY8_sf_1_nb_ll, check.attributes=FALSE) ## [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/articles/sids.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Introduction to the North Carolina SIDS data set (re-revised)","text":"data set presented first Symons, Grimson, Yuan (1983), analysed reference spatial nature data Cressie Read (1985), expanded Cressie Chan (1989), used detail Cressie (1991). 100 counties North Carolina, includes counts numbers live births (also non-white live births) numbers sudden infant deaths, July 1, 1974 June 30, 1978 July 1, 1979 June 30, 1984 periods. Cressie Read (1985), listing county neighbours based shared boundaries (contiguity) given, Cressie Chan (1989), Cressie (1991, 386–89), different listing based criterion distance county seats, cutoff 30 miles. county seat location coordinates given miles local (unknown) coordinate reference system. data also used exemplify range functions spatial statistics module user’s manual (Kaluzny et al. 1996).","code":""},{"path":"https://r-spatial.github.io/spdep/articles/sids.html","id":"getting-the-data-into-r","dir":"Articles","previous_headings":"","what":"Getting the data into R","title":"Introduction to the North Carolina SIDS data set (re-revised)","text":"using spdep spreg packages, version: spdep, version 1.4-1, 2025-06-12, sf package tmap package. data sources referred documented help page nc.sids data set spData. actual data, included shapefile county boundaries North Carolina made available maptools package 1. data known geographical coordinates (longitude-latitude decimal degrees) assumed use NAD27 datum. ESRI Shapefile deprecated, replaced GeoPackage, written reading original files spData 2.3.1: shapefile format presupposed three files extensions .shp, .shx, .dbf, first contains geometry data, second spatial index, third attribute data. required name apart extension, read using sf::st_read() sf object nc; class defined sf. centroids largest polygon county available using st_centroid method sf sfc POINT object, can used place labels extraction coordinate matrix: can examine names columns data frame see contains — fact columns examining , others useful cleaning data set. Let’s check different versions data - sf spData NC SIDS files, GeoDa Center two forms: actual CRS unknown, GeoPackage spData version updated \"EPSG:4267\". Next, geometries ? sf::st_equals returns logical matrix, ’ll check diagonal values TRUE, values TRUE summing recalling n 100: Next, let’s download GeoDa files repeat comparisons: looks though external files assuming WGS84/NAD83 datum, also contain geometries. Now contents files - sids2 also contains rates, file spData contains coordinates given Cressie (1991), parcels contiguous counties p. 554, aggregations used median polishing. spData data set columns reordered surprise: difference NWBIR74: spData follows Cressie (1991) sf Geoda follow Cressie Chan (1989) NWBIR74 Chowan county. now examine data set reproduced Cressie collaborators, included spData (formerly spdep), add neighbour relationships used Cressie Chan (1989) background map graph shown Figure \\(\\ref{plot-CC89.nb}\\): Printing neighbour object shows neighbour list object, sparse structure — displayed matrix, 3.94% cells filled. Objects class nb contain list long number counties; component list vector index numbers neighbours county question, neighbours county region.id 37001 can retreived matching indices. information can obtained using summary() nb object. Finally, associate vector names neighbour list, row.names argument. names unique, data frame row names. neighbour list object records neighbours order relation list , neighbours list county region.id “37001” seventeenth, nineteenth, thirty-second, forty-first sixty-eighth list. can retreive codes looking region.id attribute. also note neighbour criterion generates two counties neighbours, Dare Hyde, whose county seats 30 miles nearest neighbours. card() function returns cardinality neighbour set. need return methods handling -neighbour objects later . also show new neighbours lists may constructed , compare literature.","code":"library(spdep) nc <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\")[1], quiet=TRUE) #st_crs(nc) <- \"EPSG:4267\" row.names(nc) <- as.character(nc$FIPSNO) sf_use_s2(TRUE) plot(st_geometry(nc), axes=TRUE) text(st_coordinates(st_centroid(st_geometry(nc), of_largest_polygon=TRUE)), label=nc$FIPSNO, cex=0.5) names(nc) ## [1] \"CNTY_ID\" \"AREA\" \"PERIMETER\" \"CNTY_\" \"NAME\" \"FIPS\" ## [7] \"FIPSNO\" \"CRESS_ID\" \"BIR74\" \"SID74\" \"NWBIR74\" \"BIR79\" ## [13] \"SID79\" \"NWBIR79\" \"east\" \"north\" \"x\" \"y\" ## [19] \"lon\" \"lat\" \"L_id\" \"M_id\" \"geom\" summary(nc) ## CNTY_ID AREA PERIMETER CNTY_ ## Min. :1825 Min. :0.0420 Min. :0.999 Min. :1825 ## 1st Qu.:1902 1st Qu.:0.0910 1st Qu.:1.324 1st Qu.:1902 ## Median :1982 Median :0.1205 Median :1.609 Median :1982 ## Mean :1986 Mean :0.1263 Mean :1.673 Mean :1986 ## 3rd Qu.:2067 3rd Qu.:0.1542 3rd Qu.:1.859 3rd Qu.:2067 ## Max. :2241 Max. :0.2410 Max. :3.640 Max. :2241 ## NAME FIPS FIPSNO CRESS_ID ## Length:100 Length:100 Min. :37001 Min. : 1.00 ## Class :character Class :character 1st Qu.:37051 1st Qu.: 25.75 ## Mode :character Mode :character Median :37100 Median : 50.50 ## Mean :37100 Mean : 50.50 ## 3rd Qu.:37150 3rd Qu.: 75.25 ## Max. :37199 Max. :100.00 ## BIR74 SID74 NWBIR74 BIR79 ## Min. : 248 Min. : 0.00 Min. : 1.0 Min. : 319 ## 1st Qu.: 1077 1st Qu.: 2.00 1st Qu.: 190.0 1st Qu.: 1336 ## Median : 2180 Median : 4.00 Median : 697.5 Median : 2636 ## Mean : 3300 Mean : 6.67 Mean :1051.0 Mean : 4224 ## 3rd Qu.: 3936 3rd Qu.: 8.25 3rd Qu.:1168.5 3rd Qu.: 4889 ## Max. :21588 Max. :44.00 Max. :8027.0 Max. :30757 ## SID79 NWBIR79 east north ## Min. : 0.00 Min. : 3.0 Min. : 19.0 Min. : 6.0 ## 1st Qu.: 2.00 1st Qu.: 250.5 1st Qu.:178.8 1st Qu.: 97.0 ## Median : 5.00 Median : 874.5 Median :285.0 Median :125.5 ## Mean : 8.36 Mean : 1352.8 Mean :271.3 Mean :122.1 ## 3rd Qu.:10.25 3rd Qu.: 1406.8 3rd Qu.:361.2 3rd Qu.:151.5 ## Max. :57.00 Max. :11631.0 Max. :482.0 Max. :182.0 ## x y lon lat ## Min. :-328.04 Min. :3757 Min. :-84.08 Min. :33.92 ## 1st Qu.: -60.55 1st Qu.:3920 1st Qu.:-81.20 1st Qu.:35.26 ## Median : 114.38 Median :3963 Median :-79.26 Median :35.68 ## Mean : 91.46 Mean :3953 Mean :-79.51 Mean :35.62 ## 3rd Qu.: 240.03 3rd Qu.:4000 3rd Qu.:-77.87 3rd Qu.:36.05 ## Max. : 439.65 Max. :4060 Max. :-75.67 Max. :36.52 ## L_id M_id geom ## Min. :1.00 Min. :1.00 MULTIPOLYGON :100 ## 1st Qu.:1.00 1st Qu.:2.00 epsg:4267 : 0 ## Median :2.00 Median :3.00 +proj=long...: 0 ## Mean :2.12 Mean :2.67 ## 3rd Qu.:3.00 3rd Qu.:3.25 ## Max. :4.00 Max. :4.00 library(sf) nc_sf <- st_read(system.file(\"shape/nc.shp\", package=\"sf\"), quiet=TRUE) st_crs(nc_sf) ## Coordinate Reference System: ## User input: NAD27 ## wkt: ## GEOGCRS[\"NAD27\", ## DATUM[\"North American Datum 1927\", ## ELLIPSOID[\"Clarke 1866\",6378206.4,294.978698213898, ## LENGTHUNIT[\"metre\",1]]], ## PRIMEM[\"Greenwich\",0, ## ANGLEUNIT[\"degree\",0.0174532925199433]], ## CS[ellipsoidal,2], ## AXIS[\"latitude\",north, ## ORDER[1], ## ANGLEUNIT[\"degree\",0.0174532925199433]], ## AXIS[\"longitude\",east, ## ORDER[2], ## ANGLEUNIT[\"degree\",0.0174532925199433]], ## ID[\"EPSG\",4267]] nc <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\"), quiet=TRUE) st_crs(nc) ## Coordinate Reference System: ## User input: NAD27 ## wkt: ## GEOGCRS[\"NAD27\", ## DATUM[\"North American Datum 1927\", ## ELLIPSOID[\"Clarke 1866\",6378206.4,294.978698213898, ## LENGTHUNIT[\"metre\",1]]], ## PRIMEM[\"Greenwich\",0, ## ANGLEUNIT[\"degree\",0.0174532925199433]], ## CS[ellipsoidal,2], ## AXIS[\"geodetic latitude (Lat)\",north, ## ORDER[1], ## ANGLEUNIT[\"degree\",0.0174532925199433]], ## AXIS[\"geodetic longitude (Lon)\",east, ## ORDER[2], ## ANGLEUNIT[\"degree\",0.0174532925199433]], ## USAGE[ ## SCOPE[\"Geodesy.\"], ## AREA[\"North and central America: Antigua and Barbuda - onshore. Bahamas - onshore plus offshore over internal continental shelf only. Belize - onshore. British Virgin Islands - onshore. Canada onshore - Alberta, British Columbia, Manitoba, New Brunswick, Newfoundland and Labrador, Northwest Territories, Nova Scotia, Nunavut, Ontario, Prince Edward Island, Quebec, Saskatchewan and Yukon - plus offshore east coast. Cuba - onshore and offshore. El Salvador - onshore. Guatemala - onshore. Honduras - onshore. Panama - onshore. Puerto Rico - onshore. Mexico - onshore plus offshore east coast. Nicaragua - onshore. United States (USA) onshore and offshore - Alabama, Alaska, Arizona, Arkansas, California, Colorado, Connecticut, Delaware, Florida, Georgia, Idaho, Illinois, Indiana, Iowa, Kansas, Kentucky, Louisiana, Maine, Maryland, Massachusetts, Michigan, Minnesota, Mississippi, Missouri, Montana, Nebraska, Nevada, New Hampshire, New Jersey, New Mexico, New York, North Carolina, North Dakota, Ohio, Oklahoma, Oregon, Pennsylvania, Rhode Island, South Carolina, South Dakota, Tennessee, Texas, Utah, Vermont, Virginia, Washington, West Virginia, Wisconsin and Wyoming - plus offshore . US Virgin Islands - onshore.\"], ## BBOX[7.15,167.65,83.17,-47.74]], ## ID[\"EPSG\",4267]] suppressWarnings(st_crs(nc_sf) <- st_crs(nc)) xx <- st_equals(nc, nc_sf, sparse=FALSE) all(diag(xx)) && sum(xx) == 100L ## [1] TRUE td <- tempdir() #download.file(\"https://geodacenter.github.io/data-and-lab//data/sids.zip\", file.path(td, \"sids.zip\"), quiet=TRUE) # local copy (2020-10-22) as repository sometimes offline file.copy(system.file(\"etc/misc/sids.zip\", package=\"spdep\"), td) ## [1] TRUE unzip(file.path(td, \"sids.zip\"), c(\"sids/sids.dbf\", \"sids/sids.prj\", \"sids/sids.shp\", \"sids/sids.shx\"), exdir=td) sids_sf <- st_read(file.path(td, \"sids/sids.shp\"), quiet=TRUE) #download.file(\"https://geodacenter.github.io/data-and-lab//data/sids2.zip\", file.path(td, \"sids2.zip\"), quiet=TRUE) file.copy(system.file(\"etc/misc/sids2.zip\", package=\"spdep\"), td) ## [1] TRUE unzip(file.path(td, \"sids2.zip\"), c(\"sids2/sids2.dbf\", \"sids2/sids2.prj\", \"sids2/sids2.shp\", \"sids2/sids2.shx\"), exdir=td) sids2_sf <- st_read(file.path(td, \"sids2/sids2.shp\"), quiet=TRUE) st_crs(sids_sf) ## Coordinate Reference System: ## User input: WGS 84 ## wkt: ## GEOGCRS[\"WGS 84\", ## DATUM[\"World Geodetic System 1984\", ## ELLIPSOID[\"WGS 84\",6378137,298.257223563, ## LENGTHUNIT[\"metre\",1]]], ## PRIMEM[\"Greenwich\",0, ## ANGLEUNIT[\"degree\",0.0174532925199433]], ## CS[ellipsoidal,2], ## AXIS[\"latitude\",north, ## ORDER[1], ## ANGLEUNIT[\"degree\",0.0174532925199433]], ## AXIS[\"longitude\",east, ## ORDER[2], ## ANGLEUNIT[\"degree\",0.0174532925199433]], ## ID[\"EPSG\",4326]] st_crs(sids2_sf) ## Coordinate Reference System: ## User input: WGS 84 ## wkt: ## GEOGCRS[\"WGS 84\", ## DATUM[\"World Geodetic System 1984\", ## ELLIPSOID[\"WGS 84\",6378137,298.257223563, ## LENGTHUNIT[\"metre\",1]]], ## PRIMEM[\"Greenwich\",0, ## ANGLEUNIT[\"degree\",0.0174532925199433]], ## CS[ellipsoidal,2], ## AXIS[\"latitude\",north, ## ORDER[1], ## ANGLEUNIT[\"degree\",0.0174532925199433]], ## AXIS[\"longitude\",east, ## ORDER[2], ## ANGLEUNIT[\"degree\",0.0174532925199433]], ## ID[\"EPSG\",4326]] suppressWarnings(st_crs(sids_sf) <- st_crs(nc_sf)) xx <- st_equals(sids_sf, nc_sf, sparse=FALSE) all(diag(xx)) && sum(xx) == 100L ## [1] FALSE suppressWarnings(st_crs(sids2_sf) <- st_crs(nc_sf)) xx <- st_equals(sids2_sf, nc_sf, sparse=FALSE) all(diag(xx)) && sum(xx) == 100L ## [1] FALSE all.equal(as.data.frame(nc_sf)[,1:14], as.data.frame(sids_sf)[,1:14]) ## [1] \"Names: 12 string mismatches\" ## [2] \"Component 4: Modes: numeric, character\" ## [3] \"Component 4: target is numeric, current is character\" ## [4] \"Component 5: 100 string mismatches\" ## [5] \"Component 6: Modes: character, numeric\" ## [6] \"Component 6: target is character, current is numeric\" ## [7] \"Component 7: Mean relative difference: 0.9986388\" ## [8] \"Component 8: Mean relative difference: 64.33901\" ## [9] \"Component 9: Mean relative difference: 0.9979786\" ## [10] \"Component 10: Mean relative difference: 156.5427\" ## [11] \"Component 11: Mean relative difference: 3.01968\" ## [12] \"Component 12: Mean relative difference: 0.9980208\" ## [13] \"Component 13: Mean relative difference: 160.8194\" ## [14] \"Component 14: Modes: numeric, list\" ## [15] \"Component 14: Attributes: < target is NULL, current is list >\" ## [16] \"Component 14: target is numeric, current is sfc_MULTIPOLYGON\" all.equal(as.data.frame(nc_sf)[,1:14], as.data.frame(sids2_sf)[,1:14]) ## [1] \"Names: 12 string mismatches\" ## [2] \"Component 4: Modes: numeric, character\" ## [3] \"Component 4: target is numeric, current is character\" ## [4] \"Component 5: 100 string mismatches\" ## [5] \"Component 6: Modes: character, numeric\" ## [6] \"Component 6: target is character, current is numeric\" ## [7] \"Component 7: Mean relative difference: 0.9986388\" ## [8] \"Component 8: Mean relative difference: 64.33901\" ## [9] \"Component 9: Mean relative difference: 0.9979786\" ## [10] \"Component 10: Mean relative difference: 156.5427\" ## [11] \"Component 11: Mean relative difference: 3.01968\" ## [12] \"Component 12: Mean relative difference: 0.9980208\" ## [13] \"Component 13: Mean relative difference: 160.8194\" ## [14] \"Component 14: Mean relative difference: 0.9984879\" all.equal(as.data.frame(nc_sf)[,1:14], as.data.frame(nc)[,c(2,3,4,1,5:14)]) ## [1] \"Component \\\"NWBIR74\\\": Mean relative difference: 0.04891304\" which(!(nc_sf$NWBIR74 == nc$NWBIR74)) ## [1] 21 c(nc$NWBIR74[21], nc_sf$NWBIR74[21]) ## [1] 386 368 gal_file <- system.file(\"weights/ncCR85.gal\", package=\"spData\")[1] ncCR85 <- read.gal(gal_file, region.id=nc$FIPSNO) ncCR85 ## Neighbour list object: ## Number of regions: 100 ## Number of nonzero links: 492 ## Percentage nonzero weights: 4.92 ## Average number of links: 4.92 gal_file <- system.file(\"weights/ncCC89.gal\", package=\"spData\")[1] ncCC89 <- read.gal(gal_file, region.id=nc$FIPSNO) ncCC89 ## Neighbour list object: ## Number of regions: 100 ## Number of nonzero links: 394 ## Percentage nonzero weights: 3.94 ## Average number of links: 3.94 ## 2 regions with no links: ## 37055, 37095 ## 3 disjoint connected subgraphs plot(st_geometry(nc), border=\"grey\") plot(ncCC89, st_centroid(st_geometry(nc), of_largest_polygon), add=TRUE, col=\"blue\") r.id <- attr(ncCC89, \"region.id\") ncCC89[[match(\"37001\", r.id)]] ## [1] 11 26 29 30 48 r.id[ncCC89[[match(\"37001\", r.id)]]] ## [1] 37033 37081 37135 37063 37037 as.character(nc$NAME)[card(ncCC89) == 0] ## [1] \"Dare\" \"Hyde\""},{"path":"https://r-spatial.github.io/spdep/articles/sids.html","id":"probability-mapping","dir":"Articles","previous_headings":"Getting the data into R","what":"Probability mapping","title":"Introduction to the North Carolina SIDS data set (re-revised)","text":"Rather review functions measuring modelling spatial dependence spdep package, focus probability mapping disease rates data. Typically, counts incidence disease spatial unit, associated counts populations risk. task try establish whether spatial units seem characterised higher lower counts cases might expected general terms (Bailey Gatrell 1995). early approach Choynowski (1959), described Cressie Read (1985) Bailey Gatrell (1995), assumes, given true rate spatial units small, population risk increases infinity, spatial unit case counts Poisson mean value equal population risk times rate study area whole. Choynowski’s approach folds two tails measured probabilities together, small values, chosen \\(\\alpha\\), occur spatial units either unusually high low rates. reason, high low counties plotted separately . Note cut returns factor labeled cut intervals. complicated thematic maps, may helpful use ColorBrewer (https://colorbrewer2.org) colour palettes. use palettes accessed tmap, available R RColorBrewer package. choynowski() function provides probability map values required, probmap() function returns raw (crude) rates, expected counts (assuming constant rate across study area), relative risks, Poisson probability map values calculated using standard cumulative distribution function ppois(). fold tails together, counties lower observed counts expected, based population size, values lower tail, higher observed counts expected values upper tail, can see. Marilia Carvalho (personal communication) Virgilio Gómez Rubio (Gómez-Rubio, Ferrándiz-Ferragud, López-Quílez 2005) pointed unusual shape distribution Poisson probability values (histogram ), repeating doubts probability mapping voiced Cressie (1991, 392): “extreme value \\(\\ldots\\) may due lack fit Poisson model deviation constant rate assumption”. many high values one expected, suggesting perhaps overdispersion, ratio variance mean larger unity. One ad-hoc way assess impact possible failure assumption counts follow Poisson distribution estimate dispersion fitting generalized linear model observed counts including intercept (null model) offset observed population risk (suggested Marilia Carvalho associates): dispersion equal 2.2786188, much greater unity; calculate corrected probability map values taking standardised residuals model, taking size dispersion account; results shown . Many fewer counties appear now unexpectedly large small numbers cases. ad-hoc adjustment made R provides access wide range model-fitting functions can used help check assumptions. Gómez-Rubio, Ferrándiz-Ferragud, López-Quílez (2005) chose rather construct probability map hypothesis data drawn Negative Binomial distribution. far, none maps presented made use spatial dependence possibly present data. elementary step can taken map Empirical Bayes estimates rates, smoothed relation raw rates. underlying question linked larger variance associated rate estimates counties small populations risk compared counties large populations risk. Empirical Bayes estimates place credence raw rates counties large populations risk, modify much less modify rates small counties. case small populations risk, confidence placed either global rate study area whole, local Empirical Bayes estimates, rates larger moving window including neighbours county estimated. function used spdep EBlocal(), initially contributed Marilia Carvalho. parallels similar function GeoDa, uses Bailey Gatrell (1995) interpretation Marshall (1991), rather GeoDa (Anselin, Syabri, Smirnov 2002). results shown Figure \\(\\ref{EBlocal}\\). Like relevant functions spdep,EBlocal() takes zero.policy argument allow missing values passed . case, local estimate available two counties neighbours, marked stars. addition Empirical Bayes smoothing globally, used disease mapping Assuncão Reis correction Moran’s \\(\\) rates data (shrink towards global rate population risk small, Monte Carlo test), lists local neighbours can used shrink towards local rate.","code":"ch <- choynowski(nc$SID74, nc$BIR74) nc$ch_pmap_low <- ifelse(ch$type, ch$pmap, NA) nc$ch_pmap_high <- ifelse(!ch$type, ch$pmap, NA) prbs <- c(0,.001,.01,.05,.1,1) nc$high = cut(nc$ch_pmap_high, prbs) nc$low = cut(nc$ch_pmap_low,prbs ) is_tmap <- FALSE if (require(tmap, quietly=TRUE)) is_tmap <- TRUE is_tmap ## [1] FALSE library(tmap) tmap4 <- packageVersion(\"tmap\") >= \"3.99\" if (tmap4) { tm_shape(nc) + tm_polygons(fill=c(\"low\", \"high\"), fill.scale = tm_scale(values=\"brewer.set1\"), fill.legend = tm_legend(\"p-values\", frame=FALSE, item.r = 0), fill.free=FALSE, lwd=0.01) + tm_layout(panel.labels=c(\"low\", \"high\")) } else { tm_shape(nc) + tm_fill(c(\"low\", \"high\"), palette=\"Set1\", title=\"p-values\") + tm_facets(free.scales=FALSE) + tm_layout(panel.labels=c(\"low\", \"high\")) } pmap <- probmap(nc$SID74, nc$BIR74) nc$pmap <- pmap$pmap brks <- c(0,0.001,0.01,0.025,0.05,0.95,0.975,0.99,0.999,1) if (tmap4) { tm_shape(nc) + tm_polygons(fill=\"pmap\", fill.scale = tm_scale(values=\"brewer.rd_bu\", midpoint=0.5, breaks=brks), fill.legend = tm_legend(frame=FALSE, item.r = 0, position = tm_pos_out(\"right\", \"center\")), lwd=0.01) + tm_layout(component.autoscale=FALSE) } else { tm_shape(nc) + tm_fill(\"pmap\", breaks=brks, midpoint=0.5, palette=\"RdBu\") + tm_layout(legend.outside=TRUE) } hist(nc$pmap, main=\"\") res <- glm(SID74 ~ offset(log(BIR74)), data=nc, family=\"quasipoisson\") nc$stdres <- rstandard(res) brks <- c(-4, -3, -2, -1.5, -1, -0.5, 0.5, 1, 1.5, 2, 3, 4) if (tmap4) { tm_shape(nc) + tm_polygons(fill=\"stdres\", fill.scale = tm_scale(values=\"brewer.rd_bu\", midpoint=0.5, breaks=brks), fill.legend = tm_legend(frame=FALSE, item.r = 0, position = tm_pos_out(\"right\", \"center\")), lwd=0.01) + tm_layout(component.autoscale=FALSE) } else { tm_shape(nc) + tm_fill(\"stdres\", breaks=brks, midpoint=0, palette=\"RdBu\") + tm_layout(legend.outside=TRUE) } global_rate <- sum(nc$SID74)/sum(nc$BIR74) nc$Expected <- global_rate * nc$BIR74 res <- EBlocal(nc$SID74, nc$Expected, ncCC89, zero.policy=TRUE) nc$EB_loc <- res$est brks <- c(0, 0.25, 0.5, 0.75, 1, 2, 3, 4, 5) nc_miss <- st_centroid(st_geometry(nc[card(ncCC89) == 0,]), of_largest_polygon) if (tmap4) { tm_shape(nc) + tm_polygons(fill=\"stdres\", fill.scale = tm_scale(values=\"brewer.rd_bu\", midpoint=0.5, breaks=brks), fill.legend = tm_legend(frame=FALSE, item.r = 0, position = tm_pos_out(\"right\", \"center\")), lwd=0.01) + tm_layout(component.autoscale=FALSE) + tm_shape(nc_miss) + tm_symbols(shape=8, size=0.5) } else { tm_shape(nc) + tm_fill(\"EB_loc\", breaks=brks, midpoint=1, palette=\"RdBu\") + tm_layout(legend.outside=TRUE) + tm_shape(nc_miss) + tm_symbols(shape=8, size=0.5) } set.seed(1) EBImoran.mc(nc$SID74, nc$BIR74, nb2listw(ncCC89, style=\"B\", zero.policy=TRUE), nsim=999, zero.policy=TRUE) ## ## Monte-Carlo simulation of Empirical Bayes Index (mean subtracted) ## ## data: cases: nc$SID74, risk population: nc$BIR74 ## weights: nb2listw(ncCC89, style = \"B\", zero.policy = TRUE) ## number of simulations + 1: 1000 ## ## statistic = 0.25789, observed rank = 998, p-value = 0.002 ## alternative hypothesis: greater"},{"path":"https://r-spatial.github.io/spdep/articles/sids.html","id":"exploration-and-modelling-of-the-data","dir":"Articles","previous_headings":"","what":"Exploration and modelling of the data","title":"Introduction to the North Carolina SIDS data set (re-revised)","text":"One first steps taken Cressie Read (1985) try bring spatial trends dividing North Carolina \\(4\\times4\\) rough rectangles. Just see works, let us map rough rectangles proceeding . Cressie constructs transformed SIDS rates variable, 1974–78, analyses (co-workers). can replicate stem--leaf figure p. 396 book, taken Cressie Read (1989):","code":"nc$both <- factor(paste(nc$L_id, nc$M_id, sep=\":\")) nboth <- length(table(unclass(nc$both))) if (tmap4) { tm_shape(nc) + tm_polygons(fill=\"both\", fill.scale=tm_scale(values=\"brewer.set1\"), fill.legend = tm_legend(\"rough\\nrectangles\", frame=FALSE, item.r = 0, position = tm_pos_out(\"right\", \"center\")), lwd=0.01) + tm_layout(component.autoscale=FALSE) } else { tm_shape(nc) + tm_fill(\"both\", palette=\"Set1\", title=\"rough\\nrectangles\") + tm_layout(legend.outside=TRUE) } nc$ft.SID74 <- sqrt(1000)*(sqrt(nc$SID74/nc$BIR74) + sqrt((nc$SID74+1)/nc$BIR74)) stem(round(nc$ft.SID74, 1), scale=2) ## ## The decimal point is at the | ## ## 0 | 9 ## 1 | 111244 ## 1 | 567789999 ## 2 | 0011111222334444 ## 2 | 55555666677778999999999 ## 3 | 000111122333333344444444 ## 3 | 5568999 ## 4 | 013344 ## 4 | 555557 ## 5 | 2 ## 5 | ## 6 | 3"},{"path":"https://r-spatial.github.io/spdep/articles/sids.html","id":"medpol","dir":"Articles","previous_headings":"Exploration and modelling of the data","what":"Median polish smoothing","title":"Introduction to the North Carolina SIDS data set (re-revised)","text":"Cressie (1991, 46–48, 393–400) discusses detail smoothing may used partition variation data smooth rough. order try North Carolina SIDS data set, use coarse gridding four columns four rows given Cressie (1991, 553–54), four grid cells empty; given variables L_id M_id object nc. Next aggregate number live births number SIDS cases 1974–1978 grid cells: Using Freeman-Tukey transformation used county data, coerce data correctly configured matrix, cells empty. medpolish function applied matrix, told remove empty cells; function iterates rows columns matrix using median extract overall effect, row column effects, residuals: Returning factors linking rows columns counties, generating matrices dummy variables using model.matrix, can calculate fitted values Freeman-Tukey adjusted rate county, residuals subtracting fitted value observed rate. Naturally, fitted value counties grid cell: figure shows median polish smoothing results three maps, observed Freeman-Tukey transformed SIDS rates, fitted smoothed values, residuals. addition, plot median polish object also shown, plotting smooth residuals outer product row column effects divided overall effect, indicate lack additivity row column case — relevant analysis tables covariates rather geographical grids.","code":"mBIR74 <- tapply(nc$BIR74, nc$both, sum) mSID74 <- tapply(nc$SID74, nc$both, sum) mFT <- sqrt(1000)*(sqrt(mSID74/mBIR74) + sqrt((mSID74+1)/mBIR74)) # mFT1 <- t(matrix(mFT, 4, 4, byrow=TRUE)) # wrong assignment of 12 elements to a 4x4 matrix detected by CRAN test 2021-05-22 rc <- do.call(\"rbind\", lapply(strsplit(names(mFT), \":\"), as.integer)) mFT1 <- matrix(as.numeric(NA), 4, 4) for (i in 1:nrow(rc)) mFT1[rc[i,1], rc[i,2]] <- mFT[i] med <- medpolish(mFT1, na.rm=TRUE, trace.iter=FALSE) med ## ## Median Polish Results (Dataset: \"mFT1\") ## ## Overall: 2.90965 ## ## Row Effects: ## [1] -0.05686791 -0.37236370 0.05686791 0.79541774 ## ## Column Effects: ## [1] -0.005484562 -0.446250551 0.003656375 0.726443256 ## ## Residuals: ## [,1] [,2] [,3] [,4] ## [1,] NA -0.45800 0.000000 0.37556 ## [2,] -0.092554 0.00000 0.101695 0.00000 ## [3,] 0.092554 0.30464 -0.090726 -0.55364 ## [4,] NA NA 0.000000 NA mL_id <- model.matrix(~ as.factor(nc$L_id) -1) mM_id <- model.matrix(~ as.factor(nc$M_id) -1) nc$pred <- c(med$overall + mL_id %*% med$row + mM_id %*% med$col) nc$mp_resid <- nc$ft.SID74 - nc$pred if (tmap4) { out1 <- tm_shape(nc) + tm_polygons(fill=c(\"ft.SID74\", \"pred\"), fill.scale=tm_scale(values=\"brewer.yl_or_br\"), fill.legend=tm_legend(position=tm_pos_out(\"right\", \"center\"), frame=FALSE, item.r = 0), fill.free=FALSE, lwd=0.01) + tm_layout(panel.labels=c(\"Observed\", \"Median polish prediction\")) out2 <- tm_shape(nc) + tm_polygons(fill=\"mp_resid\", fill.scale=tm_scale(values=\"brewer.rd_yl_gn\", midpoint=0), fill.legend=tm_legend(position=tm_pos_out(\"right\", \"center\"), frame=FALSE, item.r = 0), lwd=0.01) } else { out1 <- tm_shape(nc) + tm_fill(c(\"ft.SID74\", \"pred\")) + tm_facets(free.scales=FALSE) + tm_layout(panel.labels=c(\"Observed\", \"Median polish prediction\")) out2 <- tm_shape(nc) + tm_fill(\"mp_resid\", midpoint=0) + tm_layout(legend.outside=TRUE) } tmap_arrange(out1, out2, ncol=1)"},{"path":[]},{"path":"https://r-spatial.github.io/spdep/articles/subgraphs.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"No-neighbour observation and subgraph handling","text":"spdep package always careful disconnected graphs, especially disconnected observations graph nodes neighbours, incoming outgoing edges. nb neighbour objects, encoded integer vectors length 1 containing integer 0, invalid index \\([1, N]\\), \\(N\\) observation count. Functions taking neighbour objects arguments use zero.policy argument guide handle -neighbour observations. spdep also n.comp.nb find number disjoint connected subgraphs nb object, contributed Nicholas Lewin-Koh 2001 using depth-first search symmetric neighbours, showing addition observations belong subgraph. Obviously, -neighbour observations singleton graph nodes, subgraphs also troubling spatial analysis, connection spatial processes subgraphs. ripples one pond cross separate pond connected. spdep 1.3-1, steps began raise awareness possibility neighbour objects might created disconnected way, mostly warnings, computation subgraph measures default. vignette intended provide background steps.","code":""},{"path":"https://r-spatial.github.io/spdep/articles/subgraphs.html","id":"no-neighbour-observations","dir":"Articles","previous_headings":"","what":"No-neighbour observations","title":"No-neighbour observation and subgraph handling","text":"start, nb objects recorded -neighbour observations integer vector unit length value 0, neighbours recorded ID values 1 N, N observation count. print summary methods always reported presence -neighbour observations, listed IDs (region.id values). nb object contains -neighbour observations, user decide whether drop observations, retained, value give weights. zero.policy argument uses zero value TRUE, FALSE causes nb2listw fail. value zero.policy call functions like nb2listw, subset.listw mat2listw creating listw objects representing sparse spatial weights matrices added created object attribute, used subsequently pass choice functions. example, moran.test takes value attribute default zero.policy argument: observation \\(\\) neighbours, weights sum \\(\\sum_{j=1}^N w_{ij} = 0\\), \\(w_{ij} = 0, \\forall j\\) (see discussion Bivand Portnov (2004)). eigenvalue also zero, consequences analytical inference: adjust.n argument measures spatial autocorrelation default TRUE, subtracts count singleton nodes \\(N\\) attempt acknowledge reduction information available. discussion address problems arising analysing areal/lattice data, neighbours defined polygon features contiguous boundaries. One way -neighbour observations may occur islands. clearly case Freni-Sterrantino, Ventrucci, Rue (2018), Capraia Giglio Isles singleton nodes. take Westminster constituencies Wales used July 2024 UK general election. GDAL least version 3.7.0, driver supports compressed GeoPackage files, must decompressed first. boundaries taken Ordnance Survey Boundary-Line site, https://osdatahub.os.uk/downloads/open/BoundaryLine, choosing 2024 Westminster constituencies, simplified using tolerance 50m reduce object size, merged selected voting outcomes constituencies Great Britain https://electionresults.parliament.uk/countries/1, (https://www.nationalarchives.gov.uk/doc/open-government-licence/version/3/). , subset Wales useful see: two subgraphs singleton Ynys Môn 31 constituencies: left map shows Ynys Môn can shown selecting name, black border, zero cardinality neighbour set, using card, filling polygon. right map shows location island, known English Anglesey, north-west Welsh mainland, neighbour links: maps, can see island close two constituencies across Afon Menai (Menai Strait English), three simplified polygons less 280m apart, measured polygon boundaries: Using snap distance 280m, can join island two obvious proximate neighbours: case, increasing snap default 10mm (close equivalents geometries known metrics; previously sqrt(.Machine$double.eps) 1.4901161^{-8} cases) helps. symmetric links added : always going case, strait narrow. islands much offshore, steps may required, large snap distance draw extra neighbours already connected observations. also possible increasing snap distance may fail link islands considered candidate neighbours, extents (bounding boxes), buffered snap value, intersect. can also use distances pick neighbour candidates meet criterion 280m, taking care lose ordering needed identify correct observations: candidates island , two neighbours across Menai Strait: addlinks1 function can used add links Ynys Môn neighbours, symmetry Ynys Môn. approach means island treated separately (scripted sequence), risk adding spurious neighbours denser parts study area. Since constituency observations areal support, surprising changing support points using \\(k\\)-nearest neighbours work adequately, distance measurements points representing polygons rather areal unit boundaries: , Clwyd North, east Bangor Aberconwy, given neighbour Ynys Môn Dwyfor Meirionnydd, west Bangor Aberconwy, . addition, two subgraphs, still remain \\(k=6\\).","code":"library(spdep) ## Loading required package: spData ## To access larger datasets in this package, install the spDataLarge ## package with: `install.packages('spDataLarge', ## repos='https://nowosad.github.io/drat/', type='source')` ## Loading required package: sf ## Linking to GEOS 3.13.0, GDAL 3.10.1, PROJ 9.5.1; sf_use_s2() is TRUE args(moran.test) ## function (x, listw, randomisation = TRUE, zero.policy = attr(listw, ## \"zero.policy\"), alternative = \"greater\", rank = FALSE, na.action = na.fail, ## spChk = NULL, adjust.n = TRUE, drop.EI2 = FALSE) ## NULL eigen(0)$values ## [1] 0 GDAL37 <- numeric_version(unname(sf::sf_extSoftVersion()[\"GDAL\"]), strict=FALSE) (GDAL37 <- ifelse(is.na(GDAL37), FALSE, GDAL37 >= \"3.7.0\")) ## [1] TRUE file <- \"etc/shapes/GB_2024_Wales_50m.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) { w50m <- st_read(zipfile) } else { td <- tempdir() bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE) target <- unzip(zipfile, files=bn, exdir=td) w50m <- st_read(target) } ## Reading layer `GB_2024_Wales_50m' from data source ## `C:\\Users\\rzomor2\\AppData\\Local\\Temp\\RtmpErQTm3\\temp_libpath1a5cde63ff3\\spdep\\etc\\shapes\\GB_2024_Wales_50m.gpkg.zip' ## using driver `GPKG' ## Simple feature collection with 32 features and 19 fields ## Geometry type: MULTIPOLYGON ## Dimension: XY ## Bounding box: xmin: 146597.1 ymin: 164536.5 xmax: 355287 ymax: 395993.5 ## Projected CRS: OSGB36 / British National Grid (nb_W_50m <- poly2nb(w50m, row.names=as.character(w50m$Constituency))) ## Warning in poly2nb(w50m, row.names = as.character(w50m$Constituency)): some observations have no neighbours; ## if this seems unexpected, try increasing the snap argument. ## Warning in poly2nb(w50m, row.names = as.character(w50m$Constituency)): neighbour object has 2 sub-graphs; ## if this sub-graph count seems unexpected, try increasing the snap argument. ## Neighbour list object: ## Number of regions: 32 ## Number of nonzero links: 136 ## Percentage nonzero weights: 13.28125 ## Average number of links: 4.25 ## 1 region with no links: ## Ynys Môn ## 2 disjoint connected subgraphs table(table(attr(nb_W_50m, \"ncomp\")$comp.id)) ## ## 1 31 ## 1 1 ynys_mon <- w50m$Constituency == \"Ynys Môn\" pts <- st_point_on_surface(st_geometry(w50m)) opar <- par(mfrow=c(1, 2)) plot(st_geometry(w50m), border=\"grey75\") plot(st_geometry(w50m)[ynys_mon], add=TRUE) plot(st_geometry(w50m)[card(nb_W_50m) == 0L], add=TRUE, border=\"transparent\", col=\"wheat1\") plot(st_geometry(w50m), border=\"grey75\") plot(nb_W_50m, pts, add=TRUE) par(opar) dym <- c(st_distance(w50m[ynys_mon,], w50m)) sort(dym)[1:12] ## Units: [m] ## [1] 0.0000 123.4132 277.5414 16658.7265 37985.7086 54096.7729 ## [7] 58146.4320 65550.2491 67696.3323 93741.9873 113007.3659 137858.1826 (nb_W_50m_snap <- poly2nb(w50m, row.names=as.character(w50m$Constituency), snap=280)) ## Neighbour list object: ## Number of regions: 32 ## Number of nonzero links: 140 ## Percentage nonzero weights: 13.67188 ## Average number of links: 4.375 plot(st_geometry(w50m), border=\"grey75\") plot(nb_W_50m_snap, pts, add=TRUE) attr(nb_W_50m_snap, \"region.id\")[nb_W_50m_snap[[which(ynys_mon)]]] ## [1] \"Bangor Aberconwy\" \"Dwyfor Meirionnydd\" (meet_criterion <- sum(dym <= units::set_units(280, \"m\"))) ## [1] 3 (cands <- attr(nb_W_50m, \"region.id\")[order(dym)[1:meet_criterion]]) ## [1] \"Ynys Môn\" \"Bangor Aberconwy\" \"Dwyfor Meirionnydd\" (nb_W_50m_add <- addlinks1(nb_W_50m, from = cands[1], to = cands[2:meet_criterion])) ## Neighbour list object: ## Number of regions: 32 ## Number of nonzero links: 140 ## Percentage nonzero weights: 13.67188 ## Average number of links: 4.375 all.equal(nb_W_50m_add, nb_W_50m_snap, check.attributes=FALSE) ## [1] TRUE k2 <- knn2nb(knearneigh(pts, k=2), row.names=as.character(w50m$Constituency), sym=TRUE) ## Warning in knn2nb(knearneigh(pts, k = 2), row.names = ## as.character(w50m$Constituency), : neighbour object has 2 sub-graphs attr(k2, \"region.id\")[k2[[which(ynys_mon)]]] ## [1] \"Bangor Aberconwy\" \"Clwyd North\""},{"path":"https://r-spatial.github.io/spdep/articles/subgraphs.html","id":"subgraphs","dir":"Articles","previous_headings":"","what":"Subgraphs","title":"No-neighbour observation and subgraph handling","text":"Subgraphs may found -neighbour observations present, also graph split two blocks observations path observation block another block, across low population density constituencies mid-Wales: can show block structure displaying binary spatial weights matrix: occurs frequently point support, may also occur areal support, Freni-Sterrantino, Ventrucci, Rue (2018) find eight municipalities island Elba. spdep 1.3-6, igraph spatialreg packages available, n.comp.nb uses igraph::components compute graph components, also using depth-first search. original implementation fast, directed (asymmetric) graphs converts first symmetry, igraph::components can handle directed graphs without conversion (see https://github.com/r-spatial/spdep/issues/160 details). Another case demonstrates cyclical subgraphs may appear; taken constituencies 2024 UK general election, subsetted England south London. second subgraph two members, others’ neighbours, known cyclical component. constituencies Isle Wight: consequences eigenvalues spatial weights matrix, pointed Smirnov Anselin (2009) Bivand, Hauke, Kossowski (2013). row-standardised weights, eigenvalues component : “takes ” lower domain boundary, whole data set now : compared lower domain boundary remainder study area: subgraph may added remainder shown : Using 5km cutoff seems prudent, work snap value. Taking Isle Wight East first, four constituencies boundaries within 5km: Obviously contiguous neighbour among zero distance, needs dropped, although addlinks1 drop duplicate: Although constituencies now linked, see whether using 5km criterion brings extra neighbours Isle Wight West: , , need beware sorting order zero self-distance contiguous neighbour distance, now second position: yields links north-west: remains add suitable generalisation addlinks1 handle vector argument argument taking list vectors.","code":"(k6 <- knn2nb(knearneigh(pts, k=6), row.names=as.character(w50m$Constituency), sym=TRUE)) ## Warning in knn2nb(knearneigh(pts, k = 6), row.names = ## as.character(w50m$Constituency), : neighbour object has 2 sub-graphs ## Neighbour list object: ## Number of regions: 32 ## Number of nonzero links: 238 ## Percentage nonzero weights: 23.24219 ## Average number of links: 7.4375 ## 2 disjoint connected subgraphs plot(st_geometry(w50m), border=\"grey75\") plot(k6, pts, add=TRUE) o <- order(attr(k6, \"ncomp\")$comp.id) image(t(nb2mat(k6, style=\"B\")[o, rev(o)]), axes=FALSE, asp=1) (k6a <- knn2nb(knearneigh(pts, k=6), row.names=as.character(w50m$Constituency))) ## Warning in knn2nb(knearneigh(pts, k = 6), row.names = ## as.character(w50m$Constituency)): neighbour object has 2 sub-graphs ## Neighbour list object: ## Number of regions: 32 ## Number of nonzero links: 192 ## Percentage nonzero weights: 18.75 ## Average number of links: 6 ## 2 disjoint connected subgraphs ## Non-symmetric neighbours list file <- \"etc/shapes/GB_2024_southcoast_50m.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) { sc50m <- st_read(zipfile) } else { td <- tempdir() bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE) target <- unzip(zipfile, files=bn, exdir=td) sc50m <- st_read(target) } ## Reading layer `GB_2024_southcoast_50m' from data source ## `C:\\Users\\rzomor2\\AppData\\Local\\Temp\\RtmpErQTm3\\temp_libpath1a5cde63ff3\\spdep\\etc\\shapes\\GB_2024_southcoast_50m.gpkg.zip' ## using driver `GPKG' ## Simple feature collection with 119 features and 19 fields ## Geometry type: MULTIPOLYGON ## Dimension: XY ## Bounding box: xmin: 82643.12 ymin: 5342.9 xmax: 640301.6 ymax: 187226.2 ## Projected CRS: OSGB36 / British National Grid (nb_sc_50m <- poly2nb(sc50m, row.names=as.character(sc50m$Constituency))) ## Warning in poly2nb(sc50m, row.names = as.character(sc50m$Constituency)): neighbour object has 2 sub-graphs; ## if this sub-graph count seems unexpected, try increasing the snap argument. ## Neighbour list object: ## Number of regions: 119 ## Number of nonzero links: 530 ## Percentage nonzero weights: 3.742674 ## Average number of links: 4.453782 ## 2 disjoint connected subgraphs nc <- attr(nb_sc_50m, \"ncomp\")$comp.id table(nc) ## nc ## 1 2 ## 117 2 (sub2 <- attr(nb_sc_50m, \"region.id\")[nc == 2L]) ## [1] \"Isle of Wight East\" \"Isle of Wight West\" pts <- st_point_on_surface(st_geometry(sc50m)) plot(st_geometry(sc50m), border=\"grey75\") plot(st_geometry(sc50m)[nc == 2L], border=\"orange\", lwd=2, add=TRUE) plot(nb_sc_50m, pts, add=TRUE) 1/range(eigen(cbind(c(0, 1), c(1, 0)))$values) ## [1] -1 1 1/range(eigen(nb2mat(subset(nb_sc_50m, nc == 2L), style=\"W\"))$values) ## [1] -1 1 1/range(eigen(nb2mat(nb_sc_50m, style=\"W\"))$values) ## [1] -1 1 1/range(eigen(nb2mat(subset(nb_sc_50m, nc == 1L), style=\"W\"))$values) ## [1] -1.094637 1.000000 iowe <- match(sub2[1], attr(nb_sc_50m, \"region.id\")) diowe <- c(st_distance(sc50m[iowe,], sc50m)) sort(diowe)[1:12] ## Units: [m] ## [1] 0.000 0.000 1886.833 3509.366 6693.575 6943.672 7678.999 ## [8] 8576.454 10579.530 12163.332 16875.920 17161.786 ioww <- match(sub2[2], attr(nb_sc_50m, \"region.id\")) dioww <- c(st_distance(sc50m[ioww,], sc50m)) sort(dioww)[1:12] ## Units: [m] ## [1] 0.000 0.000 1232.724 2541.318 5746.764 5770.602 8902.579 ## [8] 9747.265 10529.540 10909.845 12250.564 12379.871 (meet_criterion <- sum(diowe <= units::set_units(5000, \"m\"))) ## [1] 4 (cands <- attr(nb_sc_50m, \"region.id\")[order(diowe)[1:meet_criterion]]) ## [1] \"Isle of Wight East\" \"Isle of Wight West\" \"Portsmouth South\" ## [4] \"Gosport\" (nb_sc_50m_iowe <- addlinks1(nb_sc_50m, from = cands[1], to = cands[3:meet_criterion])) ## Neighbour list object: ## Number of regions: 119 ## Number of nonzero links: 534 ## Percentage nonzero weights: 3.77092 ## Average number of links: 4.487395 (meet_criterion <- sum(dioww <= units::set_units(5000, \"m\"))) ## [1] 4 (cands <- attr(nb_sc_50m, \"region.id\")[order(dioww)[1:meet_criterion]]) ## [1] \"Isle of Wight East\" \"Isle of Wight West\" \"New Forest West\" ## [4] \"New Forest East\" (nb_sc_50m_iow <- addlinks1(nb_sc_50m_iowe, from = cands[2], to = cands[3:meet_criterion])) ## Neighbour list object: ## Number of regions: 119 ## Number of nonzero links: 538 ## Percentage nonzero weights: 3.799167 ## Average number of links: 4.521008 pts <- st_point_on_surface(st_geometry(sc50m)) plot(st_geometry(sc50m), border=\"grey75\") plot(st_geometry(sc50m)[nc == 2L], border=\"orange\", lwd=2, add=TRUE) plot(nb_sc_50m_iow, pts, add=TRUE)"},{"path":"https://r-spatial.github.io/spdep/articles/subgraphs.html","id":"per-session-control-of-function-behaviour","dir":"Articles","previous_headings":"","what":"Per-session control of function behaviour","title":"No-neighbour observation and subgraph handling","text":"early , default value zero.policy argument many methods functions NULL. value NULL, zero.policy set get.ZeroPolicyOption: loading spdep, internal option set FALSE, functions methods using zero.policy need choose handle islands: case, shown island may reasonably associated proximate constituencies mainland. , however, user wishes override default, set.ZeroPolicyOption may used set different per-session default: listw object created zero.policy set TRUE, choice added output object attribute applied object used (unless specifically overridden). Note also 32 constituencies, observation count reported spweights.constants called print method listw object argument adjust.n TRUE, dropping -neighbour observations observation count. internal options introduced suppress -neighbour subgraph warnings creating nb objects. default values follows: get.NoNeighbourOption controls issuing warnings nb objects created -neighbour observations; get.SubgraphOption works similarly warnings issued one graph component; TRUE default. get.SubgraphCeiling sets integer value graph nodes plus graph edges calculating graph considered costly compute time, default 100,000. corresponds dense neighbour set just 300 nodes (almost 100000 edges) needed use inverse distance weights, just 14,000 nodes average neighbour count 6. print method nb objects reports -neighbour subgraph status anyway, careful users always examine generated objects may prefer supress warnings, warnings seem prudent users may examine objects, generation subsetting larger objects, example creation training test data sets. Welsh constituency boundaries used show behaviour internal options: Turning removes warnings: get.SubgraphOption FALSE, attribute containing output n.comp.nb added: reduction ceiling node count 32 plus edge count 136 also supresses calculation graph components: Restoring remaining default values:","code":"get.ZeroPolicyOption() ## [1] FALSE try(nb2listw(nb_W_50m)) ## Error in nb2listw(nb_W_50m) : ## Empty neighbour sets found (zero.policy: FALSE) set.ZeroPolicyOption(TRUE) get.ZeroPolicyOption() ## [1] TRUE (lw <- nb2listw(nb_W_50m)) ## Characteristics of weights list object: ## Neighbour list object: ## Number of regions: 32 ## Number of nonzero links: 136 ## Percentage nonzero weights: 13.28125 ## Average number of links: 4.25 ## 1 region with no links: ## Ynys Môn ## 2 disjoint connected subgraphs ## ## Weights style: W ## Weights constants summary: ## n nn S0 S1 S2 ## W 31 961 31 15.36355 129.051 attr(lw, \"zero.policy\") ## [1] TRUE set.ZeroPolicyOption(FALSE) get.NoNeighbourOption() ## [1] TRUE get.SubgraphOption() ## [1] TRUE get.SubgraphCeiling() ## [1] 100000 set.NoNeighbourOption(FALSE) (nb_W_50mz <- poly2nb(w50m, row.names=as.character(w50m$Constituency))) ## Warning in poly2nb(w50m, row.names = as.character(w50m$Constituency)): neighbour object has 2 sub-graphs; ## if this sub-graph count seems unexpected, try increasing the snap argument. ## Neighbour list object: ## Number of regions: 32 ## Number of nonzero links: 136 ## Percentage nonzero weights: 13.28125 ## Average number of links: 4.25 ## 1 region with no links: ## Ynys Môn ## 2 disjoint connected subgraphs set.SubgraphOption(FALSE) (nb_W_50my <- poly2nb(w50m, row.names=as.character(w50m$Constituency))) ## Neighbour list object: ## Number of regions: 32 ## Number of nonzero links: 136 ## Percentage nonzero weights: 13.28125 ## Average number of links: 4.25 ## 1 region with no links: ## Ynys Môn str(attr(nb_W_50my, \"ncomp\")) ## NULL set.SubgraphOption(TRUE) set.SubgraphCeiling(100L) (nb_W_50mx <- poly2nb(w50m, row.names=as.character(w50m$Constituency))) ## Neighbour list object: ## Number of regions: 32 ## Number of nonzero links: 136 ## Percentage nonzero weights: 13.28125 ## Average number of links: 4.25 ## 1 region with no links: ## Ynys Môn str(attr(nb_W_50mx, \"ncomp\")) ## NULL set.SubgraphCeiling(100000L) set.NoNeighbourOption(TRUE)"},{"path":"https://r-spatial.github.io/spdep/articles/subgraphs.html","id":"unintentional-disconnected-graphs","dir":"Articles","previous_headings":"","what":"Unintentional disconnected graphs","title":"No-neighbour observation and subgraph handling","text":"Sometimes apparently sensible polygons turn represented way disconnected graphs generated extracting contiguities. One case raised https://github.com/r-spatial/spdep/issues/162, subdivisions Tokyo. original data file tokyomet262.* https://sgsup.asu.edu/sites/g/files/litvpz426/files/SparcFiles/tokyo_0.zip created twenty years ago Tomoki Nakaya Martin Charlton, geometry issues known time. possibility may affect legacy files projection geometries 32-bit platforms, known whether affected file. re-packaged compressed GeoPackage: correcting invalid polygons: applying poly2nb legacy default snap value produced numerous singleton observations well many multiple-observation subgraphs: legacy default snap value coordinates measured metres 15 nanometres, effectively assumed coordinates making polygon boundaries identical: Stepping little 2mm, lack contact ceased problem. basis, default changed spdep 1.3-6 10mm projected polygons, snap value used returned attribute neighbour object: polygons represented geographical (spherical) coordinates, new default spdep 1.3-6 set value mimicking 10mm: default snap value used poly2nb polygons expressed decimal degrees : set based apparent “size” 10mm decimal degrees:","code":"file <- \"etc/shapes/tokyo.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) { tokyo <- st_read(zipfile) } else { td <- tempdir() bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE) target <- unzip(zipfile, files=bn, exdir=td) tokyo <- st_read(target) } ## Reading layer `tokyo' from data source ## `C:\\Users\\rzomor2\\AppData\\Local\\Temp\\RtmpErQTm3\\temp_libpath1a5cde63ff3\\spdep\\etc\\shapes\\tokyo.gpkg.zip' ## using driver `GPKG' ## Simple feature collection with 262 features and 3 fields ## Geometry type: MULTIPOLYGON ## Dimension: XY ## Bounding box: xmin: 266206.6 ymin: -90932.11 xmax: 411400.3 ymax: 37142.75 ## Projected CRS: Tokyo / Japan Plane Rectangular CS VI all(st_is_valid(tokyo)) ## [1] TRUE tokyo <- st_make_valid(tokyo) (nb_t0 <- poly2nb(tokyo, snap=sqrt(.Machine$double.eps))) ## Warning in poly2nb(tokyo, snap = sqrt(.Machine$double.eps)): some observations have no neighbours; ## if this seems unexpected, try increasing the snap argument. ## Warning in poly2nb(tokyo, snap = sqrt(.Machine$double.eps)): neighbour object has 23 sub-graphs; ## if this sub-graph count seems unexpected, try increasing the snap argument. ## Neighbour list object: ## Number of regions: 262 ## Number of nonzero links: 946 ## Percentage nonzero weights: 1.378125 ## Average number of links: 3.610687 ## 10 regions with no links: ## 101, 127, 134, 135, 152, 154, 167, 237, 242, 243 ## 23 disjoint connected subgraphs units::set_units(units::set_units(attr(nb_t0, \"snap\"), \"m\"), \"nm\") ## 14.90116 [nm] (nb_t1 <- poly2nb(tokyo, snap=0.002)) ## Neighbour list object: ## Number of regions: 262 ## Number of nonzero links: 1390 ## Percentage nonzero weights: 2.02494 ## Average number of links: 5.305344 units::set_units(units::set_units(attr(nb_t1, \"snap\"), \"m\"), \"mm\") ## 2 [mm] (nb_t2 <- poly2nb(tokyo)) ## Neighbour list object: ## Number of regions: 262 ## Number of nonzero links: 1390 ## Percentage nonzero weights: 2.02494 ## Average number of links: 5.305344 units::set_units(units::set_units(attr(nb_t2, \"snap\"), \"m\"), \"mm\") ## 10 [mm] (nb_t3 <- poly2nb(st_transform(tokyo, \"OGC:CRS84\"))) ## Neighbour list object: ## Number of regions: 262 ## Number of nonzero links: 1336 ## Percentage nonzero weights: 1.946274 ## Average number of links: 5.099237 attr(nb_t3, \"snap\") ## [1] 9e-08 (180 * 0.01) / (pi * 6378137) ## [1] 8.983153e-08"},{"path":[]},{"path":"https://r-spatial.github.io/spdep/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Roger Bivand. Maintainer, author. Micah Altman. Contributor. Luc Anselin. Contributor. Renato Assunção. Contributor. Anil Bera. Contributor. Olaf Berke. Contributor. F. Guillaume Blanchet. Contributor. Marilia Carvalho. Contributor. Bjarke Christensen. Contributor. Yongwan Chun. Contributor. Carsten Dormann. Contributor. Stéphane Dray. Contributor. Dewey Dunnington. Contributor. Virgilio Gómez-Rubio. Contributor. Malabika Koley. Contributor. Tomasz Kossowski. Contributor. Elias Krainski. Contributor. Pierre Legendre. Contributor. Nicholas Lewin-Koh. Contributor. Angela Li. Contributor. Giovanni Millo. Contributor. Werner Mueller. Contributor. Hisaji Ono. Contributor. Josiah Parry. Contributor. Pedro Peres-Neto. Contributor. Michał Pietrzak. Contributor. Gianfranco Piras. Contributor. Markus Reder. Contributor. Jeff Sauer. Contributor. Michael Tiefelsdorf. Contributor. René Westerholt. Contributor. Justyna Wilk. Contributor. Levi Wolf. Contributor. Danlin Yu. Contributor.","code":""},{"path":"https://r-spatial.github.io/spdep/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Bivand R, Wong D (2018). “Comparing implementations global local indicators spatial association.” TEST, 27(3), 716–748. doi:10.1007/s11749-018-0599-x. Roger Bivand (2022). “R Packages Analyzing Spatial Data: Comparative Case Study Areal Data.” Geographical Analysis, 54(3), 488-518. doi:10.1111/gean.12319. Bivand R, Pebesma E, Gómez-Rubio V (2013). Applied spatial data analysis R, Second edition. Springer, NY. https://asdar-book.org/. Pebesma E, Bivand R (2023). Spatial Data Science Applications R. Chapman & Hall. https://r-spatial.org/book/.","code":"@Article{, author = {Roger Bivand and David W. S. Wong}, title = {Comparing implementations of global and local indicators of spatial association}, journal = {TEST}, year = {2018}, volume = {27}, number = {3}, pages = {716--748}, doi = {10.1007/s11749-018-0599-x}, } @Article{, author = {{Roger Bivand}}, title = {R Packages for Analyzing Spatial Data: A Comparative Case Study with Areal Data}, journal = {Geographical Analysis}, year = {2022}, volume = {54}, number = {3}, pages = {488-518}, doi = {10.1111/gean.12319}, } @Book{, author = {Roger S. Bivand and Edzer Pebesma and Virgilio Gómez-Rubio}, title = {Applied spatial data analysis with {R}, Second edition}, year = {2013}, publisher = {Springer, NY}, url = {https://asdar-book.org/}, } @Book{, author = {Edzer Pebesma and Roger S. Bivand}, title = {Spatial Data Science With Applications in {R}}, year = {2023}, publisher = {Chapman & Hall}, url = {https://r-spatial.org/book/}, }"},{"path":[]},{"path":"https://r-spatial.github.io/spdep/index.html","id":"spatial-dependence-weighting-schemes-and-statistics","dir":"","previous_headings":"","what":"Spatial Dependence: Weighting Schemes and Statistics","title":"Spatial Dependence: Weighting Schemes, Statistics","text":"collection functions create spatial weights matrix objects polygon contiguities, point patterns distance tessellations, summarizing objects, permitting use spatial data analysis, including regional aggregation minimum spanning tree; collection tests spatial autocorrelation, including global Morans Gearys C proposed Cliff Ord (1973, ISBN: 0850860369) (1981, ISBN: 0850860814), Hubert/Mantel general cross product statistic, Empirical Bayes estimates Assunção/Reis (1999) (https://doi.org/10.1002/(SICI)1097-0258(19990830)18:16%3C2147%3A%3AAID-SIM179%3E3.0.CO%3B2-) Index, Getis/Ord G (Getis Ord 1992) (https://doi.org/10.1111/j.1538-4632.1992.tb00261.x) multicoloured join count statistics, APLE (Li et al. ) (https://doi.org/10.1111/j.1538-4632.2007.00708.x), local Morans (Anselin 1995) (https://doi.org/10.1111/j.1538-4632.1995.tb00338.x) Getis/Ord G (Ord Getis 1995) (https://doi.org/10.1111/j.1538-4632.1995.tb00912.x), saddlepoint approximations (Tiefelsdorf 2002) (https://doi.org/10.1111/j.1538-4632.2002.tb01084.x) exact tests global local Morans (Bivand et al. 2009) (https://doi.org/10.1016/j.csda.2008.07.021) LOSH local indicators spatial heteroscedasticity (Ord Getis) (https://doi.org/10.1007/s00168-011-0492-y), extensions Bivand (2022) doi:10.1111/gean.12319. implementation measures described Bivand Wong (2018) (https://doi.org/10.1007/s11749-018-0599-x). Extra measures contributed Josiah Parry. Lagrange multiplier tests spatial dependence linear models provided (Anselin et al. 1996) (https://doi.org/10.1016/0166-0462(95)02111-6), Rao’s score tests hypothesised spatial Durbin models based fitted linear models (Koley Bera 2024) (https://doi.org/10.1080/17421772.2023.2256810). local indicators categorical data (LICD) implementation based Carrer et al. (2021) (https://doi.org/10.1016/j.jas.2020.105306) Bivand et al. (2017) (https://doi.org/10.1016/j.spasta.2017.03.003) added 1.3-7. Multivariate spatialdelta (Bavaud 2024) (https://doi.org/10.1111/gean.12390) added 1.3-13. sfdep (https://cran.r-project.org/package=sfdep) provides piped interface spdep. spdep spatialreg versions >= 1.2-1, model fitting functions previously present package defunct spdep may found spatialreg. Default branch now main Moved R-Forge","code":""},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Aggregate a spatial neighbours object — aggregate.nb","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"method aggregates spatial neighbours object, creating new object listing neighbours aggregates.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"","code":"# S3 method for class 'nb' aggregate(x, IDs, remove.self = TRUE, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"x nb neighbour object IDs character vector IDs grouping members neighbour object remove.self default TRUE: remove self-neighbours resulting aggregation ... unused - arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"nb neighbour object, empty aggregates dropped.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"Method suggested Roberto Patuelli","code":""},{"path":"https://r-spatial.github.io/spdep/reference/aggregate.nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Aggregate a spatial neighbours object — aggregate.nb","text":"","code":"data(used.cars, package=\"spData\") data(state) cont_st <- match(attr(usa48.nb, \"region.id\"), state.abb) cents <- as.matrix(as.data.frame(state.center))[cont_st,] opar <- par(mfrow=c(2,1)) plot(usa48.nb, cents, xlim=c(-125, -65), ylim=c(25, 50)) IDs <- as.character(state.division[cont_st]) agg_cents <- aggregate(cents, list(IDs), mean) agg_nb <- aggregate(usa48.nb, IDs) plot(agg_nb, agg_cents[, 2:3], xlim=c(-125, -65), ylim=c(25, 50)) text(agg_cents[, 2:3], agg_cents[, 1], cex=0.6) par(opar)"},{"path":"https://r-spatial.github.io/spdep/reference/airdist.html","id":null,"dir":"Reference","previous_headings":"","what":"Measure distance from plot — airdist","title":"Measure distance from plot — airdist","text":"Measure distance two points plot using locator; function checks par(\"plt\") par(\"usr\") try ensure aspect ratio y/x 1, units measurement x y equivalent.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/airdist.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Measure distance from plot — airdist","text":"","code":"airdist(ann=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/airdist.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Measure distance from plot — airdist","text":"ann annotate plot line measured distance","code":""},{"path":"https://r-spatial.github.io/spdep/reference/airdist.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Measure distance from plot — airdist","text":"list members: dist distance measured coords coordinates distance measured","code":""},{"path":"https://r-spatial.github.io/spdep/reference/airdist.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Measure distance from plot — airdist","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":null,"dir":"Reference","previous_headings":"","what":"Distance-weighted autocovariate — autocov_dist","title":"Distance-weighted autocovariate — autocov_dist","text":"Calculates autocovariate used autonormal, autopoisson autologistic regression. Three distance-weighting schemes available.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Distance-weighted autocovariate — autocov_dist","text":"","code":"autocov_dist(z, xy, nbs = 1, type = \"inverse\", zero.policy = NULL, style = \"B\", longlat=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Distance-weighted autocovariate — autocov_dist","text":"z response variable xy matrix coordinates SpatialPoints, sf sfc points object nbs neighbourhood radius; default 1 type weighting scheme: \"one\" gives equal weight data points neighbourhood; \"inverse\" (default) weights inverse distance; \"inverse.squared\" weights square \"inverse\" zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors style default “B” (changed “W” 2015-01-27); style can take values “W”, “B”, “C”, “U”, “S” longlat TRUE point coordinates longitude-latitude decimal, case distances measured kilometers; xy SpatialPoints object, value taken object ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Distance-weighted autocovariate — autocov_dist","text":"numeric vector autocovariate values","code":""},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Distance-weighted autocovariate — autocov_dist","text":"validity approach strongly hinges correct choice neighbourhood scheme! Using style=\"B\" ensures symmetry neighbourhood matrix (.e. \\(w_{nm} = w_{mn}\\)). Please see Bardos et al. (2015) details.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Distance-weighted autocovariate — autocov_dist","text":"Augustin N.H., Mugglestone M.. Buckland S.T. (1996) autologistic model spatial distribution wildlife. Journal Applied Ecology, 33, 339-347; Gumpertz M.L., Graham J.M. Ristaino J.B. (1997) Autologistic model spatial pattern Phytophthora epidemic bell pepper: effects soil variables disease presence. Journal Agricultural, Biological Environmental Statistics, 2, 131-156; Bardos, D.C., Guillera-Arroita, G. Wintle, B.. (2015) Valid auto-models spatially autocorrelated occupancy abundance data. arXiv, 1501.06529.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Distance-weighted autocovariate — autocov_dist","text":"Carsten F. Dormann Roger Bivand","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/autocov_dist.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Distance-weighted autocovariate — autocov_dist","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) #xy <- cbind(columbus$X, columbus$Y) xy <- st_coordinates(st_centroid(st_geometry(columbus), of_largest_polygon=TRUE)) ac1a <- autocov_dist(columbus$CRIME, xy, nbs=10, style=\"B\", type=\"one\") acinva <- autocov_dist(columbus$CRIME, xy, nbs=10, style=\"B\", type=\"inverse\") acinv2a <- autocov_dist(columbus$CRIME, xy, nbs=10, style=\"B\", type=\"inverse.squared\") plot(ac1a ~ columbus$CRIME, pch=16, ylim=c(0,9000)) points(acinva ~ columbus$CRIME, pch=16, col=\"red\") points(acinv2a ~ columbus$CRIME, pch=16, col=\"blue\") legend(\"topleft\", legend=c(\"one\", \"inverse\", \"inverse.squared\"), col=c(\"black\", \"red\", \"blue\"), bty=\"n\", pch=16) nb <- dnearneigh(xy, 0, 10) lw <- nb2listw(nb, style=\"B\") ac1b <- lag(lw, columbus$CRIME) all.equal(ac1b, ac1a) #> [1] TRUE nbd <- nbdists(nb, xy) gl <- lapply(nbd, function(x) 1/x) lw <- nb2listw(nb, glist=gl, style=\"B\") acinvb <- lag(lw, columbus$CRIME) all.equal(acinvb, acinva) #> [1] TRUE gl2 <- lapply(nbd, function(x) 1/(x^2)) lw <- nb2listw(nb, glist=gl2, style=\"B\") acinv2b <- lag(lw, columbus$CRIME) all.equal(acinv2b, acinv2a) #> [1] TRUE #xy <- SpatialPoints(xy) #acinva <- autocov_dist(columbus$CRIME, xy, nbs=10, style=\"W\", # type=\"inverse\") #nb <- dnearneigh(xy, 0, 10) #nbd <- nbdists(nb, xy) #gl <- lapply(nbd, function(x) 1/x) #lw <- nb2listw(nb, glist=gl) #acinvb <- lag(lw, columbus$CRIME) #all.equal(acinvb, acinva) acinvc <- autocov_dist(columbus$CRIME, st_centroid(st_geometry(columbus), of_largest_polygon=TRUE), nbs=10, style=\"W\", type=\"inverse\") all.equal(acinvc, acinva) #> [1] \"Mean relative difference: 40.63575\""},{"path":"https://r-spatial.github.io/spdep/reference/bhicv.html","id":null,"dir":"Reference","previous_headings":"","what":"Data set with 4 life condition indices of Belo Horizonte region — bhicv","title":"Data set with 4 life condition indices of Belo Horizonte region — bhicv","text":"data collected inthe Atlas condition indices published Joao Pinheiro Foundation UNDP.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/bhicv.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Data set with 4 life condition indices of Belo Horizonte region — bhicv","text":"shape polygon object seven variables: id identificator Name Name city Population population city HLCI Health Life Condition Index ELCI Education Life Condition Index CLCI Children Life Condition Index ELCI Economic Life Condition Index","code":""},{"path":"https://r-spatial.github.io/spdep/reference/bhicv.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Data set with 4 life condition indices of Belo Horizonte region — bhicv","text":"","code":"GDAL37 <- numeric_version(unname(sf::sf_extSoftVersion()[\"GDAL\"]), strict=FALSE) (GDAL37 <- ifelse(is.na(GDAL37), FALSE, GDAL37 >= \"3.7.0\")) #> [1] TRUE file <- \"etc/shapes/bhicv.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) { bh <- st_read(zipfile) } else { td <- tempdir() bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE) target <- unzip(zipfile, files=bn, exdir=td) bh <- st_read(target) } #> Reading layer `bhicv' from data source #> `C:\\Users\\rzomor2\\AppData\\Local\\Temp\\RtmpErQTm3\\temp_libpath1a5cde63ff3\\spdep\\etc\\shapes\\bhicv.gpkg.zip' #> using driver `GPKG' #> Simple feature collection with 98 features and 8 fields #> Geometry type: POLYGON #> Dimension: XY #> Bounding box: xmin: -45.02175 ymin: -20.93007 xmax: -42.50321 ymax: -18.08342 #> Geodetic CRS: Corrego Alegre 1970-72"},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":null,"dir":"Reference","previous_headings":"","what":"Cardinalities for neighbours lists — card","title":"Cardinalities for neighbours lists — card","text":"function tallies numbers neighbours regions neighbours list.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Cardinalities for neighbours lists — card","text":"","code":"card(nb)"},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Cardinalities for neighbours lists — card","text":"nb neighbours list object class nb","code":""},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Cardinalities for neighbours lists — card","text":"integer vector numbers neighbours regions neighbours list.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Cardinalities for neighbours lists — card","text":"“nb” objects stored lists integer vectors, vectors contain either indices range 1:n n length(nb) neighbours region , .integer(0) signal neighbours. function card(nb) used extract numbers neighbours “nb” object.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Cardinalities for neighbours lists — card","text":"Bivand R, Pebesma EJ, Gomez-Rubio V, (2008) Applied Spatial Data Analysis R, Springer, New York, pp. 239-251; Bivand R, Portnov B, (2004) Exploring spatial data analysis techniques using R: case observations neighbours. : Anselin L, Florax R, Rey S, (eds.), Advances Spatial Econometrics, Methodology, Tools Applications. Berlin: Springer-Verlag, pp. 121-142, doi:10.1007/978-3-662-05617-2_6 .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Cardinalities for neighbours lists — card","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/card.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Cardinalities for neighbours lists — card","text":"","code":"col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) table(card(col.gal.nb)) #> #> 2 3 4 5 6 7 8 9 10 #> 7 7 13 4 9 6 1 1 1"},{"path":"https://r-spatial.github.io/spdep/reference/cell2nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Generate neighbours list for grid cells — cell2nb","title":"Generate neighbours list for grid cells — cell2nb","text":"function generates list neighbours grid cells. Helper functions used convert vector indices row column grid positions, rook (shared edge) queen (shared edge vertex) neighbour definitions applied type. torus TRUE, grid mapped onto torus, removing edge effects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/cell2nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generate neighbours list for grid cells — cell2nb","text":"","code":"cell2nb(nrow, ncol, type=\"rook\", torus=FALSE, legacy=FALSE, x=NULL) vi2mrc(i, nrow, ncol)"},{"path":"https://r-spatial.github.io/spdep/reference/cell2nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Generate neighbours list for grid cells — cell2nb","text":"nrow number rows grid, may also object inheriting class \"SpatialGrid\" \"GridTopology\" cell2nb ncol number columns grid; nrow x object inheriting class \"SpatialGrid\" \"GridTopology\", may omitted type default rook, may also queen torus default FALSE, TRUE map grid onto torus legacy default FALSE, nrow/ncol reversed, TRUE wrong col/row directions (see https://github.com/r-spatial/spdep/issues/20) x given, object inheriting class \"SpatialGrid\" \"GridTopology\", replaces nrow ncol vector vector indices corresponding rowcol, matrix two columns row, column indices","code":""},{"path":"https://r-spatial.github.io/spdep/reference/cell2nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Generate neighbours list for grid cells — cell2nb","text":"function returns object class nb list integer vectors containing neighbour region number ids. See card details “nb” objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/cell2nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Generate neighbours list for grid cells — cell2nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/cell2nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Generate neighbours list for grid cells — cell2nb","text":"","code":"nb7rt <- cell2nb(7, 7) summary(nb7rt) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 168 #> Percentage nonzero weights: 6.997085 #> Average number of links: 3.428571 #> Link number distribution: #> #> 2 3 4 #> 4 20 25 #> 4 least connected regions: #> 1:1 7:1 1:7 7:7 with 2 links #> 25 most connected regions: #> 2:2 3:2 4:2 5:2 6:2 2:3 3:3 4:3 5:3 6:3 2:4 3:4 4:4 5:4 6:4 2:5 3:5 4:5 5:5 6:5 2:6 3:6 4:6 5:6 6:6 with 4 links xyc <- attr(nb7rt, \"region.id\") xy <- matrix(as.integer(unlist(strsplit(xyc, \":\"))), ncol=2, byrow=TRUE) plot(nb7rt, xy) nb7rt <- cell2nb(7, 7, torus=TRUE) summary(nb7rt) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 196 #> Percentage nonzero weights: 8.163265 #> Average number of links: 4 #> Link number distribution: #> #> 4 #> 49 #> 49 least connected regions: #> 1:1 2:1 3:1 4:1 5:1 6:1 7:1 1:2 2:2 3:2 4:2 5:2 6:2 7:2 1:3 2:3 3:3 4:3 5:3 6:3 7:3 1:4 2:4 3:4 4:4 5:4 6:4 7:4 1:5 2:5 3:5 4:5 5:5 6:5 7:5 1:6 2:6 3:6 4:6 5:6 6:6 7:6 1:7 2:7 3:7 4:7 5:7 6:7 7:7 with 4 links #> 49 most connected regions: #> 1:1 2:1 3:1 4:1 5:1 6:1 7:1 1:2 2:2 3:2 4:2 5:2 6:2 7:2 1:3 2:3 3:3 4:3 5:3 6:3 7:3 1:4 2:4 3:4 4:4 5:4 6:4 7:4 1:5 2:5 3:5 4:5 5:5 6:5 7:5 1:6 2:6 3:6 4:6 5:6 6:6 7:6 1:7 2:7 3:7 4:7 5:7 6:7 7:7 with 4 links run <- FALSE if (require(\"sp\", quietly=TRUE)) run <- TRUE if (run) { # https://github.com/r-spatial/spdep/issues/20 GT <- GridTopology(c(1, 1), c(1, 1), c(10, 50)) SPix <- as(SpatialGrid(GT), \"SpatialPixels\") nb_rook_cont <- poly2nb(as(SPix, \"SpatialPolygons\"), queen=FALSE) nb_rook_dist <- dnearneigh(coordinates(SPix), 0, 1.01) all.equal(nb_rook_cont, nb_rook_dist, check.attributes=FALSE) ## [1] TRUE } #> [1] TRUE if (run) { t.nb <- cell2nb(GT, type='rook', legacy=TRUE) isTRUE(all.equal(nb_rook_cont, t.nb, check.attributes=FALSE)) ## [1] FALSE } #> [1] FALSE if (run) { t.nb <- cell2nb(GT, type='rook') isTRUE(all.equal(nb_rook_cont, t.nb, check.attributes=FALSE)) ## [1] TRUE } #> [1] TRUE if (run) { # https://github.com/r-spatial/spdep/issues/55 # problem reported in issue caused by rep() cycling in unexpected order GT <- GridTopology(c(1, 1), c(1, 1), c(22, 11)) SPix <- as(SpatialGrid(GT), \"SpatialPixels\") nb_rook_cont <- poly2nb(as(SPix, \"SpatialPolygons\"), queen=FALSE) nb_rook_dist <- dnearneigh(coordinates(SPix), 0, 1.01) all.equal(nb_rook_cont, nb_rook_dist, check.attributes=FALSE) } #> [1] TRUE if (run) { t.nb <- cell2nb(GT, type='rook', legacy=TRUE) isTRUE(all.equal(nb_rook_cont, t.nb, check.attributes=FALSE)) ## [1] FALSE } #> [1] FALSE if (run) { t.nb <- cell2nb(GT, type='rook', legacy=FALSE) isTRUE(all.equal(nb_rook_cont, t.nb, check.attributes=FALSE)) ## [1] TRUE } #> [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":null,"dir":"Reference","previous_headings":"","what":"Choynowski probability map values — choynowski","title":"Choynowski probability map values — choynowski","text":"Calculates Choynowski probability map values.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Choynowski probability map values — choynowski","text":"","code":"choynowski(n, x, row.names=NULL, tol = .Machine$double.eps^0.5, legacy=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Choynowski probability map values — choynowski","text":"n numeric vector counts cases x numeric vector populations risk row.names row names passed output data frame tol accumulate values observed counts >= expected value less tol legacy default FALSE using vectorised alternating side ppois version, true use original version written sources iterating tol","code":""},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Choynowski probability map values — choynowski","text":"data frame columns: pmap Poisson probability map values: probablility getting “extreme” count actually observed, one-tailed less expected expected folded together type logical: TRUE observed count less expected","code":""},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Choynowski probability map values — choynowski","text":"Choynowski, M (1959) Maps based probabilities, Journal American Statistical Association, 54, 385–388; Cressie, N, Read, TRC (1985), sudden infant deaths come clusters? Statistics Decisions, Supplement Issue 2, 333–349; Bailey T, Gatrell (1995) Interactive Spatial Data Analysis, Harlow: Longman, pp. 300–303.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Choynowski probability map values — choynowski","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/choynowski.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Choynowski probability map values — choynowski","text":"","code":"auckland <- st_read(system.file(\"shapes/auckland.gpkg\", package=\"spData\")[1], quiet=TRUE) auckland.nb <- poly2nb(auckland) res <- choynowski(auckland$M77_85, 9*auckland$Und5_81) resl <- choynowski(auckland$M77_85, 9*auckland$Und5_81, legacy=TRUE) all.equal(res, resl) #> [1] TRUE rt <- sum(auckland$M77_85)/sum(9*auckland$Und5_81) ch_ppois_pmap <- numeric(length(auckland$Und5_81)) side <- c(\"greater\", \"less\") for (i in seq(along=ch_ppois_pmap)) { ch_ppois_pmap[i] <- poisson.test(auckland$M77_85[i], r=rt, T=(9*auckland$Und5_81[i]), alternative=side[(res$type[i]+1)])$p.value } all.equal(ch_ppois_pmap, res$pmap) #> [1] TRUE res1 <- probmap(auckland$M77_85, 9*auckland$Und5_81) table(abs(res$pmap - res1$pmap) < 0.00001, res$type) #> #> FALSE TRUE #> FALSE 74 0 #> TRUE 0 93 lt005 <- (res$pmap < 0.05) & (res$type) ge005 <- (res$pmap < 0.05) & (!res$type) cols <- rep(\"nonsig\", length(lt005)) cols[lt005] <- \"low\" cols[ge005] <- \"high\" auckland$cols <- factor(cols) plot(auckland[,\"cols\"], main=\"Probability map\")"},{"path":"https://r-spatial.github.io/spdep/reference/COL.OLD.html","id":null,"dir":"Reference","previous_headings":"","what":"Columbus OH spatial analysis data set - old numbering — oldcol","title":"Columbus OH spatial analysis data set - old numbering — oldcol","text":"COL.OLD data frame 49 rows 22 columns. observations ordered numbered original analyses data set SpaceStat documentation Anselin, L. 1988 Spatial econometrics: methods models, Dordrecht: Kluwer. Unit analysis: 49 neighbourhoods Columbus, OH, 1980 data. addition data set includes COL.nb, neighbours list used Anselin (1988).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/COL.OLD.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Columbus OH spatial analysis data set - old numbering — oldcol","text":"","code":"data(oldcol)"},{"path":"https://r-spatial.github.io/spdep/reference/COL.OLD.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Columbus OH spatial analysis data set - old numbering — oldcol","text":"data frame contains following columns: AREA_PL computed ArcView (agrees areas polygons “columbus” data set PERIMETER computed ArcView COLUMBUS. internal polygon ID (ignore) COLUMBUS.another internal polygon ID (ignore) POLYID yet another polygon ID NEIG neighborhood id value (1-49); conforms id value used Spatial Econometrics book. HOVAL housing value ($1,000) INC household income ($1,000) CRIME residential burglaries vehicle thefts per thousand households neighborhood OPEN open space neighborhood PLUMB percentage housing units without plumbin DISCBD distance CBD X x coordinate (arbitrary digitizing units, polygon coordinates) Y y coordinate (arbitrary digitizing units, polygon coordinates) AREA_SS neighborhood area (computed SpaceStat) NSA north-south dummy (North=1) NSB north-south dummy (North=1) EW east-west dummy (East=1) CP core-periphery dummy (Core=1) THOUS constant=1,000 NEIGNO NEIG+1,000, alternative neighborhood id value PERIM polygon perimeter (computed SpaceStat)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/COL.OLD.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Columbus OH spatial analysis data set - old numbering — oldcol","text":"row names COL.OLD region.id attribute COL.nb set columbus$NEIGNO.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/COL.OLD.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Columbus OH spatial analysis data set - old numbering — oldcol","text":"Anselin, Luc. 1988. Spatial econometrics: methods models. Dordrecht: Kluwer Academic, Table 12.1 p. 189.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/COL.OLD.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Columbus OH spatial analysis data set - old numbering — oldcol","text":"source data files prepared Luc Anselin, Spatial Analysis Laboratory, Department Agricultural Consumer Economics, University Illinois, Urbana-Champaign.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/columbus.html","id":null,"dir":"Reference","previous_headings":"","what":"Columbus OH spatial analysis data set — columbus","title":"Columbus OH spatial analysis data set — columbus","text":"data set now part spData package","code":""},{"path":"https://r-spatial.github.io/spdep/reference/columbus.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Columbus OH spatial analysis data set — columbus","text":"","code":"data(columbus)"},{"path":"https://r-spatial.github.io/spdep/reference/columbus.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Columbus OH spatial analysis data set — columbus","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1])"},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":null,"dir":"Reference","previous_headings":"","what":"Depth First Search on Neighbor Lists — Graph Components","title":"Depth First Search on Neighbor Lists — Graph Components","text":"n.comp.nb() finds number disjoint connected subgraphs graph depicted nb.obj - spatial neighbours list object.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Depth First Search on Neighbor Lists — Graph Components","text":"","code":"n.comp.nb(nb.obj)"},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Depth First Search on Neighbor Lists — Graph Components","text":"nb.obj neighbours list object class nb","code":""},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Depth First Search on Neighbor Lists — Graph Components","text":"attr(nb.obj, \"sym\") FALSE igraph::components available, components directed graph found simple breadth-first search; igraph::components available, object made symmetric (may time-consuming large numbers neighbours) components found depth-first search. attr(nb.obj, \"sym\") TRUE, components directed graph found depth-first search. time complexity algorithms used native code igraph::components linear sum number nodes number edges graph, see https://github.com/r-spatial/spdep/issues/160 details; dense neighbour objects large numbers edges.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Depth First Search on Neighbor Lists — Graph Components","text":"list : nc number disjoint connected subgraphs comp.id vector indices disjoint connected subgraphs nodes nb.obj belong ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Depth First Search on Neighbor Lists — Graph Components","text":"Nicholas Lewin-Koh nikko@hailmail.net","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/compon.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Depth First Search on Neighbor Lists — Graph Components","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(st_geometry(columbus))) plot(col.gal.nb, coords, col=\"grey\") col2 <- droplinks(col.gal.nb, 21) #> Warning: some observations have no neighbours #> Warning: neighbour object has 3 sub-graphs res <- n.comp.nb(col2) table(res$comp.id) #> #> 1 2 3 #> 42 1 6 plot(col2, coords, add=TRUE) points(coords, col=res$comp.id, pch=16) run <- FALSE if (require(\"igraph\", quietly=TRUE) && require(\"spatialreg\", quietly=TRUE)) run <- TRUE if (run) { B <- as(nb2listw(col2, style=\"B\", zero.policy=TRUE), \"CsparseMatrix\") g1 <- graph_from_adjacency_matrix(B, mode=\"undirected\") c1 <- components(g1) print(c1$no == res$nc) } if (run) { print(all.equal(c1$membership, res$comp.id)) } if (run) { print(all.equal(c1$csize, c(table(res$comp.id)), check.attributes=FALSE)) } if (run) { W <- as(nb2listw(col2, style=\"W\", zero.policy=TRUE), \"CsparseMatrix\") g1W <- graph_from_adjacency_matrix(W, mode=\"directed\", weighted=\"W\") c1W <- components(g1W, mode=\"weak\") print(all.equal(c1W$membership, res$comp.id, check.attributes=FALSE)) } # \\donttest{ if (run) { data(house, package=\"spData\") house <- sf::st_as_sf(house) k6 <- knn2nb(knearneigh(house, k=6)) is.symmetric.nb(k6) } if (run) { print(k6) } if (run) { length(k6) + sum(card(k6)) } if (run) { # no pre-computed graph components str(attr(k6, \"ncomp\")) } if (run) { # raising the subgraph compute ceiling to above |N|+|E| computes and stores the # object in the neighbour object set.SubgraphCeiling(180000L) k6 <- knn2nb(knearneigh(house, k=6)) str(attr(k6, \"ncomp\")) } if (run) { print(k6) } if (run) { system.time(udir <- n.comp.nb(make.sym.nb(k6))) } if (run) { system.time(dir <- n.comp.nb(k6)) } if (run) { udir$nc } if (run) { dir$nc } if (run) { all.equal(dir, udir) } # }"},{"path":"https://r-spatial.github.io/spdep/reference/diffnb.html","id":null,"dir":"Reference","previous_headings":"","what":"Differences between neighbours lists — diffnb","title":"Differences between neighbours lists — diffnb","text":"function finds symmetric differences lists neighbours (ordering objects matter), returning nb neighbour list found","code":""},{"path":"https://r-spatial.github.io/spdep/reference/diffnb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Differences between neighbours lists — diffnb","text":"","code":"diffnb(x, y, verbose=NULL, legacy=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/diffnb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Differences between neighbours lists — diffnb","text":"x object class nb y object class nb verbose default NULL, use global option value; report regions ids taken object attribute \"region.id\" differences, ignored legacy= FALSE legacy default TRUE; use legacy code; FALSE use differences sparse matrix representations","code":""},{"path":"https://r-spatial.github.io/spdep/reference/diffnb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Differences between neighbours lists — diffnb","text":"neighbours list class nb","code":""},{"path":"https://r-spatial.github.io/spdep/reference/diffnb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Differences between neighbours lists — diffnb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/diffnb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Differences between neighbours lists — diffnb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE) rn <- row.names(columbus) knn1 <- knearneigh(coords, 1) knn2 <- knearneigh(coords, 2) nb1 <- knn2nb(knn1, row.names=rn) #> Warning: neighbour object has 13 sub-graphs nb2 <- knn2nb(knn2, row.names=rn) diffs <- diffnb(nb2, nb1, legacy=TRUE) #> Warning: neighbour object has 10 sub-graphs diffsl <- diffnb(nb2, nb1, legacy=FALSE) #> Warning: neighbour object has 10 sub-graphs all.equal(diffs, diffsl) #> [1] \"Attributes: < Component \\\"call\\\": target, current do not match when deparsed >\" # call attribute fifference expected diffsd <- union.nb(setdiff.nb(nb1, nb2), setdiff.nb(nb2, nb1)) #> Warning: neighbour object has 49 sub-graphs #> Warning: neighbour object has 10 sub-graphs #> Warning: neighbour object has 10 sub-graphs all.equal(diffs, diffsd) #> [1] \"Attributes: < Component \\\"call\\\": target, current do not match when deparsed >\" # call attribute fifference expected opar <- par(no.readonly=TRUE) plot(st_geometry(columbus), border=\"grey\", reset=FALSE, main=\"Plot of first (black) and second (red)\\nnearest neighbours\") plot(nb1, coords, add=TRUE) plot(diffs, coords, add=TRUE, col=\"red\", lty=2) par(opar)"},{"path":"https://r-spatial.github.io/spdep/reference/dnearneigh.html","id":null,"dir":"Reference","previous_headings":"","what":"Neighbourhood contiguity by distance — dnearneigh","title":"Neighbourhood contiguity by distance — dnearneigh","text":"function identifies neighbours region points Euclidean distance metric points lower (greater equal (changed version 1.1-7)) upper (less equal ) bounds, longlat = TRUE, Great Circle distance kilometers. x \"sf\" object use_s2= TRUE, spherical distances km used.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/dnearneigh.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Neighbourhood contiguity by distance — dnearneigh","text":"","code":"dnearneigh(x, d1, d2, row.names = NULL, longlat = NULL, bounds=c(\"GE\", \"LE\"), use_kd_tree=TRUE, symtest=FALSE, use_s2=packageVersion(\"s2\") > \"1.0.7\", k=200, dwithin=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/dnearneigh.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Neighbourhood contiguity by distance — dnearneigh","text":"x matrix point coordinates, object inheriting SpatialPoints \"sf\" \"sfc\" object; \"sf\" \"sfc\" object geometries geographical coordinates (use_s2=FALSE, sf::st_is_longlat(x) == TRUE sf::sf_use_s2() == TRUE), s2 used find neighbours (hope) use spatial indexing https://github.com/r-spatial/s2/issues/125 opposed legacy method uses brute-force (present s2 also uses brute-force) d1 lower distance bound metric points planar coordinates, km geographical coordinates d2 upper distance boundd metric points planar coordinates, km geographical coordinates row.names character vector region ids added neighbours list attribute region.id, default seq(1, nrow(x)) longlat TRUE point coordinates geographical longitude-latitude decimal degrees, case distances measured kilometers; x SpatialPoints object, value taken object , overrides argument NULL bounds character vector length 2, default c(\"GE\", \"LE\"), (GE: greater equal , LE: less equal ) finite closed interval [d1, d2], d1 <= x <= d2. first element may also \"GT\" (GT: greater ), second \"LT\" (LT: less ) finite, open intervals excluding bounds; first bound default changed \"GT\" \"GE\" release 1.1-7. creating multiple distance bands, finite, half-open right-closed intervals may used final interval avoid overlapping bounds: \"GE\", \"LT\", [d1, d2), d1 <= x < d2 use_kd_tree default TRUE, TRUE, use dbscan frNN available (permitting 3D distances). symtest Default FALSE; release 1.1-7, TRUE - run symmetry check output object, costly large numbers points. use_s2 default=packageVersion(\"s2\") > \"1.0.7\", s2 > 1.0-7, distance bound computations use spatial indexing sf::sf_use_s2() TRUE, s2::s2_dwithin_matrix() used distances sphere \"sf\" \"sfc\" objects s2 > 1.0-7. k default 200, number closest points consider searching using s2::s2_closest_edges() dwithin default TRUE, FALSE, use s2::s2_closest_edges(), use_s2=TRUE, sf::st_is_longlat(x) == TRUE sf::sf_use_s2() == TRUE; s2::s2_dwithin_matrix() yields lists neighbours s2::s2_closest_edges() k= set correctly.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/dnearneigh.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Neighbourhood contiguity by distance — dnearneigh","text":"function returns list integer vectors giving region id numbers neighbours satisfying distance criteria. See card details “nb” objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/dnearneigh.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Neighbourhood contiguity by distance — dnearneigh","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/dnearneigh.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Neighbourhood contiguity by distance — dnearneigh","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE) rn <- row.names(columbus) k1 <- knn2nb(knearneigh(coords)) #> Warning: neighbour object has 13 sub-graphs all.linked <- max(unlist(nbdists(k1, coords))) col.nb.0.all <- dnearneigh(coords, 0, all.linked, row.names=rn) #> Warning: neighbour object has 2 sub-graphs summary(col.nb.0.all, coords) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 252 #> Percentage nonzero weights: 10.49563 #> Average number of links: 5.142857 #> 2 disjoint connected subgraphs #> Link number distribution: #> #> 1 2 3 4 5 6 7 8 9 10 11 #> 4 8 6 2 5 8 6 2 6 1 1 #> 4 least connected regions: #> 6 10 21 47 with 1 link #> 1 most connected region: #> 28 with 11 links opar <- par(no.readonly=TRUE) plot(st_geometry(columbus), border=\"grey\", reset=FALSE, main=paste(\"Distance based neighbours 0-\", format(all.linked), sep=\"\")) plot(col.nb.0.all, coords, add=TRUE) par(opar) (sfc_obj <- st_centroid(st_geometry(columbus))) #> Geometry set for 49 features #> Geometry type: POINT #> Dimension: XY #> Bounding box: xmin: 6.221943 ymin: 11.01003 xmax: 10.95359 ymax: 14.36908 #> Projected CRS: Undefined Cartesian SRS with unknown unit #> First 5 geometries: #> POINT (8.827218 14.36908) #> POINT (8.332658 14.03162) #> POINT (9.012265 13.81972) #> POINT (8.460801 13.71696) #> POINT (9.007982 13.29637) col.nb.0.all_sf <- dnearneigh(sfc_obj, 0, all.linked, row.names=rn) #> Warning: neighbour object has 2 sub-graphs all.equal(col.nb.0.all, col.nb.0.all_sf, check.attributes=FALSE) #> [1] TRUE data(state) us48.fipsno <- read.geoda(system.file(\"etc/weights/us48.txt\", package=\"spdep\")[1]) if (as.numeric(paste(version$major, version$minor, sep=\"\")) < 19) { m50.48 <- match(us48.fipsno$\"State.name\", state.name) } else { m50.48 <- match(us48.fipsno$\"State_name\", state.name) } xy <- as.matrix(as.data.frame(state.center))[m50.48,] llk1 <- knn2nb(knearneigh(xy, k=1, longlat=FALSE)) #> Warning: neighbour object has 12 sub-graphs (all.linked <- max(unlist(nbdists(llk1, xy, longlat=FALSE)))) #> [1] 5.161223 ll.nb <- dnearneigh(xy, 0, all.linked, longlat=FALSE) #> Warning: neighbour object has 5 sub-graphs summary(ll.nb, xy, longlat=TRUE, scale=0.5) #> Neighbour list object: #> Number of regions: 48 #> Number of nonzero links: 190 #> Percentage nonzero weights: 8.246528 #> Average number of links: 3.958333 #> 5 disjoint connected subgraphs #> Link number distribution: #> #> 1 2 3 4 5 7 8 9 10 #> 11 9 4 8 4 4 4 3 1 #> 11 least connected regions: #> 2 4 8 10 24 26 29 32 35 41 45 with 1 link #> 1 most connected region: #> 28 with 10 links gck1 <- knn2nb(knearneigh(xy, k=1, longlat=TRUE)) #> Warning: neighbour object has 11 sub-graphs (all.linked <- max(unlist(nbdists(gck1, xy, longlat=TRUE)))) #> [1] 523.5819 gc.nb <- dnearneigh(xy, 0, all.linked, longlat=TRUE) #> Warning: neighbour object has 2 sub-graphs summary(gc.nb, xy, longlat=TRUE, scale=0.5) #> Neighbour list object: #> Number of regions: 48 #> Number of nonzero links: 220 #> Percentage nonzero weights: 9.548611 #> Average number of links: 4.583333 #> 2 disjoint connected subgraphs #> Link number distribution: #> #> 1 2 3 4 5 6 7 8 9 10 #> 5 9 6 8 5 2 3 3 5 2 #> 5 least connected regions: #> 2 4 8 41 45 with 1 link #> 2 most connected regions: #> 7 28 with 10 links plot(ll.nb, xy) plot(diffnb(ll.nb, gc.nb), xy, add=TRUE, col=\"red\", lty=2) #> Warning: neighbour object has 27 sub-graphs title(main=\"Differences Euclidean/Great Circle\") #xy1 <- SpatialPoints((as.data.frame(state.center))[m50.48,], # proj4string=CRS(\"+proj=longlat +ellps=GRS80\")) #gck1a <- knn2nb(knearneigh(xy1, k=1)) #(all.linked <- max(unlist(nbdists(gck1a, xy1)))) #gc.nb <- dnearneigh(xy1, 0, all.linked) #summary(gc.nb, xy1, scale=0.5) xy1 <- st_as_sf((as.data.frame(state.center))[m50.48,], coords=1:2, crs=st_crs(\"OGC:CRS84\")) old_use_s2 <- sf_use_s2() sf_use_s2(TRUE) gck1b <- knn2nb(knearneigh(xy1, k=1)) #> Warning: neighbour object has 11 sub-graphs system.time(o <- nbdists(gck1b, xy1)) #> user system elapsed #> 0 0 0 (all.linked <- max(unlist(o))) #> [1] 522.4464 # use s2 brute-force dwithin_matrix approach for s2 <= 1.0.7 system.time(gc.nb.dwithin <- dnearneigh(xy1, 0, all.linked, use_s2=TRUE, dwithin=TRUE)) #> Warning: neighbour object has 3 sub-graphs #> user system elapsed #> 0.00 0.00 0.01 summary(gc.nb, xy1, scale=0.5) #> Neighbour list object: #> Number of regions: 48 #> Number of nonzero links: 220 #> Percentage nonzero weights: 9.548611 #> Average number of links: 4.583333 #> 2 disjoint connected subgraphs #> Link number distribution: #> #> 1 2 3 4 5 6 7 8 9 10 #> 5 9 6 8 5 2 3 3 5 2 #> 5 least connected regions: #> 2 4 8 41 45 with 1 link #> 2 most connected regions: #> 7 28 with 10 links # use s2 closest_edges approach s2 > 1.0.7 if (packageVersion(\"s2\") > \"1.0.7\") { (system.time(gc.nb.closest <- dnearneigh(xy1, 0, all.linked, dwithin=FALSE))) } #> Warning: neighbour object has 3 sub-graphs #> user system elapsed #> 0 0 0 if (packageVersion(\"s2\") > \"1.0.7\") { system.time(gc.nb.dwithin <- dnearneigh(xy1, 0, all.linked, use_s2=TRUE, dwithin=TRUE)) } #> Warning: neighbour object has 3 sub-graphs #> user system elapsed #> 0.00 0.00 0.02 if (packageVersion(\"s2\") > \"1.0.7\") { summary(gc.nb.dwithin, xy1, scale=0.5) } #> Neighbour list object: #> Number of regions: 48 #> Number of nonzero links: 218 #> Percentage nonzero weights: 9.461806 #> Average number of links: 4.541667 #> 1 region with no links: #> 2 #> 3 disjoint connected subgraphs #> Link number distribution: #> #> 0 1 2 3 4 5 6 7 8 9 10 #> 1 5 8 6 8 5 2 3 3 5 2 #> 5 least connected regions: #> 4 8 29 41 45 with 1 link #> 2 most connected regions: #> 7 28 with 10 links if (packageVersion(\"s2\") > \"1.0.7\") { summary(gc.nb.closest, xy1, scale=0.5) } #> Neighbour list object: #> Number of regions: 48 #> Number of nonzero links: 218 #> Percentage nonzero weights: 9.461806 #> Average number of links: 4.541667 #> 1 region with no links: #> 2 #> 3 disjoint connected subgraphs #> Link number distribution: #> #> 0 1 2 3 4 5 6 7 8 9 10 #> 1 5 8 6 8 5 2 3 3 5 2 #> 5 least connected regions: #> 4 8 29 41 45 with 1 link #> 2 most connected regions: #> 7 28 with 10 links # use legacy symmetric brute-force approach system.time(gc.nb.legacy <- dnearneigh(xy1, 0, all.linked, use_s2=FALSE)) #> Warning: neighbour object has 3 sub-graphs #> user system elapsed #> 0.02 0.00 0.00 summary(gc.nb, xy1, scale=0.5) #> Neighbour list object: #> Number of regions: 48 #> Number of nonzero links: 220 #> Percentage nonzero weights: 9.548611 #> Average number of links: 4.583333 #> 2 disjoint connected subgraphs #> Link number distribution: #> #> 1 2 3 4 5 6 7 8 9 10 #> 5 9 6 8 5 2 3 3 5 2 #> 5 least connected regions: #> 2 4 8 41 45 with 1 link #> 2 most connected regions: #> 7 28 with 10 links if (packageVersion(\"s2\") > \"1.0.7\") all.equal(gc.nb.closest, gc.nb.dwithin, check.attributes=FALSE) #> [1] TRUE # legacy is ellipsoidal, s2 spherical, so minor differences expected if (packageVersion(\"s2\") > \"1.0.7\") all.equal(gc.nb, gc.nb.closest, check.attributes=FALSE) #> [1] \"Component 2: Mean relative difference: 1\" #> [2] \"Component 29: Numeric: lengths (2, 1) differ\" all.equal(gc.nb, gc.nb.dwithin, check.attributes=FALSE) #> [1] \"Component 2: Mean relative difference: 1\" #> [2] \"Component 29: Numeric: lengths (2, 1) differ\" sf_use_s2(old_use_s2) # example of reading points with readr::read_csv() yielding a tibble load(system.file(\"etc/misc/coords.rda\", package=\"spdep\")) class(coords) #> [1] \"spec_tbl_df\" \"tbl_df\" \"tbl\" \"data.frame\" k1 <- knn2nb(knearneigh(coords, k=1)) #> Warning: neighbour object has 29 sub-graphs all.linked <- max(unlist(nbdists(k1, coords))) dnearneigh(coords, 0, all.linked) #> Neighbour list object: #> Number of regions: 100 #> Number of nonzero links: 676 #> Percentage nonzero weights: 6.76 #> Average number of links: 6.76"},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":null,"dir":"Reference","previous_headings":"","what":"Drop and add links in a neighbours list — droplinks","title":"Drop and add links in a neighbours list — droplinks","text":"droplinks drops links just region neighbours list. example corresponds Fingleton's Table 1, (1999) p. 6, lattices 5 19. addlinks1 adds links single region specified regions.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Drop and add links in a neighbours list — droplinks","text":"","code":"droplinks(nb, drop, sym=TRUE) addlinks1(nb, from, to, sym=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Drop and add links in a neighbours list — droplinks","text":"nb neighbours list object class nb drop either logical vector length nb, character vector named regions corresponding nb's region.id attribute, integer vector region numbers sym TRUE removal \"row\" \"column\" links, FALSE \"row\" links; adding links, inserts links region regions single region adding links, either character vector length 1 named region corresponding nb's region.id attribute, integer vector length 1 holding region number regions, either character vector named regions corresponding nb's region.id attribute, integer vector region numbers","code":""},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Drop and add links in a neighbours list — droplinks","text":"function returns object class nb list integer vectors containing neighbour region number ids.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Drop and add links in a neighbours list — droplinks","text":"B. Fingleton (1999) Spurious spatial regression: Monte Carlo results spatial unit root spatial cointegration, Journal Regional Science 39, pp. 1–19.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Drop and add links in a neighbours list — droplinks","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/droplinks.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Drop and add links in a neighbours list — droplinks","text":"","code":"# \\donttest{ rho <- c(0.2, 0.5, 0.95, 0.999, 1.0) ns <- c(5, 7, 9, 11, 13, 15, 17, 19) mns <- matrix(0, nrow=length(ns), ncol=length(rho)) rownames(mns) <- ns colnames(mns) <- rho mxs <- matrix(0, nrow=length(ns), ncol=length(rho)) rownames(mxs) <- ns colnames(mxs) <- rho for (i in 1:length(ns)) { nblist <- cell2nb(ns[i], ns[i]) nbdropped <- droplinks(nblist, ((ns[i]*ns[i])+1)/2, sym=FALSE) listw <- nb2listw(nbdropped, style=\"W\", zero.policy=TRUE) wmat <- listw2mat(listw) for (j in 1:length(rho)) { mat <- diag(ns[i]*ns[i]) - rho[j] * wmat res <- diag(solve(t(mat) %*% mat)) mns[i,j] <- mean(res) mxs[i,j] <- max(res) } } #> Warning: some observations have no neighbours #> Error in n.comp.nb(nb): n.comp.nb: recursive nodeid out of bounds #> install spatialreg and igraph to avoid legacy issue print(mns) #> 0.2 0.5 0.95 0.999 1 #> 5 0 0 0 0 0 #> 7 0 0 0 0 0 #> 9 0 0 0 0 0 #> 11 0 0 0 0 0 #> 13 0 0 0 0 0 #> 15 0 0 0 0 0 #> 17 0 0 0 0 0 #> 19 0 0 0 0 0 print(mxs) #> 0.2 0.5 0.95 0.999 1 #> 5 0 0 0 0 0 #> 7 0 0 0 0 0 #> 9 0 0 0 0 0 #> 11 0 0 0 0 0 #> 13 0 0 0 0 0 #> 15 0 0 0 0 0 #> 17 0 0 0 0 0 #> 19 0 0 0 0 0 # }"},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":null,"dir":"Reference","previous_headings":"","what":"Global Empirical Bayes estimator — EBest","title":"Global Empirical Bayes estimator — EBest","text":"function computes global empirical Bayes estimates rates \"shrunk\" overall mean.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Global Empirical Bayes estimator — EBest","text":"","code":"EBest(n, x, family=\"poisson\")"},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Global Empirical Bayes estimator — EBest","text":"n numeric vector counts cases x numeric vector populations risk family either \"poisson\" rare conditions \"binomial\" non-rare conditions","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Global Empirical Bayes estimator — EBest","text":"Details implementation \"poisson\" family found Marshall, p. 284–5, Bailey Gatrell p. 303–306 exercise 8.2, pp. 328–330. \"binomial\" family, see Martuzzi Elliott (implementation Olaf Berke).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Global Empirical Bayes estimator — EBest","text":"data frame two columns: raw numerical vector raw (crude) rates estmm numerical vector empirical Bayes estimates parameters attribute list components: global method moments phi value m global method moments gamma value","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Global Empirical Bayes estimator — EBest","text":"Marshall R M (1991) Mapping disease mortality rates using Empirical Bayes Estimators, Applied Statistics, 40, 283–294; Bailey T, Gatrell (1995) Interactive Spatial Data Analysis, Harlow: Longman, pp. 303–306, Martuzzi M, Elliott P (1996) Empirical Bayes estimation small area prevalence non-rare conditions, Statistics Medicine 15, 1867–1873.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Global Empirical Bayes estimator — EBest","text":"Roger Bivand Roger.Bivand@nhh.Olaf Berke, Population Medicine, OVC, University Guelph, CANADA","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/EBest.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Global Empirical Bayes estimator — EBest","text":"","code":"auckland <- st_read(system.file(\"shapes/auckland.gpkg\", package=\"spData\")[1], quiet=TRUE) res <- EBest(auckland$M77_85, 9*auckland$Und5_81) attr(res, \"parameters\") #> $a #> [1] 7.284173e-07 #> #> $b #> [1] 0.002633436 #> auckland$estmm000 <- res$estmm*1000 plot(auckland[,\"estmm000\"], breaks=c(0,2,2.5,3,3.5,5), main=\"Infant mortality per 1000 per year\") data(huddersfield, package=\"spData\") res <- EBest(huddersfield$cases, huddersfield$total, family=\"binomial\") round(res[,1:2],4)*100 #> raw estmm #> 1 42.86 34.44 #> 2 28.95 29.56 #> 3 28.31 28.94 #> 4 21.43 28.93 #> 5 33.33 30.72 #> 6 30.86 30.43 #> 7 33.70 31.85 #> 8 45.61 35.93 #> 9 26.67 28.95 #> 10 29.41 29.95 #> 11 27.76 28.36 #> 12 33.75 31.75 #> 13 32.67 31.84 #> 14 22.91 25.36 #> 15 34.21 32.33 #> 16 33.77 31.72 #> 17 29.09 29.69 #> 18 15.87 24.36 #> 19 40.91 32.11 #> 20 40.00 31.01 #> 21 28.79 29.53 #> 22 38.89 31.47 #> 23 28.32 29.10 #> 24 33.33 31.44 #> 25 13.95 22.36 #> 26 33.77 31.72 #> 27 31.58 30.31 #> 28 33.33 30.42 #> 29 26.67 28.26 #> 30 63.64 33.57 #> 31 34.38 32.24 #> 32 20.00 27.62 #> 33 19.15 24.60 #> 34 25.53 28.54 #> 35 24.14 27.79 #> 36 44.00 32.98 #> 37 25.33 27.95 #> 38 18.18 26.96 #> 39 31.78 30.97 #> 40 32.20 30.88 #> 41 26.19 28.23 #> 42 19.05 26.65 #> 43 16.67 26.81 #> 44 20.00 28.66 #> 45 32.99 31.54 #> 46 50.00 31.97 #> 47 37.21 32.30 #> 48 32.79 31.13 #> 49 38.89 31.47 #> 50 25.00 27.26 #> 51 26.03 28.29 #> 52 30.43 30.18 #> 53 19.75 25.28 #> 54 50.00 31.61 #> 55 21.62 27.67 #> 56 22.22 27.88 #> 57 36.36 30.71 #> 58 31.25 30.22 #> 59 0.00 29.73 #> 60 29.41 29.95 #> 61 31.16 30.71 #> 62 33.33 30.58 #> 63 33.87 32.22 #> 64 30.00 30.04 #> 65 30.34 30.19 #> 66 40.74 35.00 #> 67 46.43 38.96 #> 68 34.21 31.91 #> 69 24.26 26.10 #> 70 29.41 29.75 #> 71 47.17 39.13"},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Permutation test for empirical Bayes index — EBImoran.mc","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"empirical Bayes index modification Moran's testing spatial autocorrelation rate, typically number observed cases population risk. index value tested using nsim random permutations index given spatial weighting scheme, establish rank observed statistic relation nsim simulated values.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"","code":"EBImoran.mc(n, x, listw, nsim, zero.policy = attr(listw, \"zero.policy\"), alternative = \"greater\", spChk=NULL, return_boot=FALSE, subtract_mean_in_numerator=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"n numeric vector counts cases length neighbours list listw x numeric vector populations risk length neighbours list listw listw listw object created example nb2listw nsim number permutations zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"two.sided\", \"less\" spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() return_boot return object class boot equivalent permutation bootstrap rather object class htest subtract_mean_in_numerator default TRUE, TRUE subtract mean z numerator EBI equation p. 2157 reference (consulted Renato Assunção 2016-02-19); February 2016 default FALSE agreeing printed paper.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"statistic used (m number observations): $$EBI = \\frac{m}{\\sum_{=1}^{m}\\sum_{j=1}^{m}w_{ij}} \\frac{\\sum_{=1}^{m}\\sum_{j=1}^{m}w_{ij}z_i z_j}{\\sum_{=1}^{m}(z_i - \\bar{z})^2} $$ : $$z_i = \\frac{p_i - b}{\\sqrt{v_i}}$$ : $$p_i = n_i / x_i$$ $$v_i = + (b / x_i)$$ $$b = \\sum_{=1}^{m} n_i / \\sum_{=1}^{m} x_i $$ $$= s^2 - b / (\\sum_{=1}^{m} x_i / m)$$ $$s^2 = \\sum_{=1}^{m} x_i (p_i - b)^2 / \\sum_{=1}^{m} x_i $$","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"list class htest mc.sim containing following components: statistic value observed Moran's . parameter rank observed Moran's . p.value pseudo p-value test. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data, number simulations. res nsim simulated values statistic, final value observed statistic z numerical vector Empirical Bayes indices z ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"Assunção RM, Reis EA 1999 new proposal adjust Moran's population density. Statistics Medicine 18, pp. 2147–2162; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/EBImoran.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Permutation test for empirical Bayes index — EBImoran.mc","text":"","code":"nc.sids <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\")[1], quiet=TRUE) rn <- as.character(nc.sids$FIPS) ncCC89_nb <- read.gal(system.file(\"weights/ncCC89.gal\", package=\"spData\")[1], region.id=rn) #> Warning: neighbour object has 3 sub-graphs EBImoran.mc(nc.sids$SID74, nc.sids$BIR74, nb2listw(ncCC89_nb, style=\"B\", zero.policy=TRUE), nsim=999, alternative=\"two.sided\", zero.policy=TRUE) #> The default for subtract_mean_in_numerator set TRUE from February 2016 #> #> \tMonte-Carlo simulation of Empirical Bayes Index (mean subtracted) #> #> data: cases: nc.sids$SID74, risk population: nc.sids$BIR74 #> weights: nb2listw(ncCC89_nb, style = \"B\", zero.policy = TRUE) #> number of simulations + 1: 1000 #> #> statistic = 0.25789, observed rank = 999, p-value = 0.002 #> alternative hypothesis: two.sided #> sids.p <- nc.sids$SID74 / nc.sids$BIR74 moran.mc(sids.p, nb2listw(ncCC89_nb, style=\"B\", zero.policy=TRUE), nsim=999, alternative=\"two.sided\", zero.policy=TRUE) #> #> \tMonte-Carlo simulation of Moran I #> #> data: sids.p #> weights: nb2listw(ncCC89_nb, style = \"B\", zero.policy = TRUE) #> number of simulations + 1: 1000 #> #> statistic = 0.20904, observed rank = 997, p-value = 0.006 #> alternative hypothesis: two.sided #>"},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":null,"dir":"Reference","previous_headings":"","what":"Local Empirical Bayes estimator — EBlocal","title":"Local Empirical Bayes estimator — EBlocal","text":"function computes local empirical Bayes estimates rates \"shrunk\" neighbourhood mean neighbourhoods given nb neighbourhood list.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Local Empirical Bayes estimator — EBlocal","text":"","code":"EBlocal(ri, ni, nb, zero.policy = NULL, spChk = NULL, geoda=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Local Empirical Bayes estimator — EBlocal","text":"ri numeric vector counts cases length neighbours list nb; many zero counts, estimates may affected division zero, see https://stat.ethz.ch/pipermail/r-sig-geo/2022-January/028882.html ni numeric vector populations risk length neighbours list nb nb nb object neighbour relationships zero.policy default NULL, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() geoda default=FALSE, following Marshall's algorithm interpreted Bailey Gatrell, pp. 305-307, exercise 8.2, pp. 328-330 definition phi; TRUE definition phi used GeoDa (see discussion OpenSpace mailing list June 2003: http://agec221.agecon.uiuc.edu/pipermail/openspace/2003-June/thread.html)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Local Empirical Bayes estimator — EBlocal","text":"Details implementation found Marshall, p. 286, Bailey Gatrell p. 307 exercise 8.2, pp. 328–330. example results fully correspond sources slightly differing neighbourhoods, generally close. many zero counts, estimates may affected division zero, see https://stat.ethz.ch/pipermail/r-sig-geo/2022-January/028882.html.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Local Empirical Bayes estimator — EBlocal","text":"data frame two columns: raw numerical vector raw (crude) rates est numerical vector local empirical Bayes estimates parameters attribute list components (zero, estimate NaN, https://stat.ethz.ch/pipermail/r-sig-geo/2022-January/028882.html): numerical vector local phi values m numerical vector local gamma values","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Local Empirical Bayes estimator — EBlocal","text":"Marshall R M (1991) Mapping disease mortality rates using Empirical Bayes Estimators, Applied Statistics, 40, 283–294; Bailey T, Gatrell (1995) Interactive Spatial Data Analysis, Harlow: Longman, pp. 303–306.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Local Empirical Bayes estimator — EBlocal","text":"Roger Bivand Roger.Bivand@nhh., based contributions Marilia Carvalho","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/EBlocal.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Local Empirical Bayes estimator — EBlocal","text":"","code":"auckland <- st_read(system.file(\"shapes/auckland.gpkg\", package=\"spData\")[1], quiet=TRUE) auckland.nb <- poly2nb(auckland) res <- EBlocal(auckland$M77_85, 9*auckland$Und5_81, auckland.nb) auckland$est000 <- res$est*1000 plot(auckland[,\"est000\"], breaks=c(0,2,2.5,3,3.5,8), main=\"Infant mortality per 1000 per year\")"},{"path":"https://r-spatial.github.io/spdep/reference/edit.nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Interactive editing of neighbours lists — edit.nb","title":"Interactive editing of neighbours lists — edit.nb","text":"function provides simple interactive editing neighbours lists allow unneeded links deleted, missing links inserted. uses identify pick endpoints link deleted added, asks confirmation committing. result assigned new object, editing lost - edit. method relies direct contact graphics device. use RStudio.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/edit.nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Interactive editing of neighbours lists — edit.nb","text":"","code":"# S3 method for class 'nb' edit(name, coords, polys=NULL, ..., use_region.id=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/edit.nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Interactive editing of neighbours lists — edit.nb","text":"name object class nb coords matrix region point coordinates; missing polys= inherits SpatialPolygons, label points object used polys polygon boundaries supplied, used background; must inherit SpatialPolygons ... arguments passed methods use_region.id default FALSE, identify use 1-based observation numbers, otherwise use nb region.id attribute values","code":""},{"path":"https://r-spatial.github.io/spdep/reference/edit.nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Interactive editing of neighbours lists — edit.nb","text":"function returns object class nb edited list integer vectors containing neighbour region number ids, added attributes tallying added deleted links.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/edit.nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Interactive editing of neighbours lists — edit.nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/edit.nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Interactive editing of neighbours lists — edit.nb","text":"","code":"if (FALSE) { # \\dontrun{ columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) class(columbus) if (FALSE) nnb1 <- edit.nb(col.gal.nb, polys=as(columbus, \"Spatial\")) } # }"},{"path":"https://r-spatial.github.io/spdep/reference/eire.html","id":null,"dir":"Reference","previous_headings":"","what":"Eire data sets — eire","title":"Eire data sets — eire","text":"data set now part spData package","code":""},{"path":"https://r-spatial.github.io/spdep/reference/eire.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Eire data sets — eire","text":"","code":"data(eire)"},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute Geary's C — geary","title":"Compute Geary's C — geary","text":"simple function compute Geary's C, called geary.test geary.mc; $$C = \\frac{(n-1)}{2\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}} \\frac{\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}(x_i-x_j)^2}{\\sum_{=1}^{n}(x_i - \\bar{x})^2} $$ geary.intern internal function used vary similarity criterion.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute Geary's C — geary","text":"","code":"geary(x, listw, n, n1, S0, zero.policy=attr(listw, \"zero.policy\"), scale=TRUE) "},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute Geary's C — geary","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw n number zones n1 n - 1 S0 global sum weights zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA scale default TRUE, may FALSE revert changes made accommodate localC November 2021 (see #151)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute Geary's C — geary","text":"list C Geary's C K sample kurtosis x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute Geary's C — geary","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 17.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute Geary's C — geary","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/geary.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute Geary's C — geary","text":"","code":"data(oldcol) col.W <- nb2listw(COL.nb, style=\"W\") str(geary(COL.OLD$CRIME, col.W, length(COL.nb), length(COL.nb)-1, Szero(col.W))) #> List of 2 #> $ C: num 0.53 #> $ K: num 2.23"},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Permutation test for Geary's C statistic — geary.mc","title":"Permutation test for Geary's C statistic — geary.mc","text":"permutation test Geary's C statistic calculated using nsim random permutations x given spatial weighting scheme, establish rank observed statistic relation nsim simulated values.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Permutation test for Geary's C statistic — geary.mc","text":"","code":"geary.mc(x, listw, nsim, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\", spChk=NULL, adjust.n=TRUE, return_boot=FALSE, na.action=na.fail, scale=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Permutation test for Geary's C statistic — geary.mc","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw nsim number permutations zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"less\"; reversal corresponds geary.test described section output statistic value, based Cliff Ord 1973, p. 21 (changed 2011-04-11, thanks Daniel Garavito). spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted return_boot return object class boot equivalent permutation bootstrap rather object class htest na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass permitted meaningless permutation test. scale default TRUE, may FALSE revert changes made accommodate localC November 2021 (see #151)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Permutation test for Geary's C statistic — geary.mc","text":"list class htest mc.sim containing following components: statistic value observed Geary's C. parameter rank observed Geary's C. p.value pseudo p-value test. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data, number simulations. res nsim simulated values statistic, final value observed statistic","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Permutation test for Geary's C statistic — geary.mc","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 63-5.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Permutation test for Geary's C statistic — geary.mc","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/geary.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Permutation test for Geary's C statistic — geary.mc","text":"","code":"data(oldcol) set.seed(1) sim1 <- geary.mc(COL.OLD$CRIME, nb2listw(COL.nb, style=\"W\"), nsim=99, alternative=\"less\") sim1 #> #> \tMonte-Carlo simulation of Geary C #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.nb, style = \"W\") #> number of simulations + 1: 100 #> #> statistic = 0.52987, observed rank = 1, p-value = 0.99 #> alternative hypothesis: less #> mean(sim1$res) #> [1] 1.002705 var(sim1$res) #> [1] 0.01043616 summary(sim1$res) #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> 0.5299 0.9362 1.0141 1.0027 1.0673 1.2459 colold.lags <- nblag(COL.nb, 3) sim2 <- geary.mc(COL.OLD$CRIME, nb2listw(colold.lags[[2]], style=\"W\"), nsim=99) sim2 #> #> \tMonte-Carlo simulation of Geary C #> #> data: COL.OLD$CRIME #> weights: nb2listw(colold.lags[[2]], style = \"W\") #> number of simulations + 1: 100 #> #> statistic = 0.81129, observed rank = 1, p-value = 0.01 #> alternative hypothesis: greater #> summary(sim2$res) #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> 0.8113 0.9500 1.0173 1.0147 1.0731 1.1962 sim3 <- geary.mc(COL.OLD$CRIME, nb2listw(colold.lags[[3]], style=\"W\"), nsim=99) sim3 #> #> \tMonte-Carlo simulation of Geary C #> #> data: COL.OLD$CRIME #> weights: nb2listw(colold.lags[[3]], style = \"W\") #> number of simulations + 1: 100 #> #> statistic = 1.1303, observed rank = 89, p-value = 0.89 #> alternative hypothesis: greater #> summary(sim3$res) #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> 0.7903 0.9609 0.9989 1.0148 1.0656 1.2726 crime <- COL.OLD$CRIME is.na(crime) <- sample(1:length(crime), 10) try(geary.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, na.action=na.fail)) #> Error in na.fail.default(x) : missing values in object geary.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE, na.action=na.omit) #> Warning: subsetting caused increase in subgraph count #> #> \tMonte-Carlo simulation of Geary C #> #> data: crime #> weights: nb2listw(COL.nb, style = \"W\") #> omitted: 14, 16, 17, 21, 24, 31, 32, 42, 44, 47 #> number of simulations + 1: 100 #> #> statistic = 0.49368, observed rank = 1, p-value = 0.01 #> alternative hypothesis: greater #> geary.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE, return_boot=TRUE, na.action=na.omit) #> Warning: subsetting caused increase in subgraph count #> NA observations omitted: 14, 16, 17, 21, 24, 31, 32, 42, 44, 47 #> #> DATA PERMUTATION #> #> #> Call: #> boot(data = x, statistic = geary_boot, R = nsim, sim = \"permutation\", #> listw = listw, n = n, n1 = wc$n1, S0 = wc$S0, zero.policy = zero.policy, #> scale = scale, parallel = parallel, ncpus = ncpus, cl = cl) #> #> #> Bootstrap Statistics : #> original bias std. error #> t1* 0.4936767 0.4891213 0.1517218 geary.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE, na.action=na.exclude) #> Warning: subsetting caused increase in subgraph count #> #> \tMonte-Carlo simulation of Geary C #> #> data: crime #> weights: nb2listw(COL.nb, style = \"W\") #> omitted: 14, 16, 17, 21, 24, 31, 32, 42, 44, 47 #> number of simulations + 1: 100 #> #> statistic = 0.49368, observed rank = 1, p-value = 0.01 #> alternative hypothesis: greater #> geary.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE, return_boot=TRUE, na.action=na.exclude) #> Warning: subsetting caused increase in subgraph count #> NA observations omitted: 14, 16, 17, 21, 24, 31, 32, 42, 44, 47 #> #> DATA PERMUTATION #> #> #> Call: #> boot(data = x, statistic = geary_boot, R = nsim, sim = \"permutation\", #> listw = listw, n = n, n1 = wc$n1, S0 = wc$S0, zero.policy = zero.policy, #> scale = scale, parallel = parallel, ncpus = ncpus, cl = cl) #> #> #> Bootstrap Statistics : #> original bias std. error #> t1* 0.4936767 0.4570379 0.1307276 try(geary.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, na.action=na.pass)) #> Error in geary.mc(crime, nb2listw(COL.nb, style = \"W\"), nsim = 99, na.action = na.pass) : #> na.pass not permitted"},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":null,"dir":"Reference","previous_headings":"","what":"Geary's C test for spatial autocorrelation — geary.test","title":"Geary's C test for spatial autocorrelation — geary.test","text":"Geary's test spatial autocorrelation using spatial weights matrix weights list form. assumptions underlying test sensitive form graph neighbour relationships factors, results may checked geary.mc permutations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Geary's C test for spatial autocorrelation — geary.test","text":"","code":"geary.test(x, listw, randomisation=TRUE, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\", spChk=NULL, adjust.n=TRUE, na.action=na.fail, scale=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Geary's C test for spatial autocorrelation — geary.test","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw randomisation variance calculated assumption randomisation, FALSE normality zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"less\" \"two.sided\". spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass permitted. scale default TRUE, may FALSE revert changes made accommodate localC November 2021 (see #151)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Geary's C test for spatial autocorrelation — geary.test","text":"list class htest containing following components: statistic value standard deviate Geary's C, order given Cliff Ord 1973, p. 21, (EC - C) / sqrt(VC), sign reversed respect usual (C - EC) / sqrt(VC); means “greater” alternative Geary C test corresponds “greater” alternative Moran's test. p.value p-value test. estimate value observed Geary's C, expectation variance method assumption. alternative character string describing alternative hypothesis. method character string giving assumption used calculating standard deviate. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Geary's C test for spatial autocorrelation — geary.test","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 21, Cliff, . D., Ord, J. K. 1973 Spatial Autocorrelation, Pion, pp. 15-16, 21; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Geary's C test for spatial autocorrelation — geary.test","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Geary's C test for spatial autocorrelation — geary.test","text":"derivation test (Cliff Ord, 1981, p. 18) assumes weights matrix symmetric. inherently non-symmetric matrices, k-nearest neighbour matrices, listw2U() can used make matrix symmetric. non-symmetric weights matrix cases, variance test statistic may negative (thanks Franz Munoz well documented bug report). Geary's C affected non-symmetric weights normality much Moran's . 0.4-35, sign standard deviate C changed match Cliff Ord (1973, p. 21).","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/geary.test.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Geary's C test for spatial autocorrelation — geary.test","text":"","code":"data(oldcol) geary.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"W\")) #> #> \tGeary C test under randomisation #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.nb, style = \"W\") #> #> Geary C statistic standard deviate = 4.7605, p-value = 9.655e-07 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic Expectation Variance #> 0.52986993 1.00000000 0.00975278 #> geary.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"W\"), randomisation=FALSE) #> #> \tGeary C test under normality #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.nb, style = \"W\") #> #> Geary C statistic standard deviate = 4.6388, p-value = 1.752e-06 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic Expectation Variance #> 0.52986993 1.00000000 0.01027137 #> colold.lags <- nblag(COL.nb, 3) geary.test(COL.OLD$CRIME, nb2listw(colold.lags[[2]], style=\"W\")) #> #> \tGeary C test under randomisation #> #> data: COL.OLD$CRIME #> weights: nb2listw(colold.lags[[2]], style = \"W\") #> #> Geary C statistic standard deviate = 2.2896, p-value = 0.01102 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic Expectation Variance #> 0.811285136 1.000000000 0.006793327 #> geary.test(COL.OLD$CRIME, nb2listw(colold.lags[[3]], style=\"W\"), alternative=\"greater\") #> #> \tGeary C test under randomisation #> #> data: COL.OLD$CRIME #> weights: nb2listw(colold.lags[[3]], style = \"W\") #> #> Geary C statistic standard deviate = -1.5667, p-value = 0.9414 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic Expectation Variance #> 1.130277918 1.000000000 0.006914551 #> print(is.symmetric.nb(COL.nb)) #> [1] TRUE coords.OLD <- cbind(COL.OLD$X, COL.OLD$Y) COL.k4.nb <- knn2nb(knearneigh(coords.OLD, 4)) print(is.symmetric.nb(COL.k4.nb)) #> [1] FALSE geary.test(COL.OLD$CRIME, nb2listw(COL.k4.nb, style=\"W\")) #> #> \tGeary C test under randomisation #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.k4.nb, style = \"W\") #> #> Geary C statistic standard deviate = 6.4415, p-value = 5.916e-11 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic Expectation Variance #> 0.399254423 1.000000000 0.008697812 #> geary.test(COL.OLD$CRIME, nb2listw(COL.k4.nb, style=\"W\"), randomisation=FALSE) #> #> \tGeary C test under normality #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.k4.nb, style = \"W\") #> #> Geary C statistic standard deviate = 6.2873, p-value = 1.615e-10 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic Expectation Variance #> 0.399254423 1.000000000 0.009129529 #> cat(\"Note non-symmetric weights matrix - use listw2U()\\n\") #> Note non-symmetric weights matrix - use listw2U() geary.test(COL.OLD$CRIME, listw2U(nb2listw(COL.k4.nb, style=\"W\"))) #> #> \tGeary C test under randomisation #> #> data: COL.OLD$CRIME #> weights: listw2U(nb2listw(COL.k4.nb, style = \"W\")) #> #> Geary C statistic standard deviate = 6.4415, p-value = 5.916e-11 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic Expectation Variance #> 0.399254423 1.000000000 0.008697812 #> geary.test(COL.OLD$CRIME, listw2U(nb2listw(COL.k4.nb, style=\"W\")), randomisation=FALSE) #> #> \tGeary C test under normality #> #> data: COL.OLD$CRIME #> weights: listw2U(nb2listw(COL.k4.nb, style = \"W\")) #> #> Geary C statistic standard deviate = 6.2873, p-value = 1.615e-10 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic Expectation Variance #> 0.399254423 1.000000000 0.009129529 #> crime <- COL.OLD$CRIME is.na(crime) <- sample(1:length(crime), 10) try(geary.test(crime, nb2listw(COL.nb, style=\"W\"), na.action=na.fail)) #> Error in na.fail.default(x) : missing values in object geary.test(crime, nb2listw(COL.nb, style=\"W\"), zero.policy=TRUE, na.action=na.omit) #> #> \tGeary C test under randomisation #> #> data: crime #> weights: nb2listw(COL.nb, style = \"W\") #> omitted: 3, 4, 10, 20, 21, 23, 27, 29, 31, 38 #> #> Geary C statistic standard deviate = 4.2726, p-value = 9.661e-06 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic Expectation Variance #> 0.45199742 1.00000000 0.01645071 #> geary.test(crime, nb2listw(COL.nb, style=\"W\"), zero.policy=TRUE, na.action=na.exclude) #> #> \tGeary C test under randomisation #> #> data: crime #> weights: nb2listw(COL.nb, style = \"W\") #> omitted: 3, 4, 10, 20, 21, 23, 27, 29, 31, 38 #> #> Geary C statistic standard deviate = 4.2726, p-value = 9.661e-06 #> alternative hypothesis: Expectation greater than statistic #> sample estimates: #> Geary C statistic Expectation Variance #> 0.45199742 1.00000000 0.01645071 #> try(geary.test(crime, nb2listw(COL.nb, style=\"W\"), na.action=na.pass)) #> Error in geary.test(crime, nb2listw(COL.nb, style = \"W\"), na.action = na.pass) : #> na.pass not permitted"},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":null,"dir":"Reference","previous_headings":"","what":"Global G test for spatial autocorrelation — globalG.test","title":"Global G test for spatial autocorrelation — globalG.test","text":"global G statistic spatial autocorrelation, complementing local Gi LISA measures: localG.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Global G test for spatial autocorrelation — globalG.test","text":"","code":"globalG.test(x, listw, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\", spChk=NULL, adjust.n=TRUE, B1correct=TRUE, adjust.x=TRUE, Arc_all_x=FALSE, na.action=na.fail)"},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Global G test for spatial autocorrelation — globalG.test","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw; sequence distance bands used, recommended weights style binary (one c(\"B\", \"C\", \"U\")). zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"less\" \"two.sided\". spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted B1correct default TRUE, TRUE, erratum referenced : \"page 195, coefficient W2 B1, (just center page) 6, 3.\" applied; FALSE, 3 used (CrimeStat IV) adjust.x default TRUE, TRUE, x values observations neighbours omitted denominator G Arc_all_x default FALSE, Arc_all_x=TRUE adjust.x=TRUE, use full x vector part denominator term G na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass permitted.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Global G test for spatial autocorrelation — globalG.test","text":"list class htest containing following components: statistic value standard deviate Getis-Ord G. p.value p-value test. estimate value observed statistic, expectation variance. alternative character string describing alternative hypothesis. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Global G test for spatial autocorrelation — globalG.test","text":"Getis. , Ord, J. K. 1992 analysis spatial association use distance statistics, Geographical Analysis, 24, p. 195; see also Getis. , Ord, J. K. 1993 Erratum, Geographical Analysis, 25, p. 276; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Global G test for spatial autocorrelation — globalG.test","text":"Hisaji ONO hi-ono@mn.xdsl.ne.jp Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/globalG.test.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Global G test for spatial autocorrelation — globalG.test","text":"","code":"nc.sids <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\")[1], quiet=TRUE) sidsrate79 <- (1000*nc.sids$SID79)/nc.sids$BIR79 dists <- c(10, 20, 30, 33, 40, 50, 60, 70, 80, 90, 100) ndists <- length(dists) ZG <- vector(mode=\"list\", length=ndists) names(ZG) <- as.character(dists) milesxy <- cbind(nc.sids$east, nc.sids$north) for (i in 1:ndists) { thisnb <- dnearneigh(milesxy, 0, dists[i]) thislw <- nb2listw(thisnb, style=\"B\", zero.policy=TRUE) ZG[[i]] <- globalG.test(sidsrate79, thislw, zero.policy=TRUE) } #> Warning: neighbour object has 98 sub-graphs #> Warning: neighbour object has 37 sub-graphs #> Warning: neighbour object has 3 sub-graphs t(sapply(ZG, function(x) c(x$estimate[1], x$statistic, p.value=unname(x$p.value)))) #> Global G statistic standard deviate p.value #> 10 0.33548581 0.04859237 0.4806221 #> 20 0.02024945 -0.73262399 0.7681061 #> 30 0.04032434 -0.75011405 0.7734070 #> 33 0.05312271 0.40157023 0.3440002 #> 40 0.07400279 -0.04345713 0.5173314 #> 50 0.11471743 0.58686472 0.2786473 #> 60 0.15457553 -0.35823892 0.6399177 #> 70 0.19839023 -0.27864299 0.6097406 #> 80 0.24606972 -0.18791364 0.5745278 #> 90 0.30073463 0.11457610 0.4543906 #> 100 0.34879996 0.31591356 0.3760341 for (i in 1:ndists) { thisnb <- dnearneigh(milesxy, 0, dists[i]) thislw <- nb2listw(thisnb, style=\"B\", zero.policy=TRUE) ZG[[i]] <- globalG.test(sidsrate79, thislw, zero.policy=TRUE, alternative=\"two.sided\") } #> Warning: neighbour object has 98 sub-graphs #> Warning: neighbour object has 37 sub-graphs #> Warning: neighbour object has 3 sub-graphs t(sapply(ZG, function(x) c(x$estimate[1], x$statistic, p.value=unname(x$p.value)))) #> Global G statistic standard deviate p.value #> 10 0.33548581 0.04859237 0.9612441 #> 20 0.02024945 -0.73262399 0.4637878 #> 30 0.04032434 -0.75011405 0.4531860 #> 33 0.05312271 0.40157023 0.6880003 #> 40 0.07400279 -0.04345713 0.9653371 #> 50 0.11471743 0.58686472 0.5572946 #> 60 0.15457553 -0.35823892 0.7201645 #> 70 0.19839023 -0.27864299 0.7805188 #> 80 0.24606972 -0.18791364 0.8509443 #> 90 0.30073463 0.11457610 0.9087811 #> 100 0.34879996 0.31591356 0.7520681 data(oldcol) crime <- COL.OLD$CRIME is.na(crime) <- sample(1:length(crime), 10) res <- try(globalG.test(crime, nb2listw(COL.nb, style=\"B\"), na.action=na.fail)) #> Error in na.fail.default(x) : missing values in object globalG.test(crime, nb2listw(COL.nb, style=\"B\"), zero.policy=TRUE, na.action=na.omit) #> Warning: subsetting caused increase in subgraph count #> #> \tGetis-Ord global G statistic #> #> data: crime #> weights: nb2listw(COL.nb, style = \"B\") #> omitted: 2, 3, 5, 6, 7, 10, 13, 30, 39, 49 #> n reduced by no-neighbour observations #> #> standard deviate = 3.8084, p-value = 6.993e-05 #> alternative hypothesis: greater #> sample estimates: #> Global G statistic Expectation Variance #> 1.441233e-01 1.123755e-01 6.949287e-05 #> globalG.test(crime, nb2listw(COL.nb, style=\"B\"), zero.policy=TRUE, na.action=na.exclude) #> Warning: subsetting caused increase in subgraph count #> #> \tGetis-Ord global G statistic #> #> data: crime #> weights: nb2listw(COL.nb, style = \"B\") #> omitted: 2, 3, 5, 6, 7, 10, 13, 30, 39, 49 #> n reduced by no-neighbour observations #> #> standard deviate = 3.8084, p-value = 6.993e-05 #> alternative hypothesis: greater #> sample estimates: #> Global G statistic Expectation Variance #> 1.441233e-01 1.123755e-01 6.949287e-05 #> try(globalG.test(crime, nb2listw(COL.nb, style=\"B\"), na.action=na.pass)) #> Error in globalG.test(crime, nb2listw(COL.nb, style = \"B\"), na.action = na.pass) : #> na.pass not permitted"},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":null,"dir":"Reference","previous_headings":"","what":"Graph based spatial weights — graphneigh","title":"Graph based spatial weights — graphneigh","text":"Functions return graph object containing list vertex coordinates indices defining edges. /functions assume coordinates exactly regularly spaced. helper function graph2nb converts graph object neighbour list. plot functions plot graph objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Graph based spatial weights — graphneigh","text":"","code":"gabrielneigh(coords, nnmult=3) relativeneigh(coords, nnmult=3) soi.graph(tri.nb, coords, quadsegs=10) graph2nb(gob, row.names=NULL,sym=FALSE) # S3 method for class 'Gabriel' plot(x, show.points=FALSE, add=FALSE, linecol=par(col), ...) # S3 method for class 'relative' plot(x, show.points=FALSE, add=FALSE, linecol=par(col),...)"},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Graph based spatial weights — graphneigh","text":"coords matrix region point coordinates SpatialPoints object sfc points object nnmult scaling factor memory allocation, default 3; higher values required, function exit error; example thanks Dan Putler tri.nb neighbor list created tri2nb quadsegs number line segments making quarter circle buffer, see nQuadSegs argument geos_unary gob graph object created graph funtions row.names character vector region ids added neighbours list attribute region.id, default seq(1, nrow(x)) sym logical argument indicating whether neighbors symetric (->j j->) x object plotted show.points (logical) add points plot add (logical) add existing plot linecol edge plotting colour ... graphical parameters par(..)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Graph based spatial weights — graphneigh","text":"graph functions produce graphs 2d point set subgraphs Delaunay triangulation. relative neighbor graph defined relation, x y neighbors $$d(x,y) \\le min(max(d(x,z),d(y,z))| z \\S)$$ d() distance, S set points z arbitrary point S. Gabriel graph subgraph delaunay triangulation relative neighbor graph sub-graph. relative neighbor graph defined relation x y Gabriel neighbors $$d(x,y) \\le min((d(x,z)^2 + d(y,z)^2)^{1/2} |z \\S)$$ x,y,z S . sphere influence graph defined finite point set S, let \\(r_x\\) distance point x nearest neighbor S, \\(C_x\\) circle centered x. x y SOI neigbors iff \\(C_x\\) \\(C_y\\) intersect least 2 places. 2016-05-31, Computational Geometry C code replaced calls functions dbscan sf; large quadsegs= argument, behaviour function , otherwise buffer intersections closely approximate original function. See card details “nb” objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Graph based spatial weights — graphneigh","text":"list class Graph following elements np number input points array origin ids array destination ids nedges number edges graph x input x coordinates y input y coordinates helper functions return nb object list integer vectors containing neighbour region number ids.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Graph based spatial weights — graphneigh","text":"Matula, D. W. Sokal R. R. 1980, Properties Gabriel graphs relevant geographic variation research clustering points plane, Geographic Analysis, 12(3), pp. 205-222. Toussaint, G. T. 1980, relative neighborhood graph finite planar set, Pattern Recognition, 12(4), pp. 261-268. Kirkpatrick, D. G. Radke, J. D. 1985, framework computational morphology. Computational Geometry, Ed. G. T. Toussaint, North Holland.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Graph based spatial weights — graphneigh","text":"Nicholas Lewin-Koh nikko@hailmail.net","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/graphneigh.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Graph based spatial weights — graphneigh","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) sf_obj <- st_centroid(st_geometry(columbus), of_largest_polygon) sp_obj <- as(sf_obj, \"Spatial\") coords <- st_coordinates(sf_obj) suppressMessages(col.tri.nb <- tri2nb(coords)) col.gab.nb <- graph2nb(gabrielneigh(coords), sym=TRUE) col.rel.nb <- graph2nb(relativeneigh(coords), sym=TRUE) par(mfrow=c(2,2)) plot(st_geometry(columbus), border=\"grey\") plot(col.tri.nb,coords,add=TRUE) title(main=\"Delaunay Triangulation\", cex.main=0.6) plot(st_geometry(columbus), border=\"grey\") plot(col.gab.nb, coords, add=TRUE) title(main=\"Gabriel Graph\", cex.main=0.6) plot(st_geometry(columbus), border=\"grey\") plot(col.rel.nb, coords, add=TRUE) title(main=\"Relative Neighbor Graph\", cex.main=0.6) plot(st_geometry(columbus), border=\"grey\") if (require(\"dbscan\", quietly=TRUE)) { col.soi.nb <- graph2nb(soi.graph(col.tri.nb,coords), sym=TRUE) plot(col.soi.nb, coords, add=TRUE) title(main=\"Sphere of Influence Graph\", cex.main=0.6) } par(mfrow=c(1,1)) col.tri.nb_sf <- tri2nb(sf_obj) all.equal(col.tri.nb, col.tri.nb_sf, check.attributes=FALSE) #> [1] TRUE col.tri.nb_sp <- tri2nb(sp_obj) all.equal(col.tri.nb, col.tri.nb_sp, check.attributes=FALSE) #> [1] TRUE if (require(\"dbscan\", quietly=TRUE)) { col.soi.nb_sf <- graph2nb(soi.graph(col.tri.nb, sf_obj), sym=TRUE) all.equal(col.soi.nb, col.soi.nb_sf, check.attributes=FALSE) col.soi.nb_sp <- graph2nb(soi.graph(col.tri.nb, sp_obj), sym=TRUE) all.equal(col.soi.nb, col.soi.nb_sp, check.attributes=FALSE) } col.gab.nb_sp <- graph2nb(gabrielneigh(sp_obj), sym=TRUE) all.equal(col.gab.nb, col.gab.nb_sp, check.attributes=FALSE) #> [1] TRUE col.gab.nb_sf <- graph2nb(gabrielneigh(sf_obj), sym=TRUE) all.equal(col.gab.nb, col.gab.nb_sf, check.attributes=FALSE) #> [1] TRUE col.rel.nb_sp <- graph2nb(relativeneigh(sp_obj), sym=TRUE) all.equal(col.rel.nb, col.rel.nb_sp, check.attributes=FALSE) #> [1] TRUE col.rel.nb_sf <- graph2nb(relativeneigh(sf_obj), sym=TRUE) all.equal(col.rel.nb, col.rel.nb_sf, check.attributes=FALSE) #> [1] TRUE dx <- rep(0.25*0:4,5) dy <- c(rep(0,5),rep(0.25,5),rep(0.5,5), rep(0.75,5),rep(1,5)) m <- cbind(c(dx, dx, 3+dx, 3+dx), c(dy, 3+dy, dy, 3+dy)) cat(try(res <- gabrielneigh(m), silent=TRUE), \"\\n\") #> Error in gabrielneigh(m) : number of neighbours overrun - increase nnmult #> res <- gabrielneigh(m, nnmult=4) summary(graph2nb(res)) #> Neighbour list object: #> Number of regions: 100 #> Number of nonzero links: 342 #> Percentage nonzero weights: 3.42 #> Average number of links: 3.42 #> 1 region with no links: #> 100 #> Non-symmetric neighbours list #> Link number distribution: #> #> 0 1 2 3 4 5 #> 1 8 10 18 55 8 #> 8 least connected regions: #> 46 47 48 49 96 97 98 99 with 1 link #> 8 most connected regions: #> 10 15 20 25 30 35 40 45 with 5 links grd <- as.matrix(expand.grid(x=1:5, y=1:5)) #gridded data r2 <- gabrielneigh(grd) set.seed(1) grd1 <- as.matrix(expand.grid(x=1:5, y=1:5)) + matrix(runif(50, .0001, .0006), nrow=25) r3 <- gabrielneigh(grd1) opar <- par(mfrow=c(1,2)) plot(r2, show=TRUE, linecol=2) plot(r3, show=TRUE, linecol=2) par(opar) # example of reading points with readr::read_csv() yielding a tibble load(system.file(\"etc/misc/coords.rda\", package=\"spdep\")) class(coords) #> [1] \"spec_tbl_df\" \"tbl_df\" \"tbl\" \"data.frame\" graph2nb(gabrielneigh(coords)) #> Neighbour list object: #> Number of regions: 100 #> Number of nonzero links: 179 #> Percentage nonzero weights: 1.79 #> Average number of links: 1.79 #> 23 regions with no links: #> 22, 39, 43, 53, 58, 61, 66, 70, 71, 73, 76, 78, 81, 88, 90, 93, 94, 95, #> 96, 97, 98, 99, 100 #> Non-symmetric neighbours list graph2nb(relativeneigh(coords)) #> Neighbour list object: #> Number of regions: 100 #> Number of nonzero links: 117 #> Percentage nonzero weights: 1.17 #> Average number of links: 1.17 #> 31 regions with no links: #> 22, 29, 33, 39, 41, 42, 43, 44, 53, 58, 61, 64, 65, 66, 70, 71, 73, 75, #> 76, 78, 81, 88, 90, 93, 94, 95, 96, 97, 98, 99, 100 #> Non-symmetric neighbours list"},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Construct neighbours for a GridTopology — grid2nb","title":"Construct neighbours for a GridTopology — grid2nb","text":"function builds neighbours list grid topology. works k-dimentional grid topology, k>=1.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Construct neighbours for a GridTopology — grid2nb","text":"","code":"grid2nb(grid, d = grid@cells.dim, queen = TRUE, nb = TRUE, self = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Construct neighbours for a GridTopology — grid2nb","text":"grid object class GridTopology. One can avoid supply just suplying dimentions d argument. d scalar (one dimentional grid) length k vector specyfying number grid cells direction k dimentions. queen Logical. Default TRUE. inform queen neighbourhood structure considered. FALSE, hyper-cube common face considered neighbour. TRUE, single shared coordinate meets contiguity condition. nb Default TRUE. TRUE, return result neighbours list class nb. FALSE, result matrix 3^k columns self = TRUE 3^k-1 self = FALSE. Zeros used hyper-cubes boundaries. self Default FALSE, indicate hyper-cube neighbour considered neighbour.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Construct neighbours for a GridTopology — grid2nb","text":"Either matrix, “nb” FALSE neighbours list class nb. See card details “nb” objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Construct neighbours for a GridTopology — grid2nb","text":"applies k-dimentional grid topology.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Construct neighbours for a GridTopology — grid2nb","text":"Elias T Krainski eliaskrainski@gmail.com","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/grid2nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Construct neighbours for a GridTopology — grid2nb","text":"","code":"nb <- grid2nb(d = c(5L, 5L, 5L)) nb #> Neighbour list object: #> Number of regions: 125 #> Number of nonzero links: 2072 #> Percentage nonzero weights: 13.2608 #> Average number of links: 16.576 summary(nb) #> Neighbour list object: #> Number of regions: 125 #> Number of nonzero links: 2072 #> Percentage nonzero weights: 13.2608 #> Average number of links: 16.576 #> Link number distribution: #> #> 7 11 17 26 #> 8 36 54 27 #> 8 least connected regions: #> 1 5 21 25 101 105 121 125 with 7 links #> 27 most connected regions: #> 32 33 34 37 38 39 42 43 44 57 58 59 62 63 64 67 68 69 82 83 84 87 88 89 92 93 94 with 26 links if (require(\"sp\", quietly=TRUE)) { gt <- GridTopology(c(.125,.1), c(.25,.2), c(4L, 5L)) nb1 <- grid2nb(gt, queen = FALSE) nb2 <- grid2nb(gt) sg <- SpatialGrid(gt) plot(sg, lwd=3) plot(nb1, coordinates(sg), add=TRUE, lty=2, col=2, lwd=2) plot(nb2, coordinates(sg), add=TRUE, lty=3, col=4) str(grid2nb(d=5)) } #> List of 5 #> $ : int 2 #> $ : int [1:2] 1 3 #> $ : int [1:2] 2 4 #> $ : int [1:2] 3 5 #> $ : int 4 #> - attr(*, \"class\")= chr \"nb\""},{"path":"https://r-spatial.github.io/spdep/reference/hotspotmap.html","id":null,"dir":"Reference","previous_headings":"","what":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","title":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","text":"Used return factor showing -called cluster classification local indicators spatial association local Moran's , local Geary's C (multivariate variant) local Getis-Ord G. factor vector can added spatial object mapping. obj class licd, list six factors measures local composition (analytical permutation), local configuration (analytical permutation), combined measures, interaction composition configuration, simplified recoding .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/hotspotmap.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","text":"","code":"hotspot(obj, ...) # Default S3 method hotspot(obj, ...) # S3 method for class 'localmoran' hotspot(obj, Prname, cutoff=0.005, quadrant.type=\"mean\", p.adjust=\"fdr\", droplevels=TRUE, ...) # S3 method for class 'summary.localmoransad' hotspot(obj, Prname, cutoff=0.005, quadrant.type=\"mean\", p.adjust=\"fdr\", droplevels=TRUE, ...) # S3 method for class 'data.frame.localmoranex' hotspot(obj, Prname, cutoff=0.005, quadrant.type=\"mean\", p.adjust=\"fdr\", droplevels=TRUE, ...) # S3 method for class 'localG' hotspot(obj, Prname, cutoff=0.005, p.adjust=\"fdr\", droplevels=TRUE, ...) # S3 method for class 'localC' hotspot(obj, Prname, cutoff=0.005, p.adjust=\"fdr\", droplevels=TRUE, ...) # S3 method for class 'licd' hotspot(obj, type = \"both\", cutoff = 0.05, p.adjust = \"none\", droplevels = TRUE, control = list(), ...)"},{"path":"https://r-spatial.github.io/spdep/reference/hotspotmap.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","text":"obj object class localmoran, localC localG Prname character string, name column containing probability values classified cluster type found “interesting” cutoff Default 0.005, probability value cutoff larger observation found “interesting” p.adjust Default \"fdr\", p.adjust() method used, one c(\"holm\", \"hochberg\", \"hommel\", \"bonferroni\", \"BH\", \"\", \"fdr\", \"none\") droplevels Default TRUE, empty levels input cluster factor dropped quadrant.type Default \"mean\", \"localmoran\" objects , can c(\"mean\", \"median\", \"pysal\") partition Moran scatterplot; \"mean\" partitions means variable spatial lag, \"median\" medians variable spatial lag, \"pysal\" zero centred variable spatial lag type obj class licd, default , may also comp local composition config local configuration control obj class licd, default binomial_sidak 2, binomial_overlap TRUE, jcm_sidak 3. binomial_overlap may set FALSE avoid Binomial probability values summing unity - tests Boots (2003, p. 141) overlap (>= <=), Šidák exponents may set 1 prevent -observation correction 2 Binomial 3 Normal probability values per observation ... arguments passed methods.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/hotspotmap.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","text":"factor showing -called cluster classification local indicators spatial association. obj class licd, list six factors measures local composition (analytical permutation), local configuration (analytical permutation), combined measures, interaction composition configuration, simplified recoding .","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/hotspotmap.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","text":"Roger Bivand","code":""},{"path":"https://r-spatial.github.io/spdep/reference/hotspotmap.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Cluster Classifications for Local Indicators of Spatial Association and Local Indicators for Categorical Data — hotspot","text":"","code":"orig <- spData::africa.rook.nb listw <- nb2listw(orig) x <- spData::afcon$totcon set.seed(1) C <- localC_perm(x, listw) Ch <- hotspot(C, Prname=\"Pr(z != E(Ci)) Sim\", cutoff=0.05, p.adjust=\"none\") table(addNA(Ch)) #> #> High-High Low-Low #> 4 1 37 set.seed(1) I <- localmoran_perm(x, listw) Ih <- hotspot(I, Prname=\"Pr(z != E(Ii)) Sim\", cutoff=0.05, p.adjust=\"none\") table(addNA(Ih)) #> #> High-High #> 6 36 Is <- summary(localmoran.sad(lm(x ~ 1), nb=orig)) Ish <- hotspot(Is, Prname=\"Pr. (Sad)\", cutoff=0.05, p.adjust=\"none\") table(addNA(Ish)) #> #> High-High #> 5 37 Ie <- as.data.frame(localmoran.exact(lm(x ~ 1), nb=orig)) Ieh <- hotspot(Ie, Prname=\"Pr. (exact)\", cutoff=0.05, p.adjust=\"none\") table(addNA(Ieh)) #> #> High-High #> 5 37 set.seed(1) G <- localG_perm(x, listw) Gh <- hotspot(G, Prname=\"Pr(z != E(Gi)) Sim\", cutoff=0.05, p.adjust=\"none\") table(addNA(Gh)) #> #> High #> 6 36"},{"path":"https://r-spatial.github.io/spdep/reference/include.self.html","id":null,"dir":"Reference","previous_headings":"","what":"Include self in neighbours list — include.self","title":"Include self in neighbours list — include.self","text":"function includes region list neighbours, sets attribute \"self.included\" TRUE; remove.self reverts effects include.self.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/include.self.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Include self in neighbours list — include.self","text":"","code":"include.self(nb) remove.self(nb)"},{"path":"https://r-spatial.github.io/spdep/reference/include.self.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Include self in neighbours list — include.self","text":"nb input neighbours list class nb","code":""},{"path":"https://r-spatial.github.io/spdep/reference/include.self.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Include self in neighbours list — include.self","text":"function returns object class nb list integer vectors containing neighbour region number ids; attribute \"self.included\" set TRUE.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/include.self.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Include self in neighbours list — include.self","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/include.self.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Include self in neighbours list — include.self","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries summary(col.gal.nb, coords) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> Link number distribution: #> #> 2 3 4 5 6 7 8 9 10 #> 7 7 13 4 9 6 1 1 1 #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links summary(include.self(col.gal.nb), coords) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 279 #> Percentage nonzero weights: 11.62016 #> Average number of links: 5.693878 #> Link number distribution: #> #> 3 4 5 6 7 8 9 10 11 #> 7 7 13 4 9 6 1 1 1 #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 3 links #> 1 most connected region: #> 20 with 11 links summary(remove.self(include.self(col.gal.nb)), coords) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> Link number distribution: #> #> 2 3 4 5 6 7 8 9 10 #> 7 7 13 4 9 6 1 1 1 #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links"},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Permutation test for same colour join count statistics — joincount.mc","title":"Permutation test for same colour join count statistics — joincount.mc","text":"permutation test colour join count statistics calculated using nsim random permutations fx given spatial weighting scheme, establish ranks observed statistics (colour) relation nsim simulated values.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Permutation test for same colour join count statistics — joincount.mc","text":"","code":"joincount.mc(fx, listw, nsim, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\", spChk=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Permutation test for same colour join count statistics — joincount.mc","text":"fx factor length neighbours weights objects listw; use ordered factor well understood listw listw object created example nb2listw nsim number permutations zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"two.sided\", \"less\". spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption()","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Permutation test for same colour join count statistics — joincount.mc","text":"list class jclist lists class htest mc.sim k colours containing following components: statistic value observed statistic. parameter rank observed statistic. method character string giving method used. data.name character string giving name(s) data. p.value pseudo p-value test. alternative character string describing alternative hypothesis. estimate mean variance simulated distribution. res nsim simulated values statistic, final element observed statistic","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Permutation test for same colour join count statistics — joincount.mc","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 63-5.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Permutation test for same colour join count statistics — joincount.mc","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/joincount.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Permutation test for same colour join count statistics — joincount.mc","text":"","code":"data(oldcol) HICRIME <- cut(COL.OLD$CRIME, breaks=c(0,35,80), labels=c(\"low\",\"high\")) names(HICRIME) <- rownames(COL.OLD) joincount.mc(HICRIME, nb2listw(COL.nb, style=\"B\"), nsim=99, alternative=\"two.sided\") #> #> \tMonte-Carlo simulation of join-count statistic #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"B\") #> number of simulations + 1: 100 #> #> Join-count statistic for low = 34, rank of observed statistic = 88.5, #> p-value = 0.23 #> alternative hypothesis: two.sided #> sample estimates: #> mean of simulation variance of simulation #> 28.96970 18.19295 #> #> #> \tMonte-Carlo simulation of join-count statistic #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"B\") #> number of simulations + 1: 100 #> #> Join-count statistic for high = 54, rank of observed statistic = 100, #> p-value < 2.2e-16 #> alternative hypothesis: two.sided #> sample estimates: #> mean of simulation variance of simulation #> 26.83838 20.13688 #> joincount.test(HICRIME, nb2listw(COL.nb, style=\"B\"), alternative=\"two.sided\") #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"B\") #> #> Std. deviate for low = 1.0141, p-value = 0.3105 #> alternative hypothesis: two.sided #> sample estimates: #> Same colour statistic Expectation Variance #> 34.00000 29.59184 18.89550 #> #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"B\") #> #> Std. deviate for high = 6.3307, p-value = 2.44e-10 #> alternative hypothesis: two.sided #> sample estimates: #> Same colour statistic Expectation Variance #> 54.00000 27.22449 17.88838 #>"},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":null,"dir":"Reference","previous_headings":"","what":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"function tallying join counts -colour different colour spatial objects, neighbour relations defined weights list. Given global counts colour, expected counts variances calculated non-free sampling, z-value reported. Since multiple tests reported, p-values given, allowing user adjust significance level applied. Jtot count different-colour joins.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"","code":"joincount.multi(fx, listw, zero.policy = attr(listw, \"zero.policy\"), spChk = NULL, adjust.n=TRUE) # S3 method for class 'jcmulti' print(x, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"fx factor length neighbours weights objects listw; use ordered factor well understood listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted consistently (including spdep 0.3-28 adjustment inconsistent - thanks Tomoki NAKAYA careful bug report) spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() x object printed ... arguments passed printing","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"matrix class jcmulti row column names observed expected counts, variance, z-value.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 20; Upton, G., Fingleton, B. 1985 Spatial data analysis example: point pattern qualitative data, Wiley, pp. 158–170.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"derivation test (Cliff Ord, 1981, p. 18) assumes weights matrix symmetric. inherently non-symmetric matrices, k-nearest neighbour matrices, listw2U() can used make matrix symmetric. non-symmetric weights matrix cases, variance test statistic may negative.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/joincount.multi.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"BB, BW and Jtot join count statistic for k-coloured factors — joincount.multi","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) HICRIME <- cut(columbus$CRIME, breaks=c(0,35,80), labels=c(\"low\",\"high\")) (nb <- poly2nb(columbus)) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 236 #> Percentage nonzero weights: 9.829238 #> Average number of links: 4.816327 lw <- nb2listw(nb, style=\"B\") joincount.multi(HICRIME, lw) #> Joincount Expected Variance z-value #> low:low 35.000 30.102 19.247 1.1164 #> high:high 54.000 27.694 18.219 6.1630 #> high:low 29.000 60.204 26.630 -6.0468 #> Jtot 29.000 60.204 26.630 -6.0468 col_geoms <- st_geometry(columbus) col_geoms[21] <- st_buffer(col_geoms[21], dist=-0.05) st_geometry(columbus) <- col_geoms (nb <- poly2nb(columbus)) #> Warning: some observations have no neighbours; #> if this seems unexpected, try increasing the snap argument. #> Warning: neighbour object has 3 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> 1 region with no links: #> 21 #> 3 disjoint connected subgraphs lw <- nb2listw(nb, style=\"B\", zero.policy=TRUE) joincount.multi(HICRIME, lw) #> Joincount Expected Variance z-value #> low:low 35.000 30.585 19.350 1.0036 #> high:high 52.000 28.138 18.342 5.5716 #> high:low 28.000 61.170 25.882 -6.5200 #> Jtot 28.000 61.170 33.190 -5.7577 if (FALSE) { # \\dontrun{ data(oldcol) HICRIME <- cut(COL.OLD$CRIME, breaks=c(0,35,80), labels=c(\"low\",\"high\")) names(HICRIME) <- rownames(COL.OLD) joincount.multi(HICRIME, nb2listw(COL.nb, style=\"B\")) data(hopkins, package=\"spData\") image(1:32, 1:32, hopkins[5:36,36:5], breaks=c(-0.5, 3.5, 20), col=c(\"white\", \"black\")) box() hopkins.rook.nb <- cell2nb(32, 32, type=\"rook\") unlist(spweights.constants(nb2listw(hopkins.rook.nb, style=\"B\"))) hopkins.queen.nb <- cell2nb(32, 32, type=\"queen\") hopkins.bishop.nb <- diffnb(hopkins.rook.nb, hopkins.queen.nb, verbose=FALSE) hopkins4 <- hopkins[5:36,36:5] hopkins4[which(hopkins4 > 3, arr.ind=TRUE)] <- 4 hopkins4.f <- factor(hopkins4) table(hopkins4.f) joincount.multi(hopkins4.f, nb2listw(hopkins.rook.nb, style=\"B\")) cat(\"replicates Upton & Fingleton table 3.4 (p. 166)\\n\") joincount.multi(hopkins4.f, nb2listw(hopkins.bishop.nb, style=\"B\")) cat(\"replicates Upton & Fingleton table 3.6 (p. 168)\\n\") joincount.multi(hopkins4.f, nb2listw(hopkins.queen.nb, style=\"B\")) cat(\"replicates Upton & Fingleton table 3.7 (p. 169)\\n\") } # } GDAL37 <- numeric_version(unname(sf::sf_extSoftVersion()[\"GDAL\"]), strict=FALSE) (GDAL37 <- ifelse(is.na(GDAL37), FALSE, GDAL37 >= \"3.7.0\")) #> [1] TRUE file <- \"etc/shapes/GB_2024_southcoast_50m.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) { sc50m <- st_read(zipfile) } else { td <- tempdir() bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE) target <- unzip(zipfile, files=bn, exdir=td) sc50m <- st_read(target) } #> Reading layer `GB_2024_southcoast_50m' from data source #> `C:\\Users\\rzomor2\\AppData\\Local\\Temp\\RtmpErQTm3\\temp_libpath1a5cde63ff3\\spdep\\etc\\shapes\\GB_2024_southcoast_50m.gpkg.zip' #> using driver `GPKG' #> Simple feature collection with 119 features and 19 fields #> Geometry type: MULTIPOLYGON #> Dimension: XY #> Bounding box: xmin: 82643.12 ymin: 5342.9 xmax: 640301.6 ymax: 187226.2 #> Projected CRS: OSGB36 / British National Grid sc50m$Winner <- factor(sc50m$Winner, levels=c(\"Con\", \"Green\", \"Lab\", \"LD\")) plot(sc50m[,\"Winner\"], pal=c(\"#2297E6\", \"#61D04F\", \"#DF536B\", \"#F5C710\")) nb_sc_50m <- poly2nb(sc50m, row.names=as.character(sc50m$Constituency)) #> Warning: neighbour object has 2 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. sub2 <- attr(nb_sc_50m, \"region.id\")[attr(nb_sc_50m, \"ncomp\")$comp.id == 2L] iowe <- match(sub2[1], attr(nb_sc_50m, \"region.id\")) diowe <- c(st_distance(sc50m[iowe,], sc50m)) meet_criterion <- sum(diowe <= units::set_units(5000, \"m\")) cands <- attr(nb_sc_50m, \"region.id\")[order(diowe)[1:meet_criterion]] nb_sc_50m_iowe <- addlinks1(nb_sc_50m, from = cands[1], to = cands[3:meet_criterion]) ioww <- match(sub2[2], attr(nb_sc_50m, \"region.id\")) dioww <- c(st_distance(sc50m[ioww,], sc50m)) meet_criterion <- sum(dioww <= units::set_units(5000, \"m\")) cands <- attr(nb_sc_50m, \"region.id\")[order(dioww)[1:meet_criterion]] nb_sc_50m_iow <- addlinks1(nb_sc_50m_iowe, from = cands[2], to = cands[3:meet_criterion]) nb_sc_1_2 <- nblag_cumul(nblag(nb_sc_50m_iow, 2)) joincount.multi(sc50m$Winner, nb2listw(nb_sc_1_2, style=\"B\")) #> Joincount Expected Variance z-value #> Con:Con 146.0000 84.4324 116.3530 5.7077 #> Green:Green 0.0000 0.0000 0.0000 NaN #> Lab:Lab 63.0000 98.1057 136.0379 -3.0099 #> LD:LD 100.0000 75.8866 103.9440 2.3651 #> Green:Con 4.0000 4.4438 5.8532 -0.1834 #> Lab:Con 184.0000 186.6401 180.9233 -0.1963 #> Lab:Green 3.0000 4.7856 6.4663 -0.7022 #> LD:Con 198.0000 164.4210 166.3583 2.6034 #> LD:Green 4.0000 4.2159 5.4573 -0.0924 #> LD:Lab 98.0000 177.0688 175.2035 -5.9736 #> Jtot 491.0000 541.5753 153.6123 -4.0806"},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":null,"dir":"Reference","previous_headings":"","what":"BB join count statistic for k-coloured factors — joincount.test","title":"BB join count statistic for k-coloured factors — joincount.test","text":"BB join count test spatial autocorrelation using spatial weights matrix weights list form testing whether -colour joins occur frequently expected zones labelled spatially random way. assumptions underlying test sensitive form graph neighbour relationships factors, results may checked joincount.mc permutations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"BB join count statistic for k-coloured factors — joincount.test","text":"","code":"joincount.test(fx, listw, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\", sampling=\"nonfree\", spChk=NULL, adjust.n=TRUE) # S3 method for class 'jclist' print(x, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"BB join count statistic for k-coloured factors — joincount.test","text":"fx factor length neighbours weights objects listw; use ordered factor well understood listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"less\" \"two.sided\". sampling default “nonfree”, may “free” adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted consistently (including spdep 0.3-28 adjustment inconsistent - thanks Tomoki NAKAYA careful bug report) spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() x object printed ... arguments passed printing","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"BB join count statistic for k-coloured factors — joincount.test","text":"list class jclist lists class htest k colours containing following components: statistic value standard deviate join count statistic. p.value p-value test. estimate value observed statistic, expectation variance non-free sampling. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"BB join count statistic for k-coloured factors — joincount.test","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, pp. 19-20.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"BB join count statistic for k-coloured factors — joincount.test","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"BB join count statistic for k-coloured factors — joincount.test","text":"derivation test (Cliff Ord, 1981, p. 18) assumes weights matrix symmetric. inherently non-symmetric matrices, k-nearest neighbour matrices, listw2U() can used make matrix symmetric. non-symmetric weights matrix cases, variance test statistic may negative.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/joincount.test.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"BB join count statistic for k-coloured factors — joincount.test","text":"","code":"data(oldcol) HICRIME <- cut(COL.OLD$CRIME, breaks=c(0,35,80), labels=c(\"low\",\"high\")) names(HICRIME) <- rownames(COL.OLD) joincount.test(HICRIME, nb2listw(COL.nb, style=\"B\")) #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"B\") #> #> Std. deviate for low = 1.0141, p-value = 0.1553 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 34.00000 29.59184 18.89550 #> #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"B\") #> #> Std. deviate for high = 6.3307, p-value = 1.22e-10 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 54.00000 27.22449 17.88838 #> joincount.test(HICRIME, nb2listw(COL.nb, style=\"B\"), sampling=\"free\") #> #> \tJoin count test under free sampling #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"B\") #> #> Std. deviate for low = 0.3993, p-value = 0.3448 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 34.00000 30.19575 90.76809 #> #> #> \tJoin count test under free sampling #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"B\") #> #> Std. deviate for high = 2.8518, p-value = 0.002173 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 54.0000 27.8284 84.2198 #> joincount.test(HICRIME, nb2listw(COL.nb, style=\"C\")) #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"C\") #> #> Std. deviate for low = 1.0141, p-value = 0.1553 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 7.1810345 6.2500000 0.8428969 #> #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"C\") #> #> Std. deviate for high = 6.3307, p-value = 1.22e-10 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 11.4051724 5.7500000 0.7979712 #> joincount.test(HICRIME, nb2listw(COL.nb, style=\"S\")) #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"S\") #> #> Std. deviate for low = 2.5786, p-value = 0.00496 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 8.2425673 6.2500000 0.5971141 #> #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"S\") #> #> Std. deviate for high = 6.1736, p-value = 3.337e-10 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 10.4249914 5.7500000 0.5734265 #> joincount.test(HICRIME, nb2listw(COL.nb, style=\"W\")) #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"W\") #> #> Std. deviate for low = 4.6675, p-value = 1.524e-06 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 9.5190476 6.2500000 0.4905378 #> #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: nb2listw(COL.nb, style = \"W\") #> #> Std. deviate for high = 5.1205, p-value = 1.523e-07 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 9.2920635 5.7500000 0.4784979 #> by(card(COL.nb), HICRIME, summary) #> HICRIME: low #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> 2.00 2.00 4.00 3.84 4.00 10.00 #> ------------------------------------------------------------ #> HICRIME: high #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> 3.000 4.750 6.000 5.667 7.000 9.000 print(is.symmetric.nb(COL.nb)) #> [1] TRUE coords.OLD <- cbind(COL.OLD$X, COL.OLD$Y) COL.k4.nb <- knn2nb(knearneigh(coords.OLD, 4)) print(is.symmetric.nb(COL.k4.nb)) #> [1] FALSE joincount.test(HICRIME, nb2listw(COL.k4.nb, style=\"B\")) #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: nb2listw(COL.k4.nb, style = \"B\") #> #> Std. deviate for low = 4.3698, p-value = 6.217e-06 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 36.500000 25.000000 6.925749 #> #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: nb2listw(COL.k4.nb, style = \"B\") #> #> Std. deviate for high = 6.7293, p-value = 8.523e-12 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 40.500000 23.000000 6.762918 #> cat(\"Note non-symmetric weights matrix - use listw2U()\\n\") #> Note non-symmetric weights matrix - use listw2U() joincount.test(HICRIME, listw2U(nb2listw(COL.k4.nb, style=\"B\"))) #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: listw2U(nb2listw(COL.k4.nb, style = \"B\")) #> #> Std. deviate for low = 4.3698, p-value = 6.217e-06 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 36.500000 25.000000 6.925749 #> #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: listw2U(nb2listw(COL.k4.nb, style = \"B\")) #> #> Std. deviate for high = 6.7293, p-value = 8.523e-12 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 40.500000 23.000000 6.762918 #> columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) HICRIME <- cut(columbus$CRIME, breaks=c(0,35,80), labels=c(\"low\",\"high\")) (nb <- poly2nb(columbus)) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 236 #> Percentage nonzero weights: 9.829238 #> Average number of links: 4.816327 lw <- nb2listw(nb, style=\"B\") joincount.test(HICRIME, lw) #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: lw #> #> Std. deviate for low = 1.1164, p-value = 0.1321 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 35.00000 30.10204 19.24708 #> #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: lw #> #> Std. deviate for high = 6.163, p-value = 3.57e-10 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 54.00000 27.69388 18.21936 #> col_geoms <- st_geometry(columbus) col_geoms[21] <- st_buffer(col_geoms[21], dist=-0.05) st_geometry(columbus) <- col_geoms (nb <- poly2nb(columbus)) #> Warning: some observations have no neighbours; #> if this seems unexpected, try increasing the snap argument. #> Warning: neighbour object has 3 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> 1 region with no links: #> 21 #> 3 disjoint connected subgraphs lw <- nb2listw(nb, style=\"B\", zero.policy=TRUE) joincount.test(HICRIME, lw) #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: lw #> #> Std. deviate for low = 1.0036, p-value = 0.1578 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 35.00000 30.58511 19.35032 #> #> #> \tJoin count test under nonfree sampling #> #> data: HICRIME #> weights: lw #> #> Std. deviate for high = 5.5716, p-value = 1.262e-08 #> alternative hypothesis: greater #> sample estimates: #> Same colour statistic Expectation Variance #> 52.00000 28.13830 18.34187 #>"},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":null,"dir":"Reference","previous_headings":"","what":"K nearest neighbours for spatial weights — knearneigh","title":"K nearest neighbours for spatial weights — knearneigh","text":"function returns matrix indices points belonging set k nearest neighbours . longlat = TRUE, Great Circle distances used. warning given identical points found.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"K nearest neighbours for spatial weights — knearneigh","text":"","code":"knearneigh(x, k=1, longlat = NULL, use_kd_tree=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"K nearest neighbours for spatial weights — knearneigh","text":"x matrix point coordinates, object inheriting SpatialPoints \"sf\" \"sfc\" object; \"sf\" \"sfc\" object geometries geographical coordinates (sf::st_is_longlat(x) == TRUE sf::sf_use_s2() == TRUE), s2 used find neighbours uses spatial indexing https://github.com/r-spatial/s2/issues/125 opposed legacy method uses brute-force k number nearest neighbours returned; identical points present, k least large largest count identical points (k smaller, error occur s2 used) longlat TRUE point coordinates longitude-latitude decimal degrees, case distances measured kilometers; x SpatialPoints object \"sf\" \"sfc\" object, value taken object ; longlat override kd_tree use_kd_tree logical value, dbscan package available, use finding k nearest neighbours coordinates planar, identical points; https://github.com/r-spatial/spdep/issues/38, input data may two columns dbscan used","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"K nearest neighbours for spatial weights — knearneigh","text":"underlying legacy C code based knn function class package.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"K nearest neighbours for spatial weights — knearneigh","text":"list class knn nn integer matrix region number ids np number input points k input required k dimension number columns x x input coordinates","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"K nearest neighbours for spatial weights — knearneigh","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/knearneigh.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"K nearest neighbours for spatial weights — knearneigh","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE) col.knn <- knearneigh(coords, k=4) plot(st_geometry(columbus), border=\"grey\") plot(knn2nb(col.knn), coords, add=TRUE) title(main=\"K nearest neighbours, k = 4\") data(state) us48.fipsno <- read.geoda(system.file(\"etc/weights/us48.txt\", package=\"spdep\")[1]) if (as.numeric(paste(version$major, version$minor, sep=\"\")) < 19) { m50.48 <- match(us48.fipsno$\"State.name\", state.name) } else { m50.48 <- match(us48.fipsno$\"State_name\", state.name) } xy <- as.matrix(as.data.frame(state.center))[m50.48,] llk4.nb <- knn2nb(knearneigh(xy, k=4, longlat=FALSE)) gck4.nb <- knn2nb(knearneigh(xy, k=4, longlat=TRUE)) plot(llk4.nb, xy) plot(diffnb(llk4.nb, gck4.nb), xy, add=TRUE, col=\"red\", lty=2) #> Warning: neighbour object has 22 sub-graphs title(main=\"Differences between Euclidean and Great Circle k=4 neighbours\") summary(llk4.nb, xy, longlat=TRUE, scale=0.5) #> Neighbour list object: #> Number of regions: 48 #> Number of nonzero links: 192 #> Percentage nonzero weights: 8.333333 #> Average number of links: 4 #> Non-symmetric neighbours list #> Link number distribution: #> #> 4 #> 48 #> 48 least connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links #> 48 most connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links summary(gck4.nb, xy, longlat=TRUE, scale=0.5) #> Neighbour list object: #> Number of regions: 48 #> Number of nonzero links: 192 #> Percentage nonzero weights: 8.333333 #> Average number of links: 4 #> Non-symmetric neighbours list #> Link number distribution: #> #> 4 #> 48 #> 48 least connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links #> 48 most connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links #xy1 <- SpatialPoints((as.data.frame(state.center))[m50.48,], # proj4string=CRS(\"+proj=longlat +ellps=GRS80\")) #gck4a.nb <- knn2nb(knearneigh(xy1, k=4)) #summary(gck4a.nb, xy1, scale=0.5) xy1 <- st_as_sf((as.data.frame(state.center))[m50.48,], coords=1:2, crs=st_crs(\"OGC:CRS84\")) old_use_s2 <- sf_use_s2() sf_use_s2(TRUE) system.time(gck4a.nb <- knn2nb(knearneigh(xy1, k=4))) #> user system elapsed #> 0.02 0.00 0.02 summary(gck4a.nb, xy1, scale=0.5) #> Neighbour list object: #> Number of regions: 48 #> Number of nonzero links: 192 #> Percentage nonzero weights: 8.333333 #> Average number of links: 4 #> Non-symmetric neighbours list #> Link number distribution: #> #> 4 #> 48 #> 48 least connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links #> 48 most connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links sf_use_s2(FALSE) #> Spherical geometry (s2) switched off system.time(gck4a.nb <- knn2nb(knearneigh(xy1, k=4))) #> user system elapsed #> 0.00 0.00 0.01 summary(gck4a.nb, xy1, scale=0.5) #> Neighbour list object: #> Number of regions: 48 #> Number of nonzero links: 192 #> Percentage nonzero weights: 8.333333 #> Average number of links: 4 #> Non-symmetric neighbours list #> Link number distribution: #> #> 4 #> 48 #> 48 least connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links #> 48 most connected regions: #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links sf_use_s2(old_use_s2) #> Spherical geometry (s2) switched on # https://github.com/r-spatial/spdep/issues/38 run <- FALSE if (require(\"dbscan\", quietly=TRUE)) run <- TRUE if (run) { set.seed(1) x <- cbind(runif(50), runif(50), runif(50)) out <- knearneigh(x, k=5) knn2nb(out) } if (run) { # fails because dbscan works with > 2 dimensions but does # not work with duplicate points try(out <- knearneigh(rbind(x, x[1:10,]), k=5)) }"},{"path":"https://r-spatial.github.io/spdep/reference/knn2nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Neighbours list from knn object — knn2nb","title":"Neighbours list from knn object — knn2nb","text":"function converts knn object returned knearneigh neighbours list class nb list integer vectors containing neighbour region number ids.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knn2nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Neighbours list from knn object — knn2nb","text":"","code":"knn2nb(knn, row.names = NULL, sym = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/knn2nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Neighbours list from knn object — knn2nb","text":"knn knn object returned knearneigh row.names character vector region ids added neighbours list attribute region.id, default seq(1, nrow(x)) sym force output neighbours list symmetry","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knn2nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Neighbours list from knn object — knn2nb","text":"function returns object class nb list integer vectors containing neighbour region number ids. See card details “nb” objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/knn2nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Neighbours list from knn object — knn2nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/knn2nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Neighbours list from knn object — knn2nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries col.knn <- knearneigh(coords, k=4) plot(st_geometry(columbus), border=\"grey\") plot(knn2nb(col.knn), coords, add=TRUE) title(main=\"K nearest neighbours, k = 4\") # example of reading points with readr::read_csv() yielding a tibble load(system.file(\"etc/misc/coords.rda\", package=\"spdep\")) class(coords) #> [1] \"spec_tbl_df\" \"tbl_df\" \"tbl\" \"data.frame\" knn2nb(knearneigh(coords, k=4)) #> Neighbour list object: #> Number of regions: 100 #> Number of nonzero links: 400 #> Percentage nonzero weights: 4 #> Average number of links: 4 #> Non-symmetric neighbours list"},{"path":"https://r-spatial.github.io/spdep/reference/lag.listw.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial lag of a numeric vector — lag.listw","title":"Spatial lag of a numeric vector — lag.listw","text":"Using listw sparse representation spatial weights matrix, compute lag vector \\(V x\\)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lag.listw.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial lag of a numeric vector — lag.listw","text":"","code":"# S3 method for class 'listw' lag(x, var, zero.policy=attr(listw, \"zero.policy\"), NAOK=FALSE, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/lag.listw.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial lag of a numeric vector — lag.listw","text":"x listw object created example nb2listw var numeric vector length neighbours list listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA NAOK 'FALSE', presence 'NA' values regarded error; 'TRUE' 'NA' 'NaN' 'Inf' values var represented NA lagged value. ... additional arguments","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lag.listw.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial lag of a numeric vector — lag.listw","text":"numeric vector length var","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lag.listw.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial lag of a numeric vector — lag.listw","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lag.listw.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial lag of a numeric vector — lag.listw","text":"","code":"data(oldcol) Vx <- lag.listw(nb2listw(COL.nb, style=\"W\"), COL.OLD$CRIME) plot(Vx, COL.OLD$CRIME) plot(ecdf(COL.OLD$CRIME)) plot(ecdf(Vx), add=TRUE, col.points=\"red\", col.hor=\"red\") is.na(COL.OLD$CRIME[5]) <- TRUE VxNA <- lag.listw(nb2listw(COL.nb, style=\"W\"), COL.OLD$CRIME, NAOK=TRUE) #> Warning: NAs in lagged values"},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute Lee's statistic — lee","title":"Compute Lee's statistic — lee","text":"simple function compute Lee's L statistic bivariate spatial data; $$L(x,y) = \\frac{n}{\\sum_{=1}^{n}(\\sum_{j=1}^{n}w_{ij})^2} \\frac{\\sum_{=1}^{n}(\\sum_{j=1}^{n}w_{ij}(x_i-\\bar{x})) ((\\sum_{j=1}^{n}w_{ij}(y_j-\\bar{y}))}{\\sqrt{\\sum_{=1}^{n}(x_i - \\bar{x})^2} \\sqrt{\\sum_{=1}^{n}(y_i - \\bar{y})^2}} $$","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute Lee's statistic — lee","text":"","code":"lee(x, y, listw, n, S2, zero.policy=attr(listw, \"zero.policy\"), NAOK=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute Lee's statistic — lee","text":"x numeric vector length neighbours list listw y numeric vector length neighbours list listw listw listw object created example nb2listw n number zones S2 Sum squared sum weights rows. zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA NAOK 'TRUE' 'NA' 'NaN' 'Inf' values x passed foreign function. 'FALSE', presence 'NA' 'NaN' 'Inf' values regarded error.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute Lee's statistic — lee","text":"list L Lee's L statistic local L Lee's local L statistic","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute Lee's statistic — lee","text":"Lee (2001). Developing bivariate spatial association measure: integration Pearson's r Moran's . J Geograph Syst 3: 369-385","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute Lee's statistic — lee","text":"Roger Bivand Virgiio Gómez-Rubio Virgilio.Gomez@uclm.es","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lee.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute Lee's statistic — lee","text":"","code":"data(boston, package=\"spData\") lw<-nb2listw(boston.soi) x<-boston.c$CMEDV y<-boston.c$CRIM z<-boston.c$RAD Lxy<-lee(x, y, lw, length(x), zero.policy=TRUE) Lxz<-lee(x, z, lw, length(x), zero.policy=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Permutation test for Lee's L statistic — lee.mc","title":"Permutation test for Lee's L statistic — lee.mc","text":"permutation test Lee's L statistic calculated using nsim random permutations x y given spatial weighting scheme, establish rank observed statistic relation nsim simulated values.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Permutation test for Lee's L statistic — lee.mc","text":"","code":"lee.mc(x, y, listw, nsim, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\", na.action=na.fail, spChk=NULL, return_boot=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Permutation test for Lee's L statistic — lee.mc","text":"x numeric vector length neighbours list listw y numeric vector length neighbours list listw listw listw object created example nb2listw nsim number permutations zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"two.sided\", \"less\". na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass permitted meaningless permutation test. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() return_boot return object class boot equivalent permutation bootstrap rather object class htest","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Permutation test for Lee's L statistic — lee.mc","text":"list class htest mc.sim containing following components: statistic value observed Lee's L. parameter rank observed Lee's L. p.value pseudo p-value test. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data, number simulations. res nsim simulated values statistic, final value observed statistic","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Permutation test for Lee's L statistic — lee.mc","text":"Lee (2001). Developing bivariate spatial association measure: integration Pearson's r Moran's . J Geograph Syst 3: 369-385","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Permutation test for Lee's L statistic — lee.mc","text":"Roger Bivand, Virgilio Gómez-Rubio Virgilio.Gomez@uclm.es","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lee.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Permutation test for Lee's L statistic — lee.mc","text":"","code":"data(boston, package=\"spData\") lw<-nb2listw(boston.soi) x<-boston.c$CMEDV y<-boston.c$CRIM lee.mc(x, y, nsim=99, lw, zero.policy=TRUE, alternative=\"two.sided\") #> #> \tMonte-Carlo simulation of Lee's L #> #> data: x , y #> weights: lw #> number of simulations + 1: 100 #> #> statistic = -0.3263, observed rank = 1, p-value = 0.02 #> alternative hypothesis: two.sided #> #Test with missing values x[1:5]<-NA y[3:7]<-NA lee.mc(x, y, nsim=99, lw, zero.policy=TRUE, alternative=\"two.sided\", na.action=na.omit) #> #> \tMonte-Carlo simulation of Lee's L #> #> data: x , y #> weights: lw #> omitted: 1, 2, 3, 4, 5, 6, 7 #> number of simulations + 1: 100 #> #> statistic = -0.32447, observed rank = 1, p-value = 0.02 #> alternative hypothesis: two.sided #>"},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":null,"dir":"Reference","previous_headings":"","what":"Lee's L test for spatial autocorrelation — lee.test","title":"Lee's L test for spatial autocorrelation — lee.test","text":"Lee's L test spatial autocorrelation using spatial weights matrix weights list form. assumptions underlying test sensitive form graph neighbour relationships factors, results may checked lee.mc permutations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Lee's L test for spatial autocorrelation — lee.test","text":"","code":"lee.test(x, y, listw, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\", na.action=na.fail, spChk=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Lee's L test for spatial autocorrelation — lee.test","text":"x numeric vector length neighbours list listw y numeric vector length neighbours list listw listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one greater (default), less two.sided. na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass used, zero substituted NA values calculating spatial lag spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption()","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Lee's L test for spatial autocorrelation — lee.test","text":"list class htest containing following components: statistic value standard deviate Lee's L. p.value p-value test. estimate value observed Lee's L, expectation variance method assumption. alternative character string describing alternative hypothesis. method character string giving assumption used calculating standard deviate. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Lee's L test for spatial autocorrelation — lee.test","text":"See Lee (2004) details asymptotic expectation variance Lee's L computed. particular, check Lee (2004), table 1, page 1690. test may fail large datasets computation asymptotic expectation variance requires use dense matrices.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Lee's L test for spatial autocorrelation — lee.test","text":"Lee (2004). generalized significance testing method global measures spatial association: extension Mantel test. Environment Planning 2004, volume 36, pages 1687 - 1703","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Lee's L test for spatial autocorrelation — lee.test","text":"Roger Bivand Virgilio Gómez-Rubio Virgilio.Gomez@uclm.es","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lee.test.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Lee's L test for spatial autocorrelation — lee.test","text":"","code":"data(oldcol) col.W <- nb2listw(COL.nb, style=\"W\") crime <- COL.OLD$CRIME lee.test(crime, crime, col.W, zero.policy=TRUE) #> #> \tLee's L statistic randomisation #> #> data: crime , crime #> weights: col.W #> #> Lee's L statistic standard deviate = 5.2343, p-value = 8.279e-08 #> alternative hypothesis: greater #> sample estimates: #> Lee's L statistic Expectation Variance #> 0.547064219 0.239417989 0.003454459 #> #Test with missing values x<-crime y<-crime x[1:5]<-NA y[3:7]<-NA lee.test(x, y, col.W, zero.policy=TRUE, na.action=na.omit) #> #> \tLee's L statistic randomisation #> #> data: x , y #> weights: col.W #> omitted: 1, 2, 3, 4, 5, 6, 7 #> #> Lee's L statistic standard deviate = 6.6873, p-value = 1.137e-11 #> alternative hypothesis: greater #> sample estimates: #> Lee's L statistic Expectation Variance #> 0.706469726 0.260143244 0.004454563 #> # lee.test(x, y, col.W, zero.policy=TRUE)#Stops with an error data(boston, package=\"spData\") lw<-nb2listw(boston.soi) x<-boston.c$CMEDV y<-boston.c$CRIM lee.test(x, y, lw, zero.policy=TRUE, alternative=\"less\") #> #> \tLee's L statistic randomisation #> #> data: x , y #> weights: lw #> #> Lee's L statistic standard deviate = -11.54, p-value < 2.2e-16 #> alternative hypothesis: less #> sample estimates: #> Lee's L statistic Expectation Variance #> -0.326297206 -0.105040316 0.000367637 #> #Test with missing values x[1:5]<-NA y[3:7]<-NA lee.test(x, y, lw, zero.policy=TRUE, alternative=\"less\", na.action=na.omit) #> #> \tLee's L statistic randomisation #> #> data: x , y #> weights: lw #> omitted: 1, 2, 3, 4, 5, 6, 7 #> #> Lee's L statistic standard deviate = -11.284, p-value < 2.2e-16 #> alternative hypothesis: less #> sample estimates: #> Lee's L statistic Expectation Variance #> -0.3244748280 -0.1053154332 0.0003772109 #>"},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":null,"dir":"Reference","previous_headings":"","what":"Local Indicators for Categorical Data — licd_multi","title":"Local Indicators for Categorical Data — licd_multi","text":"Local indicators categorical data combine measure local composition window given per-observation set neighbouring observations, local multi-category joincount test simplified neighbours different categories compared focal observation","code":""},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Local Indicators for Categorical Data — licd_multi","text":"","code":"licd_multi(fx, listw, zero.policy = attr(listw, \"zero.policy\"), adjust.n = TRUE, nsim = 0L, iseed = NULL, no_repeat_in_row = FALSE, control = list())"},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Local Indicators for Categorical Data — licd_multi","text":"fx factor two categories, length neighbours weights objects listw; use ordered factor well understood listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted nsim default 0, number conditonal permutation simulations iseed default NULL, used set seed; output reproducible count CPU cores across computation distributed no_repeat_in_row default FALSE, TRUE, sample conditionally row without replacements avoid duplicate values, https://github.com/r-spatial/spdep/issues/124 control comp_binary=TRUE default TRUE, ignoring weights styles binary composition measures, binomial_punif_alternative=\"greater\", jcm_same_punif_alternative=\"less\", jcm_diff_punif_alternative=\"greater\", rank_ties.method=\"min\" default \"min\", na.last=\"keep\" leading rank NA returned observed joincount variance non-positive; TRUE joincount NAs ranked highest using rank, others see ?rank, check_reps=FALSE, unique_ceiling=1/3 used check_reps TRUE, check_reps=FALSE TRUE, check report many unique draws made among nsim draws, number unique draws less unique_ceiling, compute measures unique draws copy replicated draws, pysal_rank=FALSE use rank rank_ties.method na.last; TRUE, use pysal-style ranking find rank sum(sims <= obs, na.rm=TRUE)+1 pysal_sim_obs \"GE\", sum(sims < obs, na.rm=TRUE)+1 count observed greater \"GT\" simulated values, pysal_sim_obs=\"GT\" may also \"GE\", xtras=FALSE TRUE return calculated compostion values BW chi-squared, k-colour chi-squared, BW Anscombe","code":""},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Local Indicators for Categorical Data — licd_multi","text":"original code may found doi:10.5281/zenodo.4283766","code":""},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Local Indicators for Categorical Data — licd_multi","text":"local_comp data.frame object LICD local composition columns: ID, category_i, count_like_i, prop_i, count_nbs_i, pbinom_like_BW, pbinom_unlike_BW, pbinom_unlike_BW_alt, chi_BW_i, chi_K_i, anscombe_BW local_config data.frame object LICD local configuration columns: ID, jcm_chi_obs, jcm_count_BB_obs, jcm_count_BW_obs, jcm_count_WW_obs, pval_jcm_obs_BB, pval_jcm_obs_WW, pval_jcm_obs_BW local_comp_sim data.frame object permutation-based LICD local composition columns: ID, pbinom_like_BW, pbinom_unlike_BW, pbinom_unlike_BW_alt, rank_sim_chi_BW, rank_sim_chi_K, rank_sim_anscombe local_config_sim data.frame object permutation-based LICD local configuration columns: ID, jcm_chi_sim_rank, pval_jcm_obs_BB, pval_jcm_obs_BW, pval_jcm_obs_WW","code":""},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Local Indicators for Categorical Data — licd_multi","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 20; Upton, G., Fingleton, B. 1985 Spatial data analysis example: point pattern qualitative data, Wiley, pp. 158–170; Boots, B., 2003. Developing local measures spatial association categorical data. Journal Geographical Systems 5, 139–160; Boots, B., 2006. Local configuration measures categorical spatial data: binary regular lattices. Journal Geographical Systems 8 (1), 1–24; Pietrzak, M.B., Wilk, J., Kossowski, T., Bivand, R.S., 2014. application local indicators categorical data (LICD) spatial analysis economic development. Comparative Economic Research 17 (4), 203–220 doi:10.2478/cer-2014-0041 ; Bivand, R.S., Wilk, J., Kossowski, T., 2017. Spatial association population pyramids across Europe: application symbolic data, cluster analysis join-count tests. Spatial Statistics 21 (B), 339–361 doi:10.1016/j.spasta.2017.03.003 ; Francesco Carrer, Tomasz M. Kossowski, Justyna Wilk, Michał B. Pietrzak, Roger S. Bivand, application Local Indicators Categorical Data (LICD) explore spatial dependence archaeological spaces, Journal Archaeological Science, 126, 2021, doi:10.1016/j.jas.2020.105306","code":""},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Local Indicators for Categorical Data — licd_multi","text":"Roger Bivand Roger.Bivand@nhh.based earlier code Tomasz M. Kossowski, Justyna Wilk Michał B. Pietrzak","code":""},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Local Indicators for Categorical Data — licd_multi","text":"order increase numbers neighbours using nblag nblag_cumul advisable; use binary weights advised case used composition measure","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/licd_multi.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Local Indicators for Categorical Data — licd_multi","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) HICRIME <- cut(columbus$CRIME, breaks=c(0,35,80), labels=c(\"low\",\"high\")) (nb <- poly2nb(columbus)) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 236 #> Percentage nonzero weights: 9.829238 #> Average number of links: 4.816327 lw <- nb2listw(nblag_cumul(nblag(nb, 2)), style=\"B\") obj <- licd_multi(HICRIME, lw) str(obj) #> List of 4 #> $ local_comp :'data.frame':\t49 obs. of 11 variables: #> ..$ ID : int [1:49] 1 2 3 4 5 6 7 8 9 10 ... #> ..$ category_i : num [1:49] 1 1 1 1 2 1 1 2 1 1 ... #> ..$ count_like_i : num [1:49] 4 4 6 7 12 7 2 8 10 8 ... #> ..$ prop_i : num [1:49] 0.51 0.51 0.51 0.51 0.49 ... #> ..$ count_nbs_i : num [1:49] 5 6 11 14 22 14 11 14 25 17 ... #> ..$ pbinom_like_BW : num [1:49] 0.965 0.881 0.702 0.575 0.769 ... #> ..$ pbinom_unlike_BW : num [1:49] 0.0346 0.1192 0.2979 0.4255 0.2313 ... #> ..$ pbinom_unlike_BW_alt: num [1:49] 0.201 0.363 0.528 0.634 0.379 ... #> ..$ chi_BW_i : num [1:49] NA NA NA NA NA NA NA NA NA NA ... #> ..$ chi_K_i : num [1:49] NA NA NA NA NA NA NA NA NA NA ... #> ..$ anscombe_BW : num [1:49] NA NA NA NA NA NA NA NA NA NA ... #> $ local_config :'data.frame':\t49 obs. of 8 variables: #> ..$ ID : int [1:49] 1 2 3 4 5 6 7 8 9 10 ... #> ..$ jcm_chi_obs : num [1:49] 0 0.0625 0.625 2.7468 14.1889 ... #> ..$ jcm_count_BB_obs: num [1:49] 6 6 11 12 55 15 1 27 30 25 ... #> ..$ jcm_count_BW_obs: num [1:49] 4 7 23 31 50 36 15 31 73 53 ... #> ..$ jcm_count_WW_obs: num [1:49] 0 1 10 20 21 19 32 9 61 24 ... #> ..$ pval_jcm_obs_BB : num [1:49] 1 0.207108 0.70232 0.820405 0.000214 ... #> ..$ pval_jcm_obs_WW : num [1:49] 1 0.3946 0.0981 0.0243 0.7839 ... #> ..$ pval_jcm_obs_BW : num [1:49] 1.00 1.75e-01 2.08e-01 5.10e-02 3.52e-06 ... #> $ local_comp_sim : NULL #> $ local_config_sim: NULL #> - attr(*, \"timings\")=List of 3 #> ..$ set_up : 'proc_time' Named num [1:5] 0 0 0 NA NA #> .. ..- attr(*, \"names\")= chr [1:5] \"user.self\" \"sys.self\" \"elapsed\" \"user.child\" ... #> ..$ processing : 'proc_time' Named num [1:5] 0.01 0 0.08 NA NA #> .. ..- attr(*, \"names\")= chr [1:5] \"user.self\" \"sys.self\" \"elapsed\" \"user.child\" ... #> ..$ postprocessing: 'proc_time' Named num [1:5] 0 0 0 NA NA #> .. ..- attr(*, \"names\")= chr [1:5] \"user.self\" \"sys.self\" \"elapsed\" \"user.child\" ... #> - attr(*, \"out\")= num [1:49, 1:35] 1 1 1 1 2 1 1 2 1 1 ... #> ..- attr(*, \"ncpus\")= int 1 #> ..- attr(*, \"dimnames\")=List of 2 #> .. ..$ : NULL #> .. ..$ : chr [1:35] \"category_i\" \"count_like_i\" \"prop_i\" \"count_nbs_i\" ... #> - attr(*, \"ncpus\")= int 1 #> - attr(*, \"nsim\")= int 0 #> - attr(*, \"con\")=List of 11 #> ..$ comp_binary : logi TRUE #> ..$ binomial_punif_alternative: chr \"greater\" #> ..$ jcm_same_punif_alternative: chr \"less\" #> ..$ jcm_diff_punif_alternative: chr \"greater\" #> ..$ rank_ties.method : chr \"min\" #> ..$ unique_ceiling : num 0.333 #> ..$ check_reps : logi FALSE #> ..$ pysal_rank : logi FALSE #> ..$ pysal_sim_obs : chr \"GT\" #> ..$ na.last : chr \"keep\" #> ..$ xtras : logi FALSE #> - attr(*, \"class\")= chr [1:2] \"licd\" \"list\" h_obj <- hotspot(obj) str(h_obj) #> List of 9 #> $ ID : int [1:49] 1 2 3 4 5 6 7 8 9 10 ... #> $ local_comp : Factor w/ 2 levels \"Cluster\",\"Dispersed\": 2 2 2 2 2 2 2 2 2 2 ... #> $ local_comp_sim : NULL #> $ local_config : Factor w/ 3 levels \"Cluster\",\"Dispersed\",..: 3 3 3 3 2 3 3 2 3 3 ... #> $ local_config_sim: NULL #> $ both : Factor w/ 6 levels \"Cluster.Cluster\",..: 6 6 6 6 4 6 6 4 6 6 ... #> $ both_sim : NULL #> $ both_recode : Factor w/ 4 levels \"Clump\",\"Cluster\",..: 4 4 4 4 3 4 4 3 4 4 ... #> $ both_recode_sim : NULL table(h_obj$both_recode) #> #> Clump Cluster Dispersed No cluster #> 8 3 11 27 columbus$both <- h_obj$both_recode plot(columbus[, \"both\"]) GDAL37 <- numeric_version(unname(sf::sf_extSoftVersion()[\"GDAL\"]), strict=FALSE) (GDAL37 <- ifelse(is.na(GDAL37), FALSE, GDAL37 >= \"3.7.0\")) #> [1] TRUE file <- \"etc/shapes/GB_2024_southcoast_50m.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) { sc50m <- st_read(zipfile) } else { td <- tempdir() bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE) target <- unzip(zipfile, files=bn, exdir=td) sc50m <- st_read(target) } #> Reading layer `GB_2024_southcoast_50m' from data source #> `C:\\Users\\rzomor2\\AppData\\Local\\Temp\\RtmpErQTm3\\temp_libpath1a5cde63ff3\\spdep\\etc\\shapes\\GB_2024_southcoast_50m.gpkg.zip' #> using driver `GPKG' #> Simple feature collection with 119 features and 19 fields #> Geometry type: MULTIPOLYGON #> Dimension: XY #> Bounding box: xmin: 82643.12 ymin: 5342.9 xmax: 640301.6 ymax: 187226.2 #> Projected CRS: OSGB36 / British National Grid sc50m$Winner <- factor(sc50m$Winner, levels=c(\"Con\", \"Green\", \"Lab\", \"LD\")) plot(sc50m[,\"Winner\"], pal=c(\"#2297E6\", \"#61D04F\", \"#DF536B\", \"#F5C710\")) nb_sc_50m <- poly2nb(sc50m, row.names=as.character(sc50m$Constituency)) #> Warning: neighbour object has 2 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. sub2 <- attr(nb_sc_50m, \"region.id\")[attr(nb_sc_50m, \"ncomp\")$comp.id == 2L] iowe <- match(sub2[1], attr(nb_sc_50m, \"region.id\")) diowe <- c(st_distance(sc50m[iowe,], sc50m)) meet_criterion <- sum(diowe <= units::set_units(5000, \"m\")) cands <- attr(nb_sc_50m, \"region.id\")[order(diowe)[1:meet_criterion]] nb_sc_50m_iowe <- addlinks1(nb_sc_50m, from = cands[1], to = cands[3:meet_criterion]) ioww <- match(sub2[2], attr(nb_sc_50m, \"region.id\")) dioww <- c(st_distance(sc50m[ioww,], sc50m)) meet_criterion <- sum(dioww <= units::set_units(5000, \"m\")) cands <- attr(nb_sc_50m, \"region.id\")[order(dioww)[1:meet_criterion]] nb_sc_50m_iow <- addlinks1(nb_sc_50m_iowe, from = cands[2], to = cands[3:meet_criterion]) nb_sc_1_2 <- nblag_cumul(nblag(nb_sc_50m_iow, 2)) lw <- nb2listw(nb_sc_1_2, style=\"B\") licd_obj <- licd_multi(sc50m$Winner, lw) h_obj <- hotspot(licd_obj) sc50m$both <- h_obj$both_recode plot(sc50m[, \"both\"]) ljc <- local_joincount_uni(factor(sc50m$Winner == \"LD\"), chosen=\"TRUE\", lw) sc50m$LD_pv <- ljc[, 2] plot(sc50m[, \"LD_pv\"], breaks=c(0, 0.025, 0.05, 0.1, 0.5, 1))"},{"path":"https://r-spatial.github.io/spdep/reference/listw2sn.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial neighbour sparse representation — listw2sn","title":"Spatial neighbour sparse representation — listw2sn","text":"function makes \"spatial neighbour\" object representation (similar S-PLUS spatial statististics module representation \"listw\" spatial weights object. sn2listw() inverse function listw2sn(), creating \"listw\" object \"spatial neighbour\" object.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/listw2sn.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial neighbour sparse representation — listw2sn","text":"","code":"listw2sn(listw) sn2listw(sn, style = NULL, zero.policy = NULL, from_mat2listw=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/listw2sn.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial neighbour sparse representation — listw2sn","text":"listw listw object example nb2listw sn spatial.neighbour object style default NULL, missing, set \"M\" warning given; \"M\", passed nb2listw re-build object zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors from_mat2listw default FALSE, set TRUE called mat2listw","code":""},{"path":"https://r-spatial.github.io/spdep/reference/listw2sn.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial neighbour sparse representation — listw2sn","text":"listw2sn()returns data frame three columns, class spatial.neighbour: region number id start link (S-PLUS row.id) region number id end link (S-PLUS col.id) weights weight link","code":""},{"path":"https://r-spatial.github.io/spdep/reference/listw2sn.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial neighbour sparse representation — listw2sn","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/listw2sn.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial neighbour sparse representation — listw2sn","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) col.listw <- nb2listw(col.gal.nb) col.listw$neighbours[[1]] #> [1] 2 3 col.listw$weights[[1]] #> [1] 0.5 0.5 col.sn <- listw2sn(col.listw) str(col.sn) #> Classes 'spatial.neighbour' and 'data.frame':\t230 obs. of 3 variables: #> $ from : int 1 1 2 2 2 3 3 3 3 4 ... #> $ to : int 2 3 1 3 4 1 2 4 5 2 ... #> $ weights: num 0.5 0.5 0.333 0.333 0.333 ... #> - attr(*, \"n\")= int 49 #> - attr(*, \"region.id\")= chr [1:49] \"1\" \"2\" \"3\" \"4\" ... #> - attr(*, \"neighbours.attrs\")= chr [1:7] \"class\" \"region.id\" \"GeoDa\" \"gal\" ... #> - attr(*, \"weights.attrs\")= chr [1:3] \"mode\" \"W\" \"comp\" #> - attr(*, \"GeoDa\")=List of 2 #> ..$ shpfile: chr NA #> ..$ ind : chr NA #> - attr(*, \"listw.call\")= language nb2listw(neighbours = col.gal.nb)"},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":null,"dir":"Reference","previous_headings":"","what":"Exact global Moran's I test — lm.morantest.exact","title":"Exact global Moran's I test — lm.morantest.exact","text":"function implements Tiefelsdorf's exact global Moran's test.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Exact global Moran's I test — lm.morantest.exact","text":"","code":"lm.morantest.exact(model, listw, zero.policy = attr(listw, \"zero.policy\"), alternative = \"greater\", spChk = NULL, resfun = weighted.residuals, zero.tol = 1e-07, Omega=NULL, save.M=NULL, save.U=NULL, useTP=FALSE, truncErr=1e-6, zeroTreat=0.1) # S3 method for class 'moranex' print(x, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Exact global Moran's I test — lm.morantest.exact","text":"model object class lm returned lm; weights may specified lm fit, offsets used listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one greater (default), less two.sided. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() resfun default: weighted.residuals; function used extract residuals lm object, may residuals, weighted.residuals, rstandard, rstudent zero.tol tolerance used find eigenvalues close absolute zero Omega SAR process matrix may passed test alternative hypothesis, example Omega <- invIrW(listw, rho=0.1); Omega <- tcrossprod(Omega), chol() taken internally save.M return full M matrix use spdep:::exactMoranAlt save.U return full U matrix use spdep:::exactMoranAlt useTP default FALSE, TRUE, use truncation point integration rather upper=Inf, see Tiefelsdorf (2000), eq. 6.7, p.69 truncErr useTP=TRUE, pass truncation error truncation point function zeroTreat useTP=TRUE, pass zero adjustment truncation point function x moranex object ... arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Exact global Moran's I test — lm.morantest.exact","text":"list class moranex following components: statistic value exact standard deviate global Moran's . p.value p-value test. estimate value observed global Moran's . method character string giving method used. alternative character string describing alternative hypothesis. gamma eigenvalues (excluding zero values) oType usually set \"E\" data.name character string giving name(s) data. df degrees freedom","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Exact global Moran's I test — lm.morantest.exact","text":"Markus Reder Roger Bivand","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Exact global Moran's I test — lm.morantest.exact","text":"Roger Bivand, Werner G. Müller Markus Reder (2009) \"Power calculations global local Moran's .\" Computational Statistics & Data Analysis 53, 2859-2872.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.exact.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Exact global Moran's I test — lm.morantest.exact","text":"","code":"eire <- st_read(system.file(\"shapes/eire.gpkg\", package=\"spData\")[1]) #> Reading layer `eire' from data source #> `C:\\Users\\rzomor2\\AppData\\Local\\R\\win-library\\4.4\\spData\\shapes\\eire.gpkg' #> using driver `GPKG' #> Simple feature collection with 26 features and 10 fields #> Geometry type: MULTIPOLYGON #> Dimension: XY #> Bounding box: xmin: -4.12 ymin: 5768 xmax: 300.82 ymax: 6119.25 #> Projected CRS: Undefined Cartesian SRS with unknown unit row.names(eire) <- as.character(eire$names) eire.nb <- poly2nb(eire) e.lm <- lm(OWNCONS ~ ROADACC, data=eire) lm.morantest(e.lm, nb2listw(eire.nb)) #> #> \tGlobal Moran I for regression residuals #> #> data: #> model: lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #> #> Moran I statistic standard deviate = 3.2575, p-value = 0.0005619 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I Expectation Variance #> 0.33660565 -0.05877741 0.01473183 #> lm.morantest.sad(e.lm, nb2listw(eire.nb)) #> #> \tSaddlepoint approximation for global Moran's I (Barndorff-Nielsen #> \tformula) #> #> data: #> model:lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #> #> Saddlepoint approximation = 2.9395, p-value = 0.001644 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I #> 0.3366057 #> lm.morantest.exact(e.lm, nb2listw(eire.nb)) #> #> \tGlobal Moran I statistic with exact p-value #> #> data: #> model:lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #> #> Exact standard deviate = 2.9316, p-value = 0.001686 #> alternative hypothesis: greater #> sample estimates: #> [1] 0.3366057 #> lm.morantest.exact(e.lm, nb2listw(eire.nb), useTP=TRUE) #> #> \tGlobal Moran I statistic with exact p-value #> #> data: #> model:lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #> #> Exact standard deviate = 2.9315, p-value = 0.001686 #> alternative hypothesis: greater #> sample estimates: #> [1] 0.3366057 #>"},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":null,"dir":"Reference","previous_headings":"","what":"Moran's I test for residual spatial autocorrelation — lm.morantest","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"Moran's test spatial autocorrelation residuals estimated linear model (lm()).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"","code":"lm.morantest(model, listw, zero.policy=attr(listw, \"zero.policy\"), alternative = \"greater\", spChk=NULL, resfun=weighted.residuals, naSubset=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"model object class lm returned lm; weights may specified lm fit, offsets used listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"less\" \"two.sided\". spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() resfun default: weighted.residuals; function used extract residuals lm object, may residuals, weighted.residuals, rstandard, rstudent naSubset default TRUE subset listw object omitted observations model object (change earlier behaviour, model$na.action component ignored, listw object subsetted hand)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"list class htest containing following components: statistic value standard deviate Moran's . p.value p-value test. estimate value observed Moran's , expectation variance method assumption. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 203,","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"factors ordered factors among explanatory variables regression, coding contrasts affects outcomes significance tests.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Moran's I test for residual spatial autocorrelation — lm.morantest","text":"","code":"data(oldcol) oldcrime1.lm <- lm(CRIME ~ 1, data = COL.OLD) oldcrime.lm <- lm(CRIME ~ HOVAL + INC, data = COL.OLD) lm.morantest(oldcrime.lm, nb2listw(COL.nb, style=\"W\")) #> #> \tGlobal Moran I for regression residuals #> #> data: #> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD) #> weights: nb2listw(COL.nb, style = \"W\") #> #> Moran I statistic standard deviate = 2.9539, p-value = 0.001569 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I Expectation Variance #> 0.235638354 -0.033302866 0.008289408 #> lm.LMtests(oldcrime.lm, nb2listw(COL.nb, style=\"W\")) #> Please update scripts to use lm.RStests in place of lm.LMtests #> #> \tRao's score (a.k.a Lagrange multiplier) diagnostics for spatial #> \tdependence #> #> data: #> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD) #> test weights: listw #> #> RSerr = 5.7231, df = 1, p-value = 0.01674 #> lm.morantest(oldcrime.lm, nb2listw(COL.nb, style=\"S\")) #> #> \tGlobal Moran I for regression residuals #> #> data: #> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD) #> weights: nb2listw(COL.nb, style = \"S\") #> #> Moran I statistic standard deviate = 3.1745, p-value = 0.0007504 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I Expectation Variance #> 0.239317561 -0.033431740 0.007381982 #> lm.morantest(oldcrime1.lm, nb2listw(COL.nb, style=\"W\")) #> #> \tGlobal Moran I for regression residuals #> #> data: #> model: lm(formula = CRIME ~ 1, data = COL.OLD) #> weights: nb2listw(COL.nb, style = \"W\") #> #> Moran I statistic standard deviate = 5.6754, p-value = 6.92e-09 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I Expectation Variance #> 0.510951264 -0.020833333 0.008779831 #> moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"W\"), randomisation=FALSE) #> #> \tMoran I test under normality #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.nb, style = \"W\") #> #> Moran I statistic standard deviate = 5.6754, p-value = 6.92e-09 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.510951264 -0.020833333 0.008779831 #> oldcrime.wlm <- lm(CRIME ~ HOVAL + INC, data = COL.OLD, weights = I(1/AREA_PL)) lm.morantest(oldcrime.wlm, nb2listw(COL.nb, style=\"W\"), resfun=weighted.residuals) #> #> \tGlobal Moran I for regression residuals #> #> data: #> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD, weights = #> I(1/AREA_PL)) #> weights: nb2listw(COL.nb, style = \"W\") #> #> Moran I statistic standard deviate = 3.0141, p-value = 0.001289 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I Expectation Variance #> 0.241298974 -0.032224366 0.008235091 #> lm.morantest(oldcrime.wlm, nb2listw(COL.nb, style=\"W\"), resfun=rstudent) #> #> \tGlobal Moran I for regression residuals #> #> data: #> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD, weights = #> I(1/AREA_PL)) #> weights: nb2listw(COL.nb, style = \"W\") #> #> Moran I statistic standard deviate = 2.822, p-value = 0.002387 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I Expectation Variance #> 0.223860298 -0.032224366 0.008235091 #> run <- require(\"codingMatrices\", quietly=TRUE) if (run) { COL.OLD$fEW <- factor(COL.OLD$EW) COL.OLD$fDISCBD <- ordered(cut(COL.OLD$DISCBD, c(0, 1.5, 3, 4.5, 6))) f <- formula(CRIME ~ INC + HOVAL + fDISCBD*fEW) lw <- nb2listw(COL.nb, style=\"W\") # default codings lm.morantest(lm(f, data=COL.OLD, contrasts=list(fDISCBD=\"contr.poly\", fEW=\"contr.treatment\")), lw) } if (run) { # use codingMatrices::code_diff for ordered factor lm.morantest(lm(f, data=COL.OLD, contrasts=list(fDISCBD=\"code_diff\", fEW=\"contr.treatment\")), lw) } if (run) { # use stats::contr.treatment for both factors lm.morantest(lm(f, data=COL.OLD, contrasts=list(fDISCBD=\"contr.treatment\", fEW=\"contr.treatment\")), lw) } if (run) { # use codingMatrices::code_control for factor lm.morantest(lm(f, data=COL.OLD, contrasts=list(fDISCBD=\"code_diff\", fEW=\"code_control\")), lw) } if (run) { # use codingMatrices::code_control for both lm.morantest(lm(f, data=COL.OLD, contrasts=list(fDISCBD=\"code_control\", fEW=\"code_control\")), lw) }"},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":null,"dir":"Reference","previous_headings":"","what":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"function implements Tiefelsdorf's application Saddlepoint approximation global Moran's 's reference distribution.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"","code":"lm.morantest.sad(model, listw, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\", spChk=NULL, resfun=weighted.residuals, tol=.Machine$double.eps^0.5, maxiter=1000, tol.bounds=0.0001, zero.tol = 1e-07, Omega=NULL, save.M=NULL, save.U=NULL) # S3 method for class 'moransad' print(x, ...) # S3 method for class 'moransad' summary(object, ...) # S3 method for class 'summary.moransad' print(x, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"model object class lm returned lm; weights may specified lm fit, offsets used listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one greater (default), less two.sided. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() resfun default: weighted.residuals; function used extract residuals lm object, may residuals, weighted.residuals, rstandard, rstudent tol desired accuracy (convergence tolerance) uniroot maxiter maximum number iterations uniroot tol.bounds offset bounds uniroot zero.tol tolerance used find eigenvalues close absolute zero Omega SAR process matrix may passed test alternative hypothesis, example Omega <- invIrW(listw, rho=0.1); Omega <- tcrossprod(Omega), chol() taken internally save.M return full M matrix use spdep:::exactMoranAlt save.U return full U matrix use spdep:::exactMoranAlt x object printed object object summarised ... arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"function involves finding eigenvalues n n matrix, numerically finding root Saddlepoint approximation, therefore used care n large.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"list class moransad following components: statistic value saddlepoint approximation standard deviate global Moran's . p.value p-value test. estimate value observed global Moran's . alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data. internal1 Saddlepoint omega, r u internal2 f.root, iter estim.prec uniroot df degrees freedom tau eigenvalues (excluding zero values)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"Tiefelsdorf, M. 2002 Saddlepoint approximation Moran's local Moran's Ii reference distributions numerical evaluation. Geographical Analysis, 34, pp. 187–206; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lm.morantest.sad.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Saddlepoint approximation of global Moran's I test — lm.morantest.sad","text":"","code":"eire <- st_read(system.file(\"shapes/eire.gpkg\", package=\"spData\")[1]) #> Reading layer `eire' from data source #> `C:\\Users\\rzomor2\\AppData\\Local\\R\\win-library\\4.4\\spData\\shapes\\eire.gpkg' #> using driver `GPKG' #> Simple feature collection with 26 features and 10 fields #> Geometry type: MULTIPOLYGON #> Dimension: XY #> Bounding box: xmin: -4.12 ymin: 5768 xmax: 300.82 ymax: 6119.25 #> Projected CRS: Undefined Cartesian SRS with unknown unit row.names(eire) <- as.character(eire$names) eire.nb <- poly2nb(eire) e.lm <- lm(OWNCONS ~ ROADACC, data=eire) lm.morantest(e.lm, nb2listw(eire.nb)) #> #> \tGlobal Moran I for regression residuals #> #> data: #> model: lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #> #> Moran I statistic standard deviate = 3.2575, p-value = 0.0005619 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I Expectation Variance #> 0.33660565 -0.05877741 0.01473183 #> lm.morantest.sad(e.lm, nb2listw(eire.nb)) #> #> \tSaddlepoint approximation for global Moran's I (Barndorff-Nielsen #> \tformula) #> #> data: #> model:lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #> #> Saddlepoint approximation = 2.9395, p-value = 0.001644 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I #> 0.3366057 #> summary(lm.morantest.sad(e.lm, nb2listw(eire.nb))) #> #> \tSaddlepoint approximation for global Moran's I (Barndorff-Nielsen #> \tformula) #> #> data: #> model:lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: nb2listw(eire.nb) #> #> Saddlepoint approximation = 2.9395, p-value = 0.001644 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I #> 0.3366057 #> #> Expectation Variance Std. deviate Skewness Kurtosis Minimum #> -0.05877741 0.01473183 3.25753938 0.31336881 3.05047361 -0.67545810 #> Maximum omega sad.r sad.u #> 0.89091555 0.76549075 2.77616585 4.36854629 #> f.root iter estim.prec #> 7.01314e-14 1.10000e+01 NA e.wlm <- lm(OWNCONS ~ ROADACC, data=eire, weights=RETSALE) lm.morantest(e.wlm, nb2listw(eire.nb), resfun=rstudent) #> #> \tGlobal Moran I for regression residuals #> #> data: #> model: lm(formula = OWNCONS ~ ROADACC, data = eire, weights = RETSALE) #> weights: nb2listw(eire.nb) #> #> Moran I statistic standard deviate = 3.1385, p-value = 0.0008491 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I Expectation Variance #> 0.34500329 -0.04049313 0.01508687 #> lm.morantest.sad(e.wlm, nb2listw(eire.nb), resfun=rstudent) #> #> \tSaddlepoint approximation for global Moran's I (Barndorff-Nielsen #> \tformula) #> #> data: #> model:lm(formula = OWNCONS ~ ROADACC, data = eire, weights = RETSALE) #> weights: nb2listw(eire.nb) #> #> Saddlepoint approximation = 2.8708, p-value = 0.002047 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I #> 0.3450033 #>"},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":null,"dir":"Reference","previous_headings":"","what":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"function reports estimates tests chosen among five statistics testing spatial dependence linear models. statistics simple RS test error dependence (“RSerr”), simple RS test missing spatially lagged dependent variable (“RSlag”), variants adjusted presence (“adjRSerr” tests error dependence possible presence missing lagged dependent variable, “adjRSlag” way round), portmanteau test (“SARMA”, fact “RSerr” + “adjRSlag”). Note: spdep 1.3-2, tests re-named “RS” - Rao's score tests, rather “LM” - Lagrange multiplier tests match naming tests family SDM.RStests.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"","code":"lm.RStests(model, listw, zero.policy=attr(listw, \"zero.policy\"), test=\"RSerr\", spChk=NULL, naSubset=TRUE) lm.LMtests(model, listw, zero.policy=attr(listw, \"zero.policy\"), test=\"LMerr\", spChk=NULL, naSubset=TRUE) # S3 method for class 'RStestlist' print(x, ...) # S3 method for class 'RStestlist' summary(object, p.adjust.method=\"none\", ...) # S3 method for class 'RStestlist.summary' print(x, digits=max(3, getOption(\"digits\") - 2), ...) "},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"model object class lm returned lm, optionally vector externally calculated residuals (run though na.omit NAs present) use \"RSerr\" chosen; weights offsets used lm object listw listw object created example nb2listw, expected row-standardised (W-style) zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA test character vector tests requested chosen RSerr, RSlag, adjRSerr, adjRSlag, SARMA; test=\"\" computes tests. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() naSubset default TRUE subset listw object omitted observations model object (change earlier behaviour, model$na.action component ignored, listw object subsetted hand) x, object object printed p.adjust.method character string specifying probability value adjustment (see p.adjust) multiple tests, default \"none\" digits minimum number significant digits used numbers ... printing arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"two types dependence spatial lag \\(\\rho\\) spatial error \\(\\lambda\\): $$ \\mathbf{y} = \\mathbf{X \\beta} + \\rho \\mathbf{W_{(1)} y} + \\mathbf{u}, $$ $$ \\mathbf{u} = \\lambda \\mathbf{W_{(2)} u} + \\mathbf{e} $$ \\(\\mathbf{e}\\) well-behaved, uncorrelated error term. Tests missing spatially lagged dependent variable test \\(\\rho = 0\\), tests spatial autocorrelation error \\(\\mathbf{u}\\) test whether \\(\\lambda = 0\\). \\(\\mathbf{W}\\) spatial weights matrix; tests used identical. factors ordered factors among explanatory variables regression, coding contrasts affects outcomes significance tests.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"list class RStestlist htest objects, : statistic value Rao's score (.k.Lagrange multiplier) test. parameter number degrees freedom p.value p-value test. method character string giving method used. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"Anselin, L. 1988 Spatial econometrics: methods models. (Dordrecht: Kluwer); Anselin, L., Bera, . K., Florax, R. Yoon, M. J. 1996 Simple diagnostic tests spatial dependence. Regional Science Urban Economics, 26, 77–104 doi:10.1016/0166-0462(95)02111-6 ; Malabika Koley (2024) Specification Testing General Nesting Spatial Model, https://sites.google.com/view/malabikakoley/research.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"Roger Bivand Roger.Bivand@nhh.Andrew Bernat","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/lm.RStests.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Rao's score (a.k.a Lagrange Multiplier) diagnostics for spatial dependence in linear models — lm.LMtests","text":"","code":"data(oldcol) oldcrime.lm <- lm(CRIME ~ HOVAL + INC, data = COL.OLD) summary(oldcrime.lm) #> #> Call: #> lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD) #> #> Residuals: #> Min 1Q Median 3Q Max #> -34.418 -6.388 -1.580 9.052 28.649 #> #> Coefficients: #> Estimate Std. Error t value Pr(>|t|) #> (Intercept) 68.6190 4.7355 14.490 < 2e-16 *** #> HOVAL -0.2739 0.1032 -2.654 0.0109 * #> INC -1.5973 0.3341 -4.780 1.83e-05 *** #> --- #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 #> #> Residual standard error: 11.43 on 46 degrees of freedom #> Multiple R-squared: 0.5524,\tAdjusted R-squared: 0.5329 #> F-statistic: 28.39 on 2 and 46 DF, p-value: 9.341e-09 #> lw <- nb2listw(COL.nb) res <- lm.RStests(oldcrime.lm, listw=lw, test=\"all\") summary(res) #> \tRao's score (a.k.a Lagrange multiplier) diagnostics for spatial #> \tdependence #> data: #> model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD) #> test weights: lw #> #> statistic parameter p.value #> RSerr 5.723131 1 0.016743 * #> RSlag 9.363684 1 0.002213 ** #> adjRSerr 0.079495 1 0.777983 #> adjRSlag 3.720048 1 0.053763 . #> SARMA 9.443178 2 0.008901 ** #> --- #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 if (require(\"spatialreg\", quietly=TRUE)) { oldcrime.slx <- lmSLX(CRIME ~ HOVAL + INC, data = COL.OLD, listw=lw) summary(lm.RStests(oldcrime.slx, listw=lw, test=c(\"adjRSerr\", \"adjRSlag\"))) } run <- require(\"codingMatrices\", quietly=TRUE) if (run) { COL.OLD$fEW <- factor(COL.OLD$EW) COL.OLD$fDISCBD <- ordered(cut(COL.OLD$DISCBD, c(0, 1.5, 3, 4.5, 6))) f <- formula(CRIME ~ INC + HOVAL + fDISCBD*fEW) lw <- nb2listw(COL.nb, style=\"W\") # default codings summary(lm.RStests(lm(f, data=COL.OLD, contrasts=list(fDISCBD=\"contr.poly\", fEW=\"contr.treatment\")), lw, test=c(\"adjRSerr\", \"adjRSlag\"))) } if (run) { # use codingMatrices::code_diff for ordered factor summary(lm.RStests(lm(f, data=COL.OLD, contrasts=list(fDISCBD=\"code_diff\", fEW=\"contr.treatment\")), lw, test=c(\"adjRSerr\", \"adjRSlag\"))) } if (run) { # use codingMatrices::code_control for both summary(lm.RStests(lm(f, data=COL.OLD, contrasts=list(fDISCBD=\"code_control\", fEW=\"code_control\")), lw, test=c(\"adjRSerr\", \"adjRSlag\"))) }"},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute Local Geary statistic — localC","title":"Compute Local Geary statistic — localC","text":"Local Geary local adaptation Geary's C statistic spatial autocorrelation. Local Geary uses squared differences measure dissimilarity unlike Local Moran. Low values Local Geary indicate positive spatial autocorrelation large refers negative spatial autocorrelation. Inference Local Geary based permutation approach compares observed value reference distribution spatial randomness. localC_perm() returns pseudo p-value. analytical p-value based number permutations used care.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute Local Geary statistic — localC","text":"","code":"localC(x, ..., zero.policy=NULL) # Default S3 method localC(x, listw, ..., zero.policy=attr(listw, \"zero.policy\")) # S3 method for class 'formula' localC(formula, data, listw, ..., zero.policy=attr(listw, \"zero.policy\")) # S3 method for class 'list' localC(x, listw, ..., zero.policy=attr(listw, \"zero.policy\")) # S3 method for class 'matrix' localC(x, listw, ..., zero.policy=attr(listw, \"zero.policy\")) # S3 method for class 'data.frame' localC(x, listw, ..., zero.policy=attr(listw, \"zero.policy\")) localC_perm(x, ..., zero.policy=NULL, iseed=NULL, no_repeat_in_row=FALSE) # Default S3 method localC_perm(x, listw, nsim = 499, alternative = \"two.sided\", ..., zero.policy=attr(listw, \"zero.policy\"), iseed=NULL, no_repeat_in_row=FALSE) # S3 method for class 'formula' localC_perm(formula, data, listw, nsim = 499, alternative = \"two.sided\", ..., zero.policy=attr(listw, \"zero.policy\"), iseed=NULL, no_repeat_in_row=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute Local Geary statistic — localC","text":"x numeric vector, numeric matrix, list. See details . formula one-sided formula determining variables used. listw listw object created example nb2listw. data Used formula provided. matrix data frame containing variables formula formula. nsim number simulations used permutation test. alternative character defining alternative hypothesis. Must one \"two.sided\", \"less\" \"greater\". ... arguments passed methods. zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA. iseed default NULL, used set seed;output reproducible count CPU cores across computation distributed no_repeat_in_row default FALSE, TRUE, sample conditionally row without replacements avoid duplicate values, https://github.com/r-spatial/spdep/issues/124","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Compute Local Geary statistic — localC","text":"Local Geary can extended multivariate context. x numeric vector, univariate Local Geary calculated. calculate multivariate Local Moran provide either list matrix. x list, element must numeric vector length length neighbours listw. case x matrix number rows must length neighbours listw. required univariate context, standardized Local Geary calculated. multivariate Local Geary always standardized. univariate Local Geary calculated \\(c_i = \\sum_j w_{ij}(x_i - x_j)^2\\) multivariate Local Geary calculated \\(c_{k,} = \\sum_{v=1}^{k} c_{v,}\\) described Anselin (2019).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute Local Geary statistic — localC","text":"numeric vector containing Local Geary statistic attribute pseudo-p localC_perm() used. pseudo-p 8 column matrix containing E.Ci expectation Local Geary statistic based permutation sample Var.Ci variance Local Geary based permutation sample Z.Ci standard deviate Local Geary based permutation sample Pr() p-value Local Geary statistic using pnorm() using standard deviates based permutation sample means standard deviations Pr() Sim rank() punif() observed statistic rank [0, 1] p-values using alternative= Pr(folded) Sim simulation folded [0, 0.5] range ranked p-value (based https://github.com/pysal/esda/blob/4a63e0b5df1e754b17b5f1205b8cadcbecc5e061/esda/crand.py#L211-L213) Skewness output e1071::skewness() permutation samples underlying standard deviates Kurtosis output e1071::kurtosis() permutation samples underlying standard deviates","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute Local Geary statistic — localC","text":"Anselin, L. (1995), Local Indicators Spatial Association—LISA. Geographical Analysis, 27: 93-115. doi:10.1111/j.1538-4632.1995.tb00338.x Anselin, L. (2019), Local Indicator Multivariate Spatial Association: Extending Gearys c. Geogr Anal, 51: 133-150. doi:10.1111/gean.12164","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute Local Geary statistic — localC","text":"Josiah Parry josiah.parry@gmail.com Roger Bivand","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localC.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute Local Geary statistic — localC","text":"","code":"orig <- spData::africa.rook.nb listw <- nb2listw(orig) x <- spData::afcon$totcon (A <- localC(x, listw)) #> [1] 0.39025457 0.50460439 0.15303047 2.90814878 3.40006901 0.17103368 #> [7] 0.29947832 0.72444806 2.30617282 5.70252541 2.23161263 0.17833029 #> [13] 0.18420002 0.18680408 0.37851643 0.11056720 0.14814835 0.17257920 #> [19] 0.03254150 0.18992772 0.08749322 3.71970760 0.09566918 0.26112918 #> [25] 0.09505331 2.99934478 1.17465032 1.64868780 0.87901004 0.05909537 #> [31] 2.54591475 3.85570655 2.99413462 0.96084992 0.80678832 1.56869350 #> [37] 0.86422915 0.38817470 0.23425755 1.26191610 1.34455327 1.80707481 listw1 <- nb2listw(droplinks(sym.attr.nb(orig), 3, sym=TRUE), zero.policy=TRUE) #> Warning: some observations have no neighbours #> Warning: neighbour object has 2 sub-graphs (A1 <- localC(x, listw1, zero.policy=FALSE)) #> [1] 0.39025457 0.57491918 NA 2.90814878 3.40006901 0.17103368 #> [7] 0.29947832 0.72444806 2.30617282 5.70252541 2.23161263 0.17833029 #> [13] 0.18420002 0.18680408 0.37851643 0.11056720 0.14814835 0.17257920 #> [19] 0.03254150 0.18992772 0.08749322 3.71970760 0.09566918 0.26112918 #> [25] 0.09505331 2.99934478 1.17465032 1.64868780 0.87901004 0.05909537 #> [31] 2.54591475 3.85570655 2.99413462 0.96084992 0.80678832 1.56869350 #> [37] 0.86422915 0.38817470 0.23425755 1.26191610 1.34455327 1.80707481 (A2 <- localC(x, listw1, zero.policy=TRUE)) #> [1] 0.39025457 0.57491918 0.00000000 2.90814878 3.40006901 0.17103368 #> [7] 0.29947832 0.72444806 2.30617282 5.70252541 2.23161263 0.17833029 #> [13] 0.18420002 0.18680408 0.37851643 0.11056720 0.14814835 0.17257920 #> [19] 0.03254150 0.18992772 0.08749322 3.71970760 0.09566918 0.26112918 #> [25] 0.09505331 2.99934478 1.17465032 1.64868780 0.87901004 0.05909537 #> [31] 2.54591475 3.85570655 2.99413462 0.96084992 0.80678832 1.56869350 #> [37] 0.86422915 0.38817470 0.23425755 1.26191610 1.34455327 1.80707481 run <- FALSE if (require(rgeoda, quietly=TRUE)) run <- TRUE if (run) { W <- create_weights(as.numeric(length(x))) for (i in 1:length(listw$neighbours)) { set_neighbors_with_weights(W, i, listw$neighbours[[i]], listw$weights[[i]]) update_weights(W) } set.seed(1) B <- local_geary(W, data.frame(x)) all.equal(A, lisa_values(B)) } if (run) { set.seed(1) C <- localC_perm(x, listw, nsim = 499, conditional=TRUE, alternative=\"two.sided\") cor(ifelse(lisa_pvalues(B) < 0.5, lisa_pvalues(B), 1-lisa_pvalues(B)), attr(C, \"pseudo-p\")[,6]) } # pseudo-p values probably wrongly folded https://github.com/GeoDaCenter/rgeoda/issues/28 # \\donttest{ tmap_ok <- FALSE if (require(tmap, quietly=TRUE)) tmap_ok <- TRUE if (run) { # doi: 10.1111/gean.12164 guerry_path <- system.file(\"extdata\", \"Guerry.shp\", package = \"rgeoda\") g <- st_read(guerry_path)[, 7:12] cor(st_drop_geometry(g)) #(Tab. 1) lw <- nb2listw(poly2nb(g)) moran(g$Crm_prs, lw, n=nrow(g), S0=Szero(lw))$I moran(g$Crm_prp, lw, n=nrow(g), S0=Szero(lw))$I moran(g$Litercy, lw, n=nrow(g), S0=Szero(lw))$I moran(g$Donatns, lw, n=nrow(g), S0=Szero(lw))$I moran(g$Infants, lw, n=nrow(g), S0=Szero(lw))$I moran(g$Suicids, lw, n=nrow(g), S0=Szero(lw))$I } if (run) { o <- prcomp(st_drop_geometry(g), scale.=TRUE) cor(st_drop_geometry(g), o$x[,1:2])^2 #(Tab. 2) } if (run) { g$PC1 <- o$x[, \"PC1\"] brks <- c(min(g$PC1), natural_breaks(k=6, g[\"PC1\"]), max(g$PC1)) if (tmap_ok) { tmap4 <- packageVersion(\"tmap\") >= \"3.99\" if (tmap4) { tm_shape(g) + tm_polygons(fill=\"PC1\", fill.scale=tm_scale(values=\"brewer.rd_yl_gn\", breaks=brks, midpoint=0), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"PC1\", breaks=brks, midpoint=0) + tm_borders() # Fig. 1 } } else { plot(g[\"PC1\"], breaks=brks) } } if (run) { g$PC2 <- -1*o$x[, \"PC2\"] # eigenvalue sign arbitrary brks <- c(min(g$PC2), natural_breaks(k=6, g[\"PC2\"]), max(g$PC2)) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"PC2\", fill.scale=tm_scale(values=\"brewer.rd_yl_gn\", breaks=brks, midpoint=0), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"PC2\", breaks=brks, midpoint=0) + tm_borders() # Fig. 2 } } else { plot(g[\"PC2\"], breaks=brks) } } if (run) { w <- queen_weights(g) lm_PC1 <- local_moran(w, g[\"PC1\"], significance_cutoff=0.01, permutations=99999) g$lm_PC1 <- factor(lisa_clusters(lm_PC1), levels=0:4, labels=lisa_labels(lm_PC1)[1:5]) is.na(g$lm_PC1) <- g$lm_PC1 == \"Not significant\" g$lm_PC1 <- droplevels(g$lm_PC1) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lm_PC1\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lm_PC1\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # Fig. 3 } } else { plot(g[\"lm_PC1\"]) } } if (run) { set.seed(1) lm_PC1_spdep <- localmoran_perm(g$PC1, lw, nsim=9999) q <- attr(lm_PC1_spdep, \"quadr\")$pysal g$lm_PC1_spdep <- q is.na(g$lm_PC1_spdep) <- lm_PC1_spdep[,6] > 0.02 # note folded p-values g$lm_PC1_spdep <- droplevels(g$lm_PC1_spdep) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lm_PC1_spdep\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lm_PC1_spdep\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # rep. Fig. 3 } } else { plot(g[\"lm_PC1_spdep\"]) } } if (run) { lg_PC1 <- local_g(w, g[\"PC1\"], significance_cutoff=0.01, permutations=99999) g$lg_PC1 <- factor(lisa_clusters(lg_PC1), levels=0:2, labels=lisa_labels(lg_PC1)[0:3]) is.na(g$lg_PC1) <- g$lg_PC1 == \"Not significant\" g$lg_PC1 <- droplevels(g$lg_PC1) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lg_PC1\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lg_PC1\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # Fig. 4 (wrong) } } else { plot(g[\"lg_PC1\"]) } g$lg_PC1a <- cut(g$PC1, c(-Inf, mean(g$PC1), Inf), labels=c(\"Low\", \"High\")) is.na(g$lg_PC1a) <- lisa_pvalues(lg_PC1) >= 0.01 g$lg_PC1a <- droplevels(g$lg_PC1a) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lg_PC1a\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lg_PC1a\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # Fig. 4 (guess) } } else { plot(g[\"lg_PC1\"]) } } if (run) { lc_PC1 <- local_geary(w, g[\"PC1\"], significance_cutoff=0.01, permutations=99999) g$lc_PC1 <- factor(lisa_clusters(lc_PC1), levels=0:4, labels=lisa_labels(lc_PC1)[1:5]) is.na(g$lc_PC1) <- g$lc_PC1 == \"Not significant\" g$lc_PC1 <- droplevels(g$lc_PC1) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lc_PC1\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lc_PC1\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # Fig. 5 } } else { plot(g[\"lc_PC1\"]) } } if (run) { set.seed(1) system.time(lc_PC1_spdep <- localC_perm(g$PC1, lw, nsim=9999, alternative=\"two.sided\")) } if (run) { if (require(parallel, quietly=TRUE)) { ncpus <- max(2L, detectCores(logical=FALSE), na.rm = TRUE)-1L # test with single core if (ncpus > 1L) ncpus <- 1L cores <- get.coresOption() set.coresOption(ncpus) system.time(lmc_PC1_spdep1 <- localC_perm(g$PC1, lw, nsim=9999, alternative=\"two.sided\", iseed=1)) set.coresOption(cores) } } if (run) { g$lc_PC1_spdep <- attr(lc_PC1_spdep, \"cluster\") is.na(g$lc_PC1_spdep) <- attr(lc_PC1_spdep, \"pseudo-p\")[,6] > 0.01 g$lc_PC1_spdep <- droplevels(g$lc_PC1_spdep) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lc_PC1_spdep\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lc_PC1_spdep\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # rep. Fig. 5 } } else { plot(g[\"lc_PC1_spdep\"]) } } if (run) { g$both_PC1 <- interaction(g$lc_PC1, g$lm_PC1) g$both_PC1 <- droplevels(g$both_PC1) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"both_PC1\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"both_PC1\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # Fig. 6 } } else { plot(g[\"both_PC1\"]) } } if (run) { lc005_PC1 <- local_geary(w, g[\"PC1\"], significance_cutoff=0.005, permutations=99999) g$lc005_PC1 <- factor(lisa_clusters(lc005_PC1), levels=0:4, labels=lisa_labels(lc005_PC1)[1:5]) is.na(g$lc005_PC1) <- g$lc005_PC1 == \"Not significant\" g$lc005_PC1 <- droplevels(g$lc005_PC1) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lc005_PC1\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lc005_PC1\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # Fig. 7 } } else { plot(g[\"lc005_PC1\"]) } if (run) { g$lc005_PC1_spdep <- attr(lc_PC1_spdep, \"cluster\") is.na(g$lc005_PC1_spdep) <- attr(lc_PC1_spdep, \"pseudo-p\")[,6] > 0.005 g$lc005_PC1_spdep <- droplevels(g$lc005_PC1_spdep) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lc005_PC1_spdep\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lc005_PC1_spdep\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # rep. Fig. 7 } } else { plot(g[\"lc005_PC1_spdep\"]) } } if (run) { lc001_PC1 <- local_geary(w, g[\"PC1\"], significance_cutoff=0.001, permutations=99999) g$lc001_PC1 <- factor(lisa_clusters(lc001_PC1), levels=0:4, labels=lisa_labels(lc001_PC1)[1:5]) is.na(g$lc001_PC1) <- g$lc001_PC1 == \"Not significant\" g$lc001_PC1 <- droplevels(g$lc001_PC1) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lc005_PC1\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lc001_PC1\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # Fig. 8 } } else { plot(g[\"lc001_PC1\"]) } } if (run) { g$lc001_PC1_spdep <- attr(lc_PC1_spdep, \"cluster\") is.na(g$lc001_PC1_spdep) <- attr(lc_PC1_spdep, \"pseudo-p\")[,6] > 0.001 g$lc001_PC1_spdep <- droplevels(g$lc001_PC1_spdep) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lc005_PC1_spdep\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lc001_PC1_spdep\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # rep. Fig. 8 } } else { plot(g[\"lc001_PC1_spdep\"]) } } } if (run) { lc_PC2 <- local_geary(w, g[\"PC2\"], significance_cutoff=0.01, permutations=99999) g$lc_PC2 <- factor(lisa_clusters(lc_PC2), levels=0:4, labels=lisa_labels(lc_PC2)[1:5]) is.na(g$lc_PC2) <- g$lc_PC2 == \"Not significant\" g$lc_PC2 <- droplevels(g$lc_PC2) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lc_PC2\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lc_PC2\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # Fig. 9 } } else { plot(g[\"lc_PC2\"]) } } if (run) { lmc_PC <- local_multigeary(w, g[c(\"PC1\",\"PC2\")], significance_cutoff=0.00247, permutations=99999) g$lmc_PC <- factor(lisa_clusters(lmc_PC), levels=0:1, labels=lisa_labels(lmc_PC)[1:2]) is.na(g$lmc_PC) <- g$lmc_PC == \"Not significant\" g$lmc_PC <- droplevels(g$lmc_PC) table(interaction((p.adjust(lisa_pvalues(lmc_PC), \"fdr\") < 0.01), g$lmc_PC)) } if (run) { if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lmc_PC\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lmc_PC\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # Fig. 10 } } else { plot(g[\"lmc_PC\"]) } } if (run) { set.seed(1) lmc_PC_spdep <- localC_perm(g[c(\"PC1\",\"PC2\")], lw, nsim=9999, alternative=\"two.sided\") all.equal(lisa_values(lmc_PC), c(lmc_PC_spdep)) } if (run) { cor(attr(lmc_PC_spdep, \"pseudo-p\")[,6], lisa_pvalues(lmc_PC)) } if (run) { g$lmc_PC_spdep <- attr(lmc_PC_spdep, \"cluster\") is.na(g$lmc_PC_spdep) <- p.adjust(attr(lmc_PC_spdep, \"pseudo-p\")[,6], \"fdr\") > 0.01 g$lmc_PC_spdep <- droplevels(g$lmc_PC_spdep) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lmc_PC_spdep\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lmc_PC_spdep\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # rep. Fig. 10 } } else { plot(g[\"lmc_PC_spdep\"]) } } if (run) { lmc_vars <- local_multigeary(w, st_drop_geometry(g)[, 1:6], significance_cutoff=0.00247, permutations=99999) g$lmc_vars <- factor(lisa_clusters(lmc_vars), levels=0:1, labels=lisa_labels(lmc_vars)[1:2]) is.na(g$lmc_vars) <- g$lmc_vars == \"Not significant\" g$lmc_vars <- droplevels(g$lmc_vars) table(interaction((p.adjust(lisa_pvalues(lmc_vars), \"fdr\") < 0.01), g$lmc_vars)) } if (run) { if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lmc_vars\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lmc_vars\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # Fig. 11 } } else { plot(g[\"lmc_vars\"]) } } if (run) { set.seed(1) system.time(lmc_vars_spdep <- localC_perm(st_drop_geometry(g)[, 1:6], lw, nsim=9999, alternative=\"two.sided\")) } if (run) { all.equal(lisa_values(lmc_vars), c(lmc_vars_spdep)) } if (run) { cor(attr(lmc_vars_spdep, \"pseudo-p\")[,6], lisa_pvalues(lmc_vars)) } if (run) { if (require(parallel, quietly=TRUE)) { ncpus <- max(2L, detectCores(logical=FALSE), na.rm = TRUE)-1L # test with single core if (ncpus > 1L) ncpus <- 1L cores <- get.coresOption() set.coresOption(ncpus) system.time(lmc_vars_spdep1 <- localC_perm(st_drop_geometry(g)[, 1:6], lw, nsim=9999, alternative=\"two.sided\", iseed=1)) set.coresOption(cores) } } if (run) { all.equal(lisa_values(lmc_vars), c(lmc_vars_spdep1)) } if (run) { cor(attr(lmc_vars_spdep1, \"pseudo-p\")[,6], lisa_pvalues(lmc_vars)) } if (run) { g$lmc_vars_spdep <- attr(lmc_vars_spdep1, \"cluster\") is.na(g$lmc_vars_spdep) <- p.adjust(attr(lmc_vars_spdep1, \"pseudo-p\")[,6], \"fdr\") > 0.01 g$lmc_vars_spdep <- droplevels(g$lmc_vars_spdep) if (tmap_ok) { if (tmap4) { tm_shape(g) + tm_polygons(fill=\"lmc_vars_spdep\", fill.scale=tm_scale(values=\"brewer.set3\", value.na=\"gray95\", label.na=\"Insignificant\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r=0)) } else { tm_shape(g) + tm_fill(\"lmc_vars_spdep\", textNA=\"Insignificant\", colorNA=\"gray95\") + tm_borders() # rep. Fig. 11 } } else { plot(g[\"lmc_vars_spdep\"]) } } # } if (FALSE) { # \\dontrun{ library(reticulate) use_python(\"/usr/bin/python\", required = TRUE) gp <- import(\"geopandas\") ps <- import(\"libpysal\") W <- listw2mat(listw) w <- ps$weights$full2W(W, rownames(W)) w$transform <- \"R\" esda <- import(\"esda\") lM <- esda$Moran_Local(x, w) all.equal(unname(localmoran(x, listw, mlvar=FALSE)[,1]), c(lM$Is)) # confirm x and w the same lC <- esda$Geary_Local(connectivity=w)$fit(scale(x)) # np$std missing ddof=1 n <- length(x) D0 <- spdep:::geary.intern((x - mean(x)) / sqrt(var(x)*(n-1)/n), listw, n=n) # lC components probably wrongly ordered https://github.com/pysal/esda/issues/192 o <- match(round(D0, 6), round(lC$localG, 6)) all.equal(c(lC$localG)[o], D0) # simulation order not retained lC$p_sim[o] attr(C, \"pseudo-p\")[,6] } # }"},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":null,"dir":"Reference","previous_headings":"","what":"G and Gstar local spatial statistics — localG","title":"G and Gstar local spatial statistics — localG","text":"local spatial statistic G calculated zone based spatial weights object used. value returned Z-value, may used diagnostic tool. High positive values indicate posibility local cluster high values variable analysed, low relative values similar cluster low values. inference, Bonferroni-type test suggested references, tables critical values may found (see also details ).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"G and Gstar local spatial statistics — localG","text":"","code":"localG(x, listw, zero.policy=attr(listw, \"zero.policy\"), spChk=NULL, GeoDa=FALSE, alternative = \"two.sided\", return_internals=TRUE) localG_perm(x, listw, nsim=499, zero.policy=attr(listw, \"zero.policy\"), spChk=NULL, alternative = \"two.sided\", iseed=NULL, fix_i_in_Gstar_permutations=TRUE, no_repeat_in_row=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"G and Gstar local spatial statistics — localG","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw zero.policy default NULL, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() GeoDa default FALSE, TRUE, drop x values -neighbour self-neighbour observations summations nsim default 499, number conditonal permutation simulations alternative character string specifying alternative hypothesis, must one \"two.sided\" (default), \"greater\" \"less\". return_internals default TRUE, unused iseed default NULL, used set seed; output reproducible count CPU cores across computation distributed fix_i_in_Gstar_permutations default TRUE (fix x self permutations local G-star), set FALSE use pre-1.2-8 behaviour no_repeat_in_row default FALSE, TRUE, sample conditionally row without replacements avoid duplicate values, https://github.com/r-spatial/spdep/issues/124","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"G and Gstar local spatial statistics — localG","text":"neighbours member listw \"self.included\" attribute set TRUE, Gstar variant, including self-weight \\(w_{ii} > 0\\), calculated returned. returned vector \"gstari\" attribute set TRUE. Self-weights must included using include.self function converting neighbour list spatial weights list nb2listw shown example. critical values statistic assumptions given references 95th percentile n=1: 1.645, n=50: 3.083, n=100: 3.289, n=1000: 3.886.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"G and Gstar local spatial statistics — localG","text":"vector G Gstar standard deviate values, attributes \"gstari\" set TRUE FALSE, \"call\" set function call, class \"localG\". conditional permutation, returned value localG(), simulated standard deviate returned column \"StdDev.Gi\" attr(., \"internals\").","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"G and Gstar local spatial statistics — localG","text":"Conditional permutations added comparative purposes; permutations whole data vector omitting observation , 1.2-8 fixing observation neighbour local G-star.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"G and Gstar local spatial statistics — localG","text":"Ord, J. K. Getis, . 1995 Local spatial autocorrelation statistics: distributional issues application. Geographical Analysis, 27, 286–306; Getis, . Ord, J. K. 1996 Local spatial statistics: overview. P. Longley M. Batty (eds) Spatial analysis: modelling GIS environment (Cambridge: Geoinformation International), 261–277; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"G and Gstar local spatial statistics — localG","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localG.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"G and Gstar local spatial statistics — localG","text":"","code":"data(getisord, package=\"spData\") # spData 0.3.2 changes x, y, xyz object names to go_x, go_y, go_xyz to # avoid putting these objects into the global environment via lazy loading if (exists(\"go_xyz\") && packageVersion(\"spData\") >= \"0.3.2\") { xyz <- go_xyz x <- go_x y <- go_y } xycoords <- cbind(xyz$x, xyz$y) nb30 <- dnearneigh(xycoords, 0, 30) G30 <- localG(xyz$val, nb2listw(nb30, style=\"B\")) G30[length(xyz$val)-136] #> [1] 1.221979 set.seed(1) G30_sim <- localG_perm(xyz$val, nb2listw(nb30, style=\"B\")) G30_sim[length(xyz$val)-136] #> [1] 1.221979 nb60 <- dnearneigh(xycoords, 0, 60) G60 <- localG(xyz$val, nb2listw(nb60, style=\"B\")) G60[length(xyz$val)-136] #> [1] 1.748098 nb90 <- dnearneigh(xycoords, 0, 90) G90 <- localG(xyz$val, nb2listw(nb90, style=\"B\")) G90[length(xyz$val)-136] #> [1] 1.986135 nb120 <- dnearneigh(xycoords, 0, 120) G120 <- localG(xyz$val, nb2listw(nb120, style=\"B\")) G120[length(xyz$val)-136] #> [1] 1.893374 nb150 <- dnearneigh(xycoords, 0, 150) G150 <- localG(xyz$val, nb2listw(nb150, style=\"B\")) G150[length(xyz$val)-136] #> [1] 1.237454 brks <- seq(-5,5,1) cm.col <- cm.colors(length(brks)-1) image(x, y, t(matrix(G30, nrow=16, ncol=16, byrow=TRUE)), breaks=brks, col=cm.col, asp=1) text(xyz$x, xyz$y, round(G30, digits=1), cex=0.7) polygon(c(195,225,225,195), c(195,195,225,225), lwd=2) title(main=expression(paste(\"Values of the \", G[i], \" statistic\"))) G30s <- localG(xyz$val, nb2listw(include.self(nb30), style=\"B\")) cat(\"value according to Getis and Ord's eq. 14.2, p. 263 (1996)\\n\") #> value according to Getis and Ord's eq. 14.2, p. 263 (1996) G30s[length(xyz$val)-136] #> [1] 1.45078 cat(paste(\"value given by Getis and Ord (1996), p. 267\", \"(division by n-1 rather than n \\n in variance)\\n\")) #> value given by Getis and Ord (1996), p. 267 (division by n-1 rather than n #> in variance) G30s[length(xyz$val)-136] * (sqrt(sum(scale(xyz$val, scale=FALSE)^2)/length(xyz$val)) / sqrt(var(xyz$val))) #> [1] 1.447943 image(x, y, t(matrix(G30s, nrow=16, ncol=16, byrow=TRUE)), breaks=brks, col=cm.col, asp=1) text(xyz$x, xyz$y, round(G30s, digits=1), cex=0.7) polygon(c(195,225,225,195), c(195,195,225,225), lwd=2) title(main=expression(paste(\"Values of the \", G[i]^\"*\", \" statistic\")))"},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":null,"dir":"Reference","previous_headings":"","what":"A local hotspot statistic for analysing multiscale datasets — localGS","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"function implements \\(GS_i\\) test statistic local hotspots specific pairwise evaluated distance bands, proposed Westerholt et al. (2015). Like hotspot estimator \\(G_i^*\\), \\(GS_i\\) statistic given z-scores can evaluated accordingly. idea method identify hotspots datasets comprise several, difficult--separate processes operating different scales. often case complex user-generated datasets Twitter feeds. example, football match reflected tweets pubs, homes, stadium vicinity. exemplified phenomena represent different processes may detected different geometric scales. \\(GS_i\\) method enables identification specifying geometric scale band strictly calculating statistical quantities mean variance solely respective relevant observations interact range adjusted scale band. addition, neighbourhood relationships respective central unit, scale-relevant relationships considered. way, hotspots can detected specific scale ranges independently scales. statistic given : $$GS_i = \\frac{\\displaystyle\\sum_{j; k < j}{w_{ij}w_{ik}\\phi_{jk}a_{jk}} - \\frac{W_i}{\\Phi} \\displaystyle\\sum_{j; k < j}{\\phi_{jk}a_{jk}}}{\\sqrt{\\frac{W_i}{\\Phi}\\displaystyle\\sum_{j; k < j}{\\phi_{jk}a_{jk}^2} + \\frac{W_i\\left(W_i-1\\right)}{\\Phi\\left(\\Phi-1\\right)}\\left(\\Gamma^2 -\\!\\! \\displaystyle\\sum_{j; k < j}{\\left(\\phi_{jk}a_{jk}\\right)^2}\\right) - \\left(\\frac{W_i}{\\Phi}\\displaystyle\\sum_{j; k < j}{\\phi_{jk}a_{jk}}\\right)^2}}$$ $$a_{jk} = x_j + x_k,\\;\\;\\; W_i = \\displaystyle\\sum_{j; k < j}{w_{ij}w_{ik}\\phi_{jk}},\\;\\;\\; \\Phi = \\displaystyle\\sum_{j; k < j}{\\phi_{jk}},\\;\\;\\; \\textrm{} \\;\\;\\; \\Gamma = \\displaystyle\\sum_{j; k < j}{\\phi_{jk}a_{jk}}.$$","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"","code":"localGS(x, listw, dmin, dmax, attr, longlat = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"x sf sp object listw listw object dmin lower distance bound (greater equal) dmax upper distance bound (less equal) attr name attribute interest longlat default NULL; TRUE point coordinates longitude-latitude decimal degrees, case distances measured kilometres; x SpatialPoints object, value taken object , overrides argument NULL; distances measured map units FALSE NULL","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"pairs observations shared distance (map units) interval [dmin, dmax] within maximum radius dmax around corresponding output observation considered. Thereby, also mean values variance terms estimated within measure adjusted scale range consideration. application examples method see Westerholt et al. (2015) (applied tweets) Sonea & Westerholt (2021) (applied access banking scenario).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"vector \\(GS_i\\) values given z-scores.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"Westerholt, R., Resch, B. & Zipf, . 2015. local scale-sensitive indicator spatial autocorrelation assessing high-low-value clusters multiscale datasets. International Journal Geographical Information Science, 29(5), 868–887, doi:10.1080/13658816.2014.1002499 . Sonea, . Westerholt, R. (2021): Geographic temporal access basic banking services Wales. Applied Spatial Analysis Policy, 14 (4), 879–905, doi:10.1007/s12061-021-09386-3 .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"René Westerholt rene.westerholt@tu-dortmund.de","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/localGS.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"A local hotspot statistic for analysing multiscale datasets — localGS","text":"","code":"# \\donttest{ boston.tr <- sf::st_read(system.file(\"shapes/boston_tracts.gpkg\", package=\"spData\")[1]) #> Reading layer `boston_tracts' from data source #> `C:\\Users\\rzomor2\\AppData\\Local\\R\\win-library\\4.4\\spData\\shapes\\boston_tracts.gpkg' #> using driver `GPKG' #> Simple feature collection with 506 features and 36 fields #> Geometry type: POLYGON #> Dimension: XY #> Bounding box: xmin: -71.52311 ymin: 42.00305 xmax: -70.63823 ymax: 42.67307 #> Geodetic CRS: NAD27 boston.tr_utm <- st_transform(boston.tr, 32619) #26786 boston_listw1 <- nb2listwdist(dnearneigh(st_centroid(boston.tr_utm), 1, 2000), boston.tr_utm, type = \"dpd\", alpha = 2, zero.policy = TRUE, dmax = 9500) #> Warning: st_centroid assumes attributes are constant over geometries #> Warning: neighbour object has 120 sub-graphs boston_listw2 <- nb2listwdist(dnearneigh(st_centroid(boston.tr_utm), 5000, 9500), boston.tr_utm, type = \"dpd\", alpha = 2, zero.policy = TRUE, dmax = 9500) #> Warning: st_centroid assumes attributes are constant over geometries boston_RM_gsi_1 <- localGS(boston.tr_utm, boston_listw1, 1, 2000, \"RM\", FALSE) boston_RM_gsi_2 <- localGS(boston.tr_utm, boston_listw2, 2000, 9500, \"RM\", FALSE) # }"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":null,"dir":"Reference","previous_headings":"","what":"Exact local Moran's Ii tests — localmoran.exact","title":"Exact local Moran's Ii tests — localmoran.exact","text":"localmoran.exact provides exact local Moran's Ii tests null hypothesis, localmoran.exact.alt provides exact local Moran's Ii tests alternative hypothesis. case, model may fitted model derived model fitted spatialreg::errorsarlm, covariance matrix can passed Omega= argument.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Exact local Moran's Ii tests — localmoran.exact","text":"","code":"localmoran.exact(model, select, nb, glist = NULL, style = \"W\", zero.policy = NULL, alternative = \"two.sided\", spChk = NULL, resfun = weighted.residuals, save.Vi = FALSE, useTP=FALSE, truncErr=1e-6, zeroTreat=0.1) localmoran.exact.alt(model, select, nb, glist = NULL, style = \"W\", zero.policy = NULL, alternative = \"two.sided\", spChk = NULL, resfun = weighted.residuals, Omega = NULL, save.Vi = FALSE, save.M = FALSE, useTP=FALSE, truncErr=1e-6, zeroTreat=0.1) # S3 method for class 'localmoranex' print(x, ...) # S3 method for class 'localmoranex' as.data.frame(x, row.names=NULL, optional=FALSE, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Exact local Moran's Ii tests — localmoran.exact","text":"model object class lm returned lm (assuming global spatial autocorrelation), object class sarlm returned spatial simultaneous autoregressive model fit (assuming global spatial autocorrelation represented model spatial coefficient); weights may specified lm fit, offsets used select integer vector id. numbers zones tested; missing, zones nb list neighbours class nb glist list general weights corresponding neighbours style can take values W, B, C, S zero.policy default NULL, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one greater (default), less two.sided. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() resfun default: weighted.residuals; function used extract residuals lm object, may residuals, weighted.residuals, rstandard, rstudent Omega SAR process matrix may passed test alternative hypothesis, example Omega <- invIrW(listw, rho=0.1); Omega <- tcrossprod(Omega), chol() taken internally save.Vi TRUE, return star-shaped weights lists zone tested save.M TRUE, save list left right M products useTP default FALSE, TRUE, use truncation point integration rather upper=Inf, see Tiefelsdorf (2000), eq. 6.7, p.69 truncErr useTP=TRUE, pass truncation error truncation point function zeroTreat useTP=TRUE, pass zero adjustment truncation point function x object printed row.names ignored argument .data.frame.localmoranex; row names assigned localmoranex object optional ignored argument .data.frame.localmoranex; row names assigned localmoranex object ... arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Exact local Moran's Ii tests — localmoran.exact","text":"list class localmoranex containing \"select\" lists, class moranex following components: statistic value exact standard deviate global Moran's . p.value p-value test. estimate value observed local Moran's Ii. method character string giving method used. alternative character string describing alternative hypothesis. gamma eigenvalues (two extreme values null, vector alternative) oType usually set \"E\", set \"N\" integration leads domain value qnorm, Normal assumption substituted. occurs output p-value close zero data.name character string giving name(s) data. df degrees freedom zone tested Vi zone tested alternative tested, list left right M products attribute M.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Exact local Moran's Ii tests — localmoran.exact","text":"Bivand RS, Müller W, Reder M (2009) Power calculations global local Moran’s . Comput Stat Data Anal 53:2859–2872; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Exact local Moran's Ii tests — localmoran.exact","text":"Markus Reder Roger Bivand","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.exact.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Exact local Moran's Ii tests — localmoran.exact","text":"","code":"eire <- st_read(system.file(\"shapes/eire.gpkg\", package=\"spData\")[1]) #> Reading layer `eire' from data source #> `C:\\Users\\rzomor2\\AppData\\Local\\R\\win-library\\4.4\\spData\\shapes\\eire.gpkg' #> using driver `GPKG' #> Simple feature collection with 26 features and 10 fields #> Geometry type: MULTIPOLYGON #> Dimension: XY #> Bounding box: xmin: -4.12 ymin: 5768 xmax: 300.82 ymax: 6119.25 #> Projected CRS: Undefined Cartesian SRS with unknown unit row.names(eire) <- as.character(eire$names) eire.nb <- poly2nb(eire) e.lm <- lm(OWNCONS ~ ROADACC, data=eire) localmoran.sad(e.lm, nb=eire.nb) #> Local Morans I Saddlepoint Pr. (Sad) #> 1 Carlow 0.21699668 0.95074844 3.417321e-01 #> 2 Cavan -0.37257361 -1.00603119 3.144006e-01 #> 3 Clare 0.23197510 0.67166518 5.017969e-01 #> 4 Cork 0.78193548 1.74761575 8.053059e-02 #> 5 Donegal -1.69064059 -1.72031078 8.537596e-02 #> 6 Dublin -0.16069692 -0.35212627 7.247436e-01 #> 7 Galway 1.31371473 2.66849536 7.619183e-03 #> 8 Kerry 0.36534866 0.78073279 4.349597e-01 #> 9 Kildare -0.02557544 0.04167665 9.667565e-01 #> 10 Kilkenny 0.57684331 1.70897697 8.745521e-02 #> 11 Laoghis -0.05951798 -0.12155465 9.032517e-01 #> 12 Leitrim 0.38484587 1.47227033 1.409479e-01 #> 13 Limerick 0.11817987 0.45727712 6.474719e-01 #> 14 Longford 1.41643200 2.51113769 1.203427e-02 #> 15 Louth 0.56242920 1.07441571 2.826364e-01 #> 16 Mayo 0.87572704 2.05251226 4.011990e-02 #> 17 Meath 0.00367856 0.12813539 8.980418e-01 #> 18 Monaghan 0.55098311 1.23999193 2.149784e-01 #> 19 Offaly 0.15155556 0.80786519 4.191682e-01 #> 20 Roscommon 2.04368839 4.53187292 5.846302e-06 #> 21 Sligo -0.47579871 -0.94578114 3.442602e-01 #> 22 Tipperary -0.03454106 -0.06919691 9.448329e-01 #> 23 Waterford 0.85723423 1.91385108 5.563919e-02 #> 24 Westmeath 0.45138572 1.36017204 1.737755e-01 #> 25 Wexford 0.64371834 1.63188492 1.027037e-01 #> 26 Wicklow 0.02441950 0.21197000 8.321304e-01 localmoran.exact(e.lm, nb=eire.nb) #> Local Morans I Exact SD Pr. (exact) #> 1 Carlow 0.21699668 1.02706083 3.043918e-01 #> 2 Cavan -0.37257361 -1.04864802 2.943401e-01 #> 3 Clare 0.23197510 0.76362894 4.450884e-01 #> 4 Cork 0.78193548 1.77727656 7.552275e-02 #> 5 Donegal -1.69064059 -1.74428756 8.110896e-02 #> 6 Dublin -0.16069692 -0.44236119 6.582279e-01 #> 7 Galway 1.31371473 2.69199974 7.102500e-03 #> 8 Kerry 0.36534866 0.85742696 3.912090e-01 #> 9 Kildare -0.02557544 -0.03475476 9.722753e-01 #> 10 Kilkenny 0.57684331 1.74146177 8.160267e-02 #> 11 Laoghis -0.05951798 -0.21824035 8.272419e-01 #> 12 Leitrim 0.38484587 1.51434641 1.299380e-01 #> 13 Limerick 0.11817987 0.56922630 5.692026e-01 #> 14 Longford 1.41643200 2.53491837 1.124735e-02 #> 15 Louth 0.56242920 1.12775107 2.594251e-01 #> 16 Mayo 0.87572704 2.08125803 3.741029e-02 #> 17 Meath 0.00367856 0.16372685 8.699462e-01 #> 18 Monaghan 0.55098311 1.28435459 1.990179e-01 #> 19 Offaly 0.15155556 0.89537870 3.705847e-01 #> 20 Roscommon 2.04368839 4.55244870 5.302509e-06 #> 21 Sligo -0.47579871 -0.98101752 3.265841e-01 #> 22 Tipperary -0.03454106 -0.16132608 8.718366e-01 #> 23 Waterford 0.85723423 1.94188723 5.215075e-02 #> 24 Westmeath 0.45138572 1.40091422 1.612397e-01 #> 25 Wexford 0.64371834 1.66488051 9.593660e-02 #> 26 Wicklow 0.02441950 0.29717701 7.663314e-01 localmoran.exact(e.lm, nb=eire.nb, useTP=TRUE) #> Local Morans I Exact SD Pr. (exact) #> 1 Carlow 0.21699668 1.02706127 3.043916e-01 #> 2 Cavan -0.37257361 -1.04864834 2.943400e-01 #> 3 Clare 0.23197510 0.76362936 4.450881e-01 #> 4 Cork 0.78193548 1.77727666 7.552273e-02 #> 5 Donegal -1.69064059 -1.74428741 8.110899e-02 #> 6 Dublin -0.16069692 -0.44236158 6.582276e-01 #> 7 Galway 1.31371473 2.69199162 7.102673e-03 #> 8 Kerry 0.36534866 0.85742736 3.912087e-01 #> 9 Kildare -0.02557544 -0.03540278 9.717586e-01 #> 10 Kilkenny 0.57684331 1.74146192 8.160264e-02 #> 11 Laoghis -0.05951798 -0.21823772 8.272439e-01 #> 12 Leitrim 0.38484587 1.51434680 1.299379e-01 #> 13 Limerick 0.11817987 0.56922674 5.692023e-01 #> 14 Longford 1.41643200 2.53491383 1.124750e-02 #> 15 Louth 0.56242920 1.12775145 2.594249e-01 #> 16 Mayo 0.87572704 2.08125778 3.741032e-02 #> 17 Meath 0.00367856 0.15714487 8.751307e-01 #> 18 Monaghan 0.55098311 1.28435495 1.990178e-01 #> 19 Offaly 0.15155556 0.89537914 3.705844e-01 #> 20 Roscommon 2.04368839 4.53362873 5.797890e-06 #> 21 Sligo -0.47579871 -0.98101780 3.265840e-01 #> 22 Tipperary -0.03454106 -0.16116590 8.719627e-01 #> 23 Waterford 0.85723423 1.94188711 5.215077e-02 #> 24 Westmeath 0.45138572 1.40091457 1.612396e-01 #> 25 Wexford 0.64371834 1.66488069 9.593656e-02 #> 26 Wicklow 0.02441950 0.29790569 7.657751e-01 run <- FALSE if (requireNamespace(\"spatialreg\", quietly=TRUE)) run <- TRUE if (run) { e.errorsar <- spatialreg::errorsarlm(OWNCONS ~ ROADACC, data=eire, listw=nb2listw(eire.nb)) lm.target <- lm(e.errorsar$tary ~ e.errorsar$tarX - 1) localmoran.exact.alt(lm.target, nb=eire.nb) } if (run) { Omega <- spatialreg::invIrW(nb2listw(eire.nb), rho=e.errorsar$lambda) Omega1 <- tcrossprod(Omega) localmoran.exact.alt(lm.target, nb=eire.nb, Omega=Omega1) } if (run) { localmoran.exact.alt(lm.target, nb=eire.nb, Omega=Omega1, useTP=TRUE) }"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":null,"dir":"Reference","previous_headings":"","what":"Local Moran's I statistic — localmoran","title":"Local Moran's I statistic — localmoran","text":"local spatial statistic Moran's calculated zone based spatial weights object used. values returned include Z-value, may used diagnostic tool. statistic : $$I_i = \\frac{(x_i-\\bar{x})}{{\\sum_{k=1}^{n}(x_k-\\bar{x})^2}/(n-1)}{\\sum_{j=1}^{n}w_{ij}(x_j-\\bar{x})}$$, expectation variance given Anselin (1995), Sokal et al. (1998) implemented .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Local Moran's I statistic — localmoran","text":"","code":"localmoran(x, listw, zero.policy=attr(listw, \"zero.policy\"), na.action=na.fail, conditional=TRUE, alternative = \"two.sided\", mlvar=TRUE, spChk=NULL, adjust.x=FALSE) localmoran_perm(x, listw, nsim=499, zero.policy=attr(listw, \"zero.policy\"), na.action=na.fail, alternative = \"two.sided\", mlvar=TRUE, spChk=NULL, adjust.x=FALSE, sample_Ei=TRUE, iseed=NULL, no_repeat_in_row=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Local Moran's I statistic — localmoran","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw zero.policy default default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass used, zero substituted NA values calculating spatial lag. (Note na.exclude work properly starting R 1.9.0, na.omit na.exclude assign wrong classes 1.8.*) conditional default TRUE: expectation variance calculated using conditional randomization null (Sokal 1998 Eqs. A7 & A8). Elaboration changes available Sauer et al. (2021). FALSE: expectation variance calculated using total randomization null (Sokal 1998 Eqs. A3 & A4). alternative character string specifying alternative hypothesis, must one greater, less two.sided (default). mlvar default TRUE: values local Moran's reported using variance variable interest (sum squared deviances n), can reported sample variance, dividing (n-1) instead; used implementations. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() adjust.x default FALSE, TRUE, x values observations neighbours omitted mean x nsim default 499, number conditonal permutation simulations sample_Ei default TRUE; conditional permutation, use sample $E_i$ values, analytical values, leaving variances calculated simulation. iseed default NULL, used set seed; output reproducible count CPU cores across computation distributed no_repeat_in_row default FALSE, TRUE, sample conditionally row without replacements avoid duplicate values, https://github.com/r-spatial/spdep/issues/124","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Local Moran's I statistic — localmoran","text":"values local Moran's divided variance (sample variance) variable interest accord Table 1, p. 103, formula (12), p. 99, Anselin (1995), rather formula (7), p. 98. variance local Moran statistic taken Sokal et al. (1998) p. 334, equations 4 & 5 equations 7 & 8 located depending user specification. default, implementation divides n, (n-1) calculating variance higher moments. Conditional code contributed Jeff Sauer Levi Wolf.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Local Moran's I statistic — localmoran","text":"Ii local moran statistic E.Ii expectation local moran statistic; localmoran_permthe permutation sample means Var.Ii variance local moran statistic; localmoran_permthe permutation sample standard deviations Z.Ii standard deviate local moran statistic; localmoran_perm based permutation sample means standard deviations Pr() p-value local moran statistic using pnorm(); localmoran_perm using standard deviatse based permutation sample means standard deviations Pr() Sim localmoran_perm, rank() punif() observed statistic rank [0, 1] p-values using alternative= Pr(folded) Sim simulation folded [0, 0.5] range ranked p-value (based https://github.com/pysal/esda/blob/4a63e0b5df1e754b17b5f1205b8cadcbecc5e061/esda/crand.py#L211-L213) Skewness localmoran_perm, output e1071::skewness() permutation samples underlying standard deviates Kurtosis localmoran_perm, output e1071::kurtosis() permutation samples underlying standard deviates addition, attribute data frame \"quadr\" mean median quadrant columns, column splitting demeaned variable lagged demeaned variable zero.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Local Moran's I statistic — localmoran","text":"Conditional permutations added comparative purposes; permutations whole data vector omitting observation . p-value adjustment, use p.adjust() p.adjustSP() output vector.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Local Moran's I statistic — localmoran","text":"Anselin, L. 1995. Local indicators spatial association, Geographical Analysis, 27, 93–115; Getis, . Ord, J. K. 1996 Local spatial statistics: overview. P. Longley M. Batty (eds) Spatial analysis: modelling GIS environment (Cambridge: Geoinformation International), 261–277; Sokal, R. R, Oden, N. L. Thomson, B. . 1998. Local Spatial Autocorrelation Biological Model. Geographical Analysis, 30. 331–354; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x ; Sauer, J., Oshan, T. M., Rey, S., & Wolf, L. J. 2021. Importance Null Hypotheses: Understanding Differences Local Moran’s Heteroskedasticity. Geographical Analysis. doi:10.1111/gean.12304 Bivand, R. (2022), R Packages Analyzing Spatial Data: Comparative Case Study Areal Data. Geographical Analysis, 54(3), 488-518. doi:10.1111/gean.12319","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Local Moran's I statistic — localmoran","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Local Moran's I statistic — localmoran","text":"","code":"data(afcon, package=\"spData\") oid <- order(afcon$id) resI <- localmoran(afcon$totcon, nb2listw(paper.nb)) printCoefmat(data.frame(resI[oid,], row.names=afcon$name[oid]), check.names=FALSE) #> Ii E.Ii Var.Ii Z.Ii #> THE GAMBIA 3.7523e-01 -2.4317e-02 9.9646e-01 4.0025e-01 #> MALI 4.6363e-01 -2.1841e-02 1.0896e-01 1.4708e+00 #> SENEGAL 2.5670e-01 -3.4444e-03 3.3339e-02 1.4248e+00 #> BENIN 1.9412e-01 -2.4556e-03 2.3792e-02 1.2744e+00 #> MAURITANIA 9.7053e-02 -5.7508e-03 5.5533e-02 4.3625e-01 #> NIGER 2.3071e-01 -1.9459e-02 9.7310e-02 8.0198e-01 #> IVORY COAST 2.9004e-01 -6.9359e-03 5.2072e-02 1.3014e+00 #> GUINEA 1.8263e-01 -2.2246e-03 1.6780e-02 1.4270e+00 #> BURKINA FASO 5.0828e-01 -1.9893e-02 1.1942e-01 1.5284e+00 #> LIBERIA 1.8565e-01 -2.7127e-03 3.5982e-02 9.9300e-01 #> SIERRA LEONE 2.6523e-01 -1.6994e-02 3.4204e-01 4.8257e-01 #> GHANA 1.4764e-01 -1.3414e-03 1.7817e-02 1.1161e+00 #> TOGO 2.1934e-01 -4.9892e-03 6.6025e-02 8.7305e-01 #> CAMEROON 2.5925e-01 -1.1009e-02 8.2313e-02 9.4198e-01 #> NIGERIA 1.1377e-01 -9.6126e-04 9.3272e-03 1.1880e+00 #> GABON 2.0366e-01 -5.4771e-03 1.1153e-01 6.2625e-01 #> CENTRAL AFRICAN REPUBLIC -4.4206e-01 -1.0600e-02 7.9287e-02 -1.5323e+00 #> CHAD -1.0528e-01 -4.0998e-03 2.5008e-02 -6.3985e-01 #> CONGO 1.1380e-02 -8.5953e-04 8.3410e-03 1.3402e-01 #> ZAIRE 7.0978e-01 -5.9545e-02 2.0906e-01 1.6826e+00 #> ANGOLA 1.1797e-01 -6.2140e-04 8.2594e-03 1.3050e+00 #> UGANDA 1.9425e+00 -6.2812e-02 4.4503e-01 3.0060e+00 #> KENYA 1.1969e+00 -1.6803e-02 1.2489e-01 3.4344e+00 #> TANZANIA 2.7185e-01 -4.6254e-02 1.9107e-01 7.2774e-01 #> BURUNDI -4.8428e-01 -1.1009e-02 1.4481e-01 -1.2437e+00 #> RWANDA -7.5236e-01 -1.4730e-02 1.4096e-01 -1.9647e+00 #> SOMALIA 4.5277e-01 -1.1751e-02 2.3778e-01 9.5260e-01 #> ETHIOPIA 7.2512e-01 -5.4929e-03 7.2655e-02 2.7106e+00 #> ZAMBIA 4.2160e-02 -8.1691e-04 3.5354e-03 7.2280e-01 #> ZIMBABWE -9.5068e-03 -6.0969e-03 5.8855e-02 -1.4056e-02 #> MALAWI -2.2888e-01 -1.0284e-02 1.3537e-01 -5.9413e-01 #> MOZAMBIQUE 1.6790e-02 -6.1629e-03 3.7515e-02 1.1850e-01 #> SOUTH AFRICA -1.8254e-01 -5.4306e-03 2.7546e-02 -1.0671e+00 #> LESOTHO -4.1935e-01 -1.9263e-02 7.9348e-01 -4.4914e-01 #> BOTSWANA -3.9316e-03 -1.4141e-04 1.8805e-03 -8.7403e-02 #> SWAZILAND 1.6684e-02 -2.8611e-02 5.6905e-01 6.0045e-02 #> MOROCCO -9.6961e-02 -5.1445e-03 1.0479e-01 -2.8363e-01 #> ALGERIA -1.0037e-02 -9.7828e-05 5.9914e-04 -4.0605e-01 #> TUNISIA 5.3873e-03 -3.0273e-06 6.1985e-05 6.8466e-01 #> LIBYA 8.0382e-01 -1.9923e-02 1.1960e-01 2.3820e+00 #> SUDAN 2.9878e+00 -2.2835e-01 7.6320e-01 3.6814e+00 #> EGYPT 6.9467e+00 -2.9968e-01 4.2971e+00 3.4957e+00 #> Pr.z....E.Ii.. #> THE GAMBIA 0.6890 #> MALI 0.1414 #> SENEGAL 0.1542 #> BENIN 0.2025 #> MAURITANIA 0.6627 #> NIGER 0.4226 #> IVORY COAST 0.1931 #> GUINEA 0.1536 #> BURKINA FASO 0.1264 #> LIBERIA 0.3207 #> SIERRA LEONE 0.6294 #> GHANA 0.2644 #> TOGO 0.3826 #> CAMEROON 0.3462 #> NIGERIA 0.2348 #> GABON 0.5312 #> CENTRAL AFRICAN REPUBLIC 0.1255 #> CHAD 0.5223 #> CONGO 0.8934 #> ZAIRE 0.0925 #> ANGOLA 0.1919 #> UGANDA 0.0026 #> KENYA 0.0006 #> TANZANIA 0.4668 #> BURUNDI 0.2136 #> RWANDA 0.0494 #> SOMALIA 0.3408 #> ETHIOPIA 0.0067 #> ZAMBIA 0.4698 #> ZIMBABWE 0.9888 #> MALAWI 0.5524 #> MOZAMBIQUE 0.9057 #> SOUTH AFRICA 0.2859 #> LESOTHO 0.6533 #> BOTSWANA 0.9304 #> SWAZILAND 0.9521 #> MOROCCO 0.7767 #> ALGERIA 0.6847 #> TUNISIA 0.4936 #> LIBYA 0.0172 #> SUDAN 0.0002 #> EGYPT 0.0005 hist(resI[,5]) mean(resI[,1]) #> [1] 0.4167956 sum(resI[,1])/Szero(nb2listw(paper.nb)) #> [1] 0.4167956 moran.test(afcon$totcon, nb2listw(paper.nb)) #> #> \tMoran I test under randomisation #> #> data: afcon$totcon #> weights: nb2listw(paper.nb) #> #> Moran I statistic standard deviate = 4.3485, p-value = 6.854e-06 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.41679563 -0.02439024 0.01029358 #> # note equality for mean() only when the sum of weights equals # the number of observations (thanks to Juergen Symanzik) resI <- localmoran(afcon$totcon, nb2listw(paper.nb)) printCoefmat(data.frame(resI[oid,], row.names=afcon$name[oid]), check.names=FALSE) #> Ii E.Ii Var.Ii Z.Ii #> THE GAMBIA 3.7523e-01 -2.4317e-02 9.9646e-01 4.0025e-01 #> MALI 4.6363e-01 -2.1841e-02 1.0896e-01 1.4708e+00 #> SENEGAL 2.5670e-01 -3.4444e-03 3.3339e-02 1.4248e+00 #> BENIN 1.9412e-01 -2.4556e-03 2.3792e-02 1.2744e+00 #> MAURITANIA 9.7053e-02 -5.7508e-03 5.5533e-02 4.3625e-01 #> NIGER 2.3071e-01 -1.9459e-02 9.7310e-02 8.0198e-01 #> IVORY COAST 2.9004e-01 -6.9359e-03 5.2072e-02 1.3014e+00 #> GUINEA 1.8263e-01 -2.2246e-03 1.6780e-02 1.4270e+00 #> BURKINA FASO 5.0828e-01 -1.9893e-02 1.1942e-01 1.5284e+00 #> LIBERIA 1.8565e-01 -2.7127e-03 3.5982e-02 9.9300e-01 #> SIERRA LEONE 2.6523e-01 -1.6994e-02 3.4204e-01 4.8257e-01 #> GHANA 1.4764e-01 -1.3414e-03 1.7817e-02 1.1161e+00 #> TOGO 2.1934e-01 -4.9892e-03 6.6025e-02 8.7305e-01 #> CAMEROON 2.5925e-01 -1.1009e-02 8.2313e-02 9.4198e-01 #> NIGERIA 1.1377e-01 -9.6126e-04 9.3272e-03 1.1880e+00 #> GABON 2.0366e-01 -5.4771e-03 1.1153e-01 6.2625e-01 #> CENTRAL AFRICAN REPUBLIC -4.4206e-01 -1.0600e-02 7.9287e-02 -1.5323e+00 #> CHAD -1.0528e-01 -4.0998e-03 2.5008e-02 -6.3985e-01 #> CONGO 1.1380e-02 -8.5953e-04 8.3410e-03 1.3402e-01 #> ZAIRE 7.0978e-01 -5.9545e-02 2.0906e-01 1.6826e+00 #> ANGOLA 1.1797e-01 -6.2140e-04 8.2594e-03 1.3050e+00 #> UGANDA 1.9425e+00 -6.2812e-02 4.4503e-01 3.0060e+00 #> KENYA 1.1969e+00 -1.6803e-02 1.2489e-01 3.4344e+00 #> TANZANIA 2.7185e-01 -4.6254e-02 1.9107e-01 7.2774e-01 #> BURUNDI -4.8428e-01 -1.1009e-02 1.4481e-01 -1.2437e+00 #> RWANDA -7.5236e-01 -1.4730e-02 1.4096e-01 -1.9647e+00 #> SOMALIA 4.5277e-01 -1.1751e-02 2.3778e-01 9.5260e-01 #> ETHIOPIA 7.2512e-01 -5.4929e-03 7.2655e-02 2.7106e+00 #> ZAMBIA 4.2160e-02 -8.1691e-04 3.5354e-03 7.2280e-01 #> ZIMBABWE -9.5068e-03 -6.0969e-03 5.8855e-02 -1.4056e-02 #> MALAWI -2.2888e-01 -1.0284e-02 1.3537e-01 -5.9413e-01 #> MOZAMBIQUE 1.6790e-02 -6.1629e-03 3.7515e-02 1.1850e-01 #> SOUTH AFRICA -1.8254e-01 -5.4306e-03 2.7546e-02 -1.0671e+00 #> LESOTHO -4.1935e-01 -1.9263e-02 7.9348e-01 -4.4914e-01 #> BOTSWANA -3.9316e-03 -1.4141e-04 1.8805e-03 -8.7403e-02 #> SWAZILAND 1.6684e-02 -2.8611e-02 5.6905e-01 6.0045e-02 #> MOROCCO -9.6961e-02 -5.1445e-03 1.0479e-01 -2.8363e-01 #> ALGERIA -1.0037e-02 -9.7828e-05 5.9914e-04 -4.0605e-01 #> TUNISIA 5.3873e-03 -3.0273e-06 6.1985e-05 6.8466e-01 #> LIBYA 8.0382e-01 -1.9923e-02 1.1960e-01 2.3820e+00 #> SUDAN 2.9878e+00 -2.2835e-01 7.6320e-01 3.6814e+00 #> EGYPT 6.9467e+00 -2.9968e-01 4.2971e+00 3.4957e+00 #> Pr.z....E.Ii.. #> THE GAMBIA 0.6890 #> MALI 0.1414 #> SENEGAL 0.1542 #> BENIN 0.2025 #> MAURITANIA 0.6627 #> NIGER 0.4226 #> IVORY COAST 0.1931 #> GUINEA 0.1536 #> BURKINA FASO 0.1264 #> LIBERIA 0.3207 #> SIERRA LEONE 0.6294 #> GHANA 0.2644 #> TOGO 0.3826 #> CAMEROON 0.3462 #> NIGERIA 0.2348 #> GABON 0.5312 #> CENTRAL AFRICAN REPUBLIC 0.1255 #> CHAD 0.5223 #> CONGO 0.8934 #> ZAIRE 0.0925 #> ANGOLA 0.1919 #> UGANDA 0.0026 #> KENYA 0.0006 #> TANZANIA 0.4668 #> BURUNDI 0.2136 #> RWANDA 0.0494 #> SOMALIA 0.3408 #> ETHIOPIA 0.0067 #> ZAMBIA 0.4698 #> ZIMBABWE 0.9888 #> MALAWI 0.5524 #> MOZAMBIQUE 0.9057 #> SOUTH AFRICA 0.2859 #> LESOTHO 0.6533 #> BOTSWANA 0.9304 #> SWAZILAND 0.9521 #> MOROCCO 0.7767 #> ALGERIA 0.6847 #> TUNISIA 0.4936 #> LIBYA 0.0172 #> SUDAN 0.0002 #> EGYPT 0.0005 hist(p.adjust(resI[,5], method=\"bonferroni\")) totcon <-afcon$totcon is.na(totcon) <- sample(1:length(totcon), 5) totcon #> [1] 1363 1421 1861 2355 5246 811 299 358 895 4751 1878 933 347 1130 241 #> [16] 604 1015 998 2122 1090 848 618 NA 423 NA 3087 2273 3134 1142 824 #> [31] 2881 487 604 1528 1554 629 NA 795 NA 1875 NA 363 resI.na <- localmoran(totcon, nb2listw(paper.nb), na.action=na.exclude, zero.policy=TRUE) if (class(attr(resI.na, \"na.action\")) == \"exclude\") { print(data.frame(resI.na[oid,], row.names=afcon$name[oid]), digits=2) } else print(resI.na, digits=2) #> Ii E.Ii Var.Ii Z.Ii Pr.z....E.Ii.. #> THE GAMBIA 0.4383 -2.9e-02 1.1e+00 0.46 0.6483 #> MALI 0.5172 -2.6e-02 1.4e-01 1.47 0.1406 #> SENEGAL 0.3087 -5.1e-03 4.3e-02 1.52 0.1287 #> BENIN 0.2426 -3.8e-03 3.2e-02 1.37 0.1696 #> MAURITANIA 0.1374 -7.9e-03 6.6e-02 0.56 0.5721 #> NIGER 0.2905 -2.4e-02 1.0e-01 0.99 0.3241 #> IVORY COAST NA NA NA NA NA #> GUINEA 0.2697 -3.5e-03 4.1e-02 1.35 0.1764 #> BURKINA FASO 0.5725 -2.4e-02 1.6e-01 1.52 0.1297 #> LIBERIA NA NA NA NA NA #> SIERRA LEONE 0.3094 -2.1e-02 7.6e-01 0.38 0.7046 #> GHANA 0.2090 -2.4e-03 4.2e-02 1.03 0.3039 #> TOGO 0.2665 -7.0e-03 8.0e-02 0.96 0.3350 #> CAMEROON 0.3110 -1.4e-02 9.1e-02 1.08 0.2811 #> NIGERIA 0.1583 -1.8e-03 1.5e-02 1.29 0.1975 #> GABON 0.2498 -7.6e-03 1.3e-01 0.70 0.4832 #> CENTRAL AFRICAN REPUBLIC -0.4053 -1.4e-02 8.8e-02 -1.32 0.1866 #> CHAD -0.0834 -5.9e-03 3.1e-02 -0.44 0.6592 #> CONGO 0.0305 -1.7e-03 1.4e-02 0.27 0.7870 #> ZAIRE 0.5334 -5.7e-02 1.7e-01 1.43 0.1537 #> ANGOLA 0.0566 -2.1e-04 2.5e-03 1.14 0.2545 #> UGANDA 1.6232 -6.1e-02 3.7e-01 2.76 0.0059 #> KENYA 0.9678 -1.5e-02 9.6e-02 3.17 0.0015 #> TANZANIA 0.2773 -4.4e-02 1.8e-01 0.75 0.4541 #> BURUNDI -0.4467 -1.4e-02 1.6e-01 -1.08 0.2815 #> RWANDA -0.7037 -1.8e-02 1.5e-01 -1.76 0.0793 #> SOMALIA 0.3380 -1.0e-02 1.8e-01 0.82 0.4107 #> ETHIOPIA 0.5485 -4.2e-03 4.9e-02 2.49 0.0126 #> ZAMBIA 0.0356 -3.4e-04 1.8e-03 0.85 0.3955 #> ZIMBABWE -0.1362 -8.3e-03 1.5e-01 -0.33 0.7395 #> MALAWI -0.4725 -1.3e-02 2.3e-01 -0.95 0.3431 #> MOZAMBIQUE NA NA NA NA NA #> SOUTH AFRICA -0.1231 -4.2e-03 3.5e-02 -0.63 0.5263 #> LESOTHO -0.3572 -2.4e-02 8.5e-01 -0.36 0.7174 #> BOTSWANA NA NA NA NA NA #> SWAZILAND NA NA NA NA NA #> MOROCCO -0.1011 -3.9e-03 7.0e-02 -0.37 0.7141 #> ALGERIA 0.0011 -6.4e-07 3.4e-06 0.57 0.5689 #> TUNISIA -0.0220 -8.4e-05 1.5e-03 -0.56 0.5734 #> LIBYA 0.6345 -1.8e-02 9.3e-02 2.14 0.0325 #> SUDAN 2.5128 -2.3e-01 6.6e-01 3.39 0.0007 #> EGYPT 6.0832 -3.0e-01 3.8e+00 3.28 0.0011 resG <- localG(afcon$totcon, nb2listw(include.self(paper.nb))) print(data.frame(resG[oid], row.names=afcon$name[oid]), digits=2) #> resG.oid. #> THE GAMBIA -0.984 #> MALI -1.699 #> SENEGAL -1.463 #> BENIN -1.301 #> MAURITANIA -0.605 #> NIGER -1.049 #> IVORY COAST -1.417 #> GUINEA -1.449 #> BURKINA FASO -1.751 #> LIBERIA -1.041 #> SIERRA LEONE -0.870 #> GHANA -1.103 #> TOGO -0.991 #> CAMEROON -1.133 #> NIGERIA -1.173 #> GABON -0.789 #> CENTRAL AFRICAN REPUBLIC 1.173 #> CHAD 0.463 #> CONGO -0.203 #> ZAIRE 2.023 #> ANGOLA 1.235 #> UGANDA 3.336 #> KENYA 3.503 #> TANZANIA 1.098 #> BURUNDI 0.774 #> RWANDA 1.457 #> SOMALIA 1.183 #> ETHIOPIA 2.627 #> ZAMBIA 0.753 #> ZIMBABWE -0.200 #> MALAWI 0.212 #> MOZAMBIQUE -0.288 #> SOUTH AFRICA -0.868 #> LESOTHO -0.298 #> BOTSWANA 0.041 #> SWAZILAND -0.659 #> MOROCCO 0.022 #> ALGERIA -0.363 #> TUNISIA 0.579 #> LIBYA 2.553 #> SUDAN 4.039 #> EGYPT 4.421 set.seed(1) resI_p <- localmoran_perm(afcon$totcon, nb2listw(paper.nb)) printCoefmat(data.frame(resI_p[oid,], row.names=afcon$name[oid]), check.names=FALSE) #> Ii E.Ii Var.Ii Z.Ii #> THE GAMBIA 3.7523e-01 -3.0853e-02 9.0476e-01 4.2692e-01 #> MALI 4.6363e-01 -2.1690e-02 1.2192e-01 1.3899e+00 #> SENEGAL 2.5670e-01 -1.1288e-02 3.2719e-02 1.4816e+00 #> BENIN 1.9412e-01 -6.5012e-03 2.6046e-02 1.2431e+00 #> MAURITANIA 9.7053e-02 -2.0574e-03 5.7209e-02 4.1437e-01 #> NIGER 2.3071e-01 -2.8428e-02 1.1981e-01 7.4867e-01 #> IVORY COAST 2.9004e-01 -8.1011e-03 5.5564e-02 1.2648e+00 #> GUINEA 1.8263e-01 5.3454e-04 1.8397e-02 1.3425e+00 #> BURKINA FASO 5.0828e-01 -2.9727e-02 1.4019e-01 1.4369e+00 #> LIBERIA 1.8565e-01 -1.9247e-03 3.6524e-02 9.8147e-01 #> SIERRA LEONE 2.6523e-01 1.0225e-02 3.1505e-01 4.5432e-01 #> GHANA 1.4764e-01 -6.7639e-03 1.8646e-02 1.1307e+00 #> TOGO 2.1934e-01 -1.8012e-03 6.5187e-02 8.6616e-01 #> CAMEROON 2.5925e-01 -1.0726e-02 9.4789e-02 8.7688e-01 #> NIGERIA 1.1377e-01 -2.5672e-03 8.7720e-03 1.2421e+00 #> GABON 2.0366e-01 -3.5024e-03 1.0958e-01 6.2584e-01 #> CENTRAL AFRICAN REPUBLIC -4.4206e-01 2.3901e-02 8.1700e-02 -1.6302e+00 #> CHAD -1.0528e-01 5.9042e-03 3.0168e-02 -6.4016e-01 #> CONGO 1.1380e-02 7.0349e-03 8.9435e-03 4.5949e-02 #> ZAIRE 7.0978e-01 -2.9589e-02 2.9068e-01 1.3714e+00 #> ANGOLA 1.1797e-01 -3.0421e-04 8.6526e-03 1.2716e+00 #> UGANDA 1.9425e+00 -7.0491e-02 5.2046e-01 2.7903e+00 #> KENYA 1.1969e+00 -1.6362e-02 1.3644e-01 3.2847e+00 #> TANZANIA 2.7185e-01 -7.3309e-02 2.3454e-01 7.1272e-01 #> BURUNDI -4.8428e-01 9.5351e-03 1.4866e-01 -1.2807e+00 #> RWANDA -7.5236e-01 -4.0426e-02 1.7628e-01 -1.6956e+00 #> SOMALIA 4.5277e-01 -1.1165e-02 2.6266e-01 9.0523e-01 #> ETHIOPIA 7.2512e-01 8.3618e-04 7.8477e-02 2.5855e+00 #> ZAMBIA 4.2160e-02 -5.1840e-03 3.6852e-03 7.7989e-01 #> ZIMBABWE -9.5068e-03 -6.5338e-03 6.5357e-02 -1.1629e-02 #> MALAWI -2.2888e-01 3.6276e-03 1.3417e-01 -6.3477e-01 #> MOZAMBIQUE 1.6790e-02 -2.0694e-03 4.5436e-02 8.8476e-02 #> SOUTH AFRICA -1.8254e-01 -1.1611e-02 3.0240e-02 -9.8293e-01 #> LESOTHO -4.1935e-01 -6.6258e-02 8.7314e-01 -3.7787e-01 #> BOTSWANA -3.9316e-03 -4.7713e-03 2.2167e-03 1.7833e-02 #> SWAZILAND 1.6684e-02 -8.4486e-02 6.4807e-01 1.2567e-01 #> MOROCCO -9.6961e-02 -2.1623e-03 1.1253e-01 -2.8260e-01 #> ALGERIA -1.0037e-02 -3.4326e-04 6.3541e-04 -3.8456e-01 #> TUNISIA 5.3873e-03 -1.6456e-04 6.4187e-05 6.9298e-01 #> LIBYA 8.0382e-01 -2.9038e-02 1.3319e-01 2.2821e+00 #> SUDAN 2.9878e+00 -2.5952e-01 8.2522e-01 3.5747e+00 #> EGYPT 6.9467e+00 -3.7869e-01 4.1318e+00 3.6038e+00 #> Pr.z....E.Ii.. Pr.z....E.Ii...Sim Pr.folded..Sim #> THE GAMBIA 6.6944e-01 8.3200e-01 4.2800e-01 #> MALI 1.6455e-01 8.8000e-02 4.4000e-02 #> SENEGAL 1.3846e-01 6.4000e-02 3.2000e-02 #> BENIN 2.1384e-01 1.3200e-01 6.6000e-02 #> MAURITANIA 6.7860e-01 7.5600e-01 3.7800e-01 #> NIGER 4.5406e-01 5.0000e-01 2.5000e-01 #> IVORY COAST 2.0595e-01 1.1600e-01 5.8000e-02 #> GUINEA 1.7943e-01 7.2000e-02 3.6000e-02 #> BURKINA FASO 1.5075e-01 9.2000e-02 4.6000e-02 #> LIBERIA 3.2636e-01 3.0400e-01 1.5200e-01 #> SIERRA LEONE 6.4960e-01 8.2400e-01 4.1200e-01 #> GHANA 2.5816e-01 1.8400e-01 9.2000e-02 #> TOGO 3.8640e-01 3.6800e-01 1.8400e-01 #> CAMEROON 3.8055e-01 4.3200e-01 2.1600e-01 #> NIGERIA 2.1418e-01 1.4400e-01 7.2000e-02 #> GABON 5.3142e-01 5.8400e-01 2.9600e-01 #> CENTRAL AFRICAN REPUBLIC 1.0306e-01 1.8400e-01 9.2000e-02 #> CHAD 5.2207e-01 4.5200e-01 2.2600e-01 #> CONGO 9.6335e-01 8.5600e-01 4.2800e-01 #> ZAIRE 1.7026e-01 2.0000e-01 1.0000e-01 #> ANGOLA 2.0353e-01 2.3600e-01 1.1800e-01 #> UGANDA 5.2662e-03 4.0000e-02 2.0000e-02 #> KENYA 1.0210e-03 8.0000e-03 4.0000e-03 #> TANZANIA 4.7602e-01 4.2400e-01 2.1200e-01 #> BURUNDI 2.0029e-01 2.6800e-01 1.3400e-01 #> RWANDA 8.9953e-02 1.4000e-01 7.0000e-02 #> SOMALIA 3.6535e-01 2.8800e-01 1.4600e-01 #> ETHIOPIA 9.7244e-03 3.6000e-02 1.8000e-02 #> ZAMBIA 4.3546e-01 4.1200e-01 2.0600e-01 #> ZIMBABWE 9.9072e-01 8.6800e-01 4.3400e-01 #> MALAWI 5.2558e-01 4.5600e-01 2.2800e-01 #> MOZAMBIQUE 9.2950e-01 9.4400e-01 4.7200e-01 #> SOUTH AFRICA 3.2564e-01 3.5200e-01 1.7600e-01 #> LESOTHO 7.0553e-01 4.6800e-01 2.2400e-01 #> BOTSWANA 9.8577e-01 8.4400e-01 4.2200e-01 #> SWAZILAND 8.9999e-01 8.8400e-01 4.4200e-01 #> MOROCCO 7.7749e-01 9.7600e-01 4.8800e-01 #> ALGERIA 7.0057e-01 8.0400e-01 4.0200e-01 #> TUNISIA 4.8832e-01 4.2800e-01 2.1600e-01 #> LIBYA 2.2482e-02 4.8000e-02 2.4000e-02 #> SUDAN 3.5067e-04 8.0000e-03 4.0000e-03 #> EGYPT 3.1358e-04 1.6000e-02 8.0000e-03 #> Skewness Kurtosis #> THE GAMBIA -1.7643e+00 3.3422 #> MALI -8.2875e-01 0.8397 #> SENEGAL -7.1779e-01 0.3689 #> BENIN -8.5318e-01 0.5520 #> MAURITANIA -9.6301e-01 1.3949 #> NIGER -6.3767e-01 0.2577 #> IVORY COAST -8.3750e-01 0.6786 #> GUINEA -8.8298e-01 0.7691 #> BURKINA FASO -7.7665e-01 0.5911 #> LIBERIA -9.7191e-01 1.2327 #> SIERRA LEONE -1.0737e+00 0.6367 #> GHANA -9.6554e-01 0.8587 #> TOGO -1.0772e+00 1.2283 #> CAMEROON -8.1844e-01 1.1746 #> NIGERIA -6.3061e-01 0.1168 #> GABON -1.1947e+00 1.1977 #> CENTRAL AFRICAN REPUBLIC -6.7964e-01 -0.1428 #> CHAD -9.5123e-01 0.8025 #> CONGO -9.5359e-01 0.9288 #> ZAIRE 6.6929e-01 0.5829 #> ANGOLA 1.0230e+00 1.0841 #> UGANDA 9.6607e-01 1.3331 #> KENYA 8.5205e-01 0.5240 #> TANZANIA 8.5767e-01 1.2127 #> BURUNDI -1.0634e+00 0.9779 #> RWANDA -9.5905e-01 0.8365 #> SOMALIA 1.5185e+00 2.7876 #> ETHIOPIA 9.9587e-01 0.7374 #> ZAMBIA 4.9495e-01 0.1900 #> ZIMBABWE -8.0240e-01 0.4192 #> MALAWI -1.1246e+00 1.7228 #> MOZAMBIQUE -7.6989e-01 0.5793 #> SOUTH AFRICA 5.6394e-01 0.1988 #> LESOTHO -1.7905e+00 2.9865 #> BOTSWANA -9.4637e-01 0.5722 #> SWAZILAND -1.3081e+00 1.7612 #> MOROCCO 1.2705e+00 1.5574 #> ALGERIA 6.3958e-01 0.2677 #> TUNISIA 1.2498e+00 1.2249 #> LIBYA 7.3453e-01 0.5219 #> SUDAN 4.3993e-01 -0.1019 #> EGYPT 1.1875e+00 1.6480"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":null,"dir":"Reference","previous_headings":"","what":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"function implements Tiefelsdorf's application Saddlepoint approximation local Moran's Ii's reference distribution. model object class \"lm\", global independence assumed; class \"sarlm\", global dependence assumed represented spatial parameter model. Tests reported separately zone selected, may summarised using summary.localmoransad. Values local Moran's Ii agree localmoran(), function, standard deviate - Saddlepoint approximation - based randomisation assumption.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"","code":"localmoran.sad(model, select, nb, glist=NULL, style=\"W\", zero.policy=NULL, alternative=\"two.sided\", spChk=NULL, resfun=weighted.residuals, save.Vi=FALSE, tol = .Machine$double.eps^0.5, maxiter = 1000, tol.bounds=0.0001, save.M=FALSE, Omega = NULL) # S3 method for class 'localmoransad' print(x, ...) # S3 method for class 'localmoransad' summary(object, ...) # S3 method for class 'summary.localmoransad' print(x, ...) listw2star(listw, ireg, style, n, D, a, zero.policy=attr(listw, \"zero.policy\"))"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"model object class lm returned lm (assuming global spatial autocorrelation), object class sarlm returned spatial simultaneous autoregressive model fit (assuming global spatial autocorrelation represented model spatial coefficient); weights may specified lm fit, offsets used select integer vector id. numbers zones tested; missing, zones nb list neighbours class nb glist list general weights corresponding neighbours style can take values W, B, C, S zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one greater (default), less two.sided. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() resfun default: weighted.residuals; function used extract residuals lm object, may residuals, weighted.residuals, rstandard, rstudent save.Vi TRUE, return star-shaped weights lists zone tested tol desired accuracy (convergence tolerance) uniroot maxiter maximum number iterations uniroot tol.bounds offset bounds uniroot save.M TRUE, save list left right M products list conditional tests, list regression model matrix components Omega SAR process matrix may passed test alternative hypothesis, example Omega <- invIrW(listw, rho=0.1); Omega <- tcrossprod(Omega), chol() taken internally x object printed object object summarised ... arguments passed listw listw object created example nb2listw ireg zone number n internal value depending listw style D internal value depending listw style internal value depending listw style","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"function implements analytical eigenvalue calculation together trace shortcuts given suggested Tiefelsdorf (2002), partly following remarks J. Keith Ord, uses Saddlepoint analytical solution Tiefelsdorf's SPSS code. histogram probability values saddlepoint estimate assumption global independence approximately flat, assumption probably unjustified, re-estimation global dependence recommended. n n matrices needed point test assuming global dependence, star-shaped weights matrices handled listw lists. test made residuals spatial regression, taking global process account. n n matrices necessary, memory constraints may reached large lattices.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"list class localmoransad containing \"select\" lists, class moransad following components: statistic value saddlepoint approximation standard deviate local Moran's Ii. p.value p-value test. estimate value observed local Moran's Ii. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data. internal1 Saddlepoint omega, r u df degrees freedom tau maximum minimum analytical eigenvalues zone tested","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"Tiefelsdorf, M. 2002 Saddlepoint approximation Moran's local Moran's Ii reference distributions numerical evaluation. Geographical Analysis, 34, pp. 187–206.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/localmoran.sad.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Saddlepoint approximation of local Moran's Ii tests — localmoran.sad","text":"","code":"eire <- st_read(system.file(\"shapes/eire.gpkg\", package=\"spData\")[1]) #> Reading layer `eire' from data source #> `C:\\Users\\rzomor2\\AppData\\Local\\R\\win-library\\4.4\\spData\\shapes\\eire.gpkg' #> using driver `GPKG' #> Simple feature collection with 26 features and 10 fields #> Geometry type: MULTIPOLYGON #> Dimension: XY #> Bounding box: xmin: -4.12 ymin: 5768 xmax: 300.82 ymax: 6119.25 #> Projected CRS: Undefined Cartesian SRS with unknown unit row.names(eire) <- as.character(eire$names) eire.nb <- poly2nb(eire) lw <- nb2listw(eire.nb) e.lm <- lm(OWNCONS ~ ROADACC, data=eire) e.locmor <- summary(localmoran.sad(e.lm, nb=eire.nb)) e.locmor #> Local Morans I Stand. dev. (N) Pr. (N) Saddlepoint #> 1 Carlow 0.21699668 0.74177148 4.582258e-01 0.95074844 #> 2 Cavan -0.37257361 -0.81297374 1.583767e+00 -1.00603119 #> 3 Clare 0.23197510 0.49502499 6.205825e-01 0.67166518 #> 4 Cork 0.78193548 1.75999915 7.840795e-02 1.74761575 #> 5 Donegal -1.69064059 -1.98244914 1.952571e+00 -1.72031078 #> 6 Dublin -0.16069692 -0.15041940 1.119566e+00 -0.35212627 #> 7 Galway 1.31371473 3.34305297 8.286208e-04 2.66849536 #> 8 Kerry 0.36534866 0.58147812 5.609183e-01 0.78073279 #> 9 Kildare -0.02557544 0.15146558 8.796085e-01 0.04167665 #> 10 Kilkenny 0.57684331 1.62868431 1.033799e-01 1.70897697 #> 11 Laoghis -0.05951798 0.01724651 9.862400e-01 -0.12155465 #> 12 Leitrim 0.38484587 1.27548777 2.021367e-01 1.47227033 #> 13 Limerick 0.11817987 0.34038037 7.335701e-01 0.45727712 #> 14 Longford 1.41643200 3.10732224 1.887905e-03 2.51113769 #> 15 Louth 0.56242920 0.87665682 3.806731e-01 1.07441571 #> 16 Mayo 0.87572704 2.02375701 4.299516e-02 2.05251226 #> 17 Meath 0.00367856 0.16081712 8.722374e-01 0.12813539 #> 18 Monaghan 0.55098311 1.06684464 2.860420e-01 1.23999193 #> 19 Offaly 0.15155556 0.61933942 5.356928e-01 0.80786519 #> 20 Roscommon 2.04368839 6.66107106 2.718381e-11 4.53187292 #> 21 Sligo -0.47579871 -0.73430274 1.537236e+00 -0.94578114 #> 22 Tipperary -0.03454106 0.04843351 9.613708e-01 -0.06919691 #> 23 Waterford 0.85723423 1.98516133 4.712653e-02 1.91385108 #> 24 Westmeath 0.45138572 1.20305006 2.289569e-01 1.36017204 #> 25 Wexford 0.64371834 1.55468550 1.200210e-01 1.63188492 #> 26 Wicklow 0.02441950 0.21823347 8.272472e-01 0.21197000 #> Pr. (Sad) Expectation Variance Skewness Kurtosis Minimum #> 1 Carlow 3.417321e-01 -0.06471134 0.14423085 -0.7895263 7.059116 -5.461326 #> 2 Cavan 3.144006e-01 -0.04030838 0.16703857 -0.4622793 6.813004 -5.567356 #> 3 Clare 5.017969e-01 -0.04219377 0.30674823 -0.3579185 6.761932 -7.406885 #> 4 Cork 8.053059e-02 -0.04363826 0.22003250 -0.4363325 6.799081 -6.360927 #> 5 Donegal 8.537596e-02 -0.11935726 0.62821008 -0.7004303 6.979051 -11.236382 #> 6 Dublin 7.247436e-01 -0.08240217 0.27093033 -0.7352902 7.009201 -7.420687 #> 7 Galway 7.619183e-03 -0.04389010 0.16491503 -0.5059997 6.838308 -5.573707 #> 8 Kerry 4.349597e-01 -0.03212369 0.46724761 -0.2212594 6.714810 -8.915104 #> 9 Kildare 9.667565e-01 -0.07623733 0.11187546 -1.0416026 7.339962 -4.999621 #> 10 Kilkenny 8.745521e-02 -0.05911601 0.15247016 -0.7040737 6.982131 -5.538889 #> 11 Laoghis 9.032517e-01 -0.06620117 0.15016408 -0.7915137 7.061015 -5.574277 #> 12 Leitrim 1.409479e-01 -0.06828680 0.12621127 -0.8864130 7.157471 -5.186756 #> 13 Limerick 6.474719e-01 -0.04172917 0.22070746 -0.4167943 6.789132 -6.348870 #> 14 Longford 1.203427e-02 -0.04055162 0.21985521 -0.4059156 6.783792 -6.324457 #> 15 Louth 2.826364e-01 -0.04386717 0.47831137 -0.2983105 6.738631 -9.149779 #> 16 Mayo 4.011990e-02 -0.10340651 0.23408152 -0.9804377 7.264328 -7.165847 #> 17 Meath 8.980418e-01 -0.04799533 0.10324707 -0.6949022 6.974408 -4.551176 #> 18 Monaghan 2.149784e-01 -0.04136950 0.30828917 -0.3501006 6.758633 -7.415047 #> 19 Offaly 4.191682e-01 -0.04662212 0.10238870 -0.6782821 6.960676 -4.519986 #> 20 Roscommon 5.846302e-06 -0.04435301 0.09826301 -0.6591526 6.945294 -4.414164 #> 21 Sligo 3.442602e-01 -0.11041170 0.24760301 -1.0156782 7.307311 -7.409091 #> 22 Tipperary 9.448329e-01 -0.04872132 0.08571886 -0.7716947 7.042300 -4.198353 #> 23 Waterford 5.563919e-02 -0.05435079 0.21086415 -0.5533724 6.868342 -6.353514 #> 24 Westmeath 1.737755e-01 -0.04181671 0.16806722 -0.4779156 6.821788 -5.599610 #> 25 Wexford 1.027037e-01 -0.05432673 0.20159596 -0.5654870 6.876461 -6.225016 #> 26 Wicklow 8.321304e-01 -0.07022471 0.18808122 -0.7515626 7.023792 -6.198974 #> Maximum omega sad.r sad.u #> 1 Carlow 3.908254 0.071122863 0.71853146 0.84900467 #> 2 Cavan 4.599954 -0.051532330 -0.69003582 -0.85816092 #> 3 Clare 6.394234 0.031939551 0.46982957 0.51656357 #> 4 Cork 5.313609 0.083281515 1.43928884 2.24323856 #> 5 Donegal 8.371808 -0.039371561 -1.39288713 -2.19776923 #> 6 Dublin 5.443035 -0.010354512 -0.14127218 -0.14554367 #> 7 Galway 4.520344 0.134873939 2.39189491 4.63522665 #> 8 Kerry 8.144135 0.028431952 0.54051534 0.61545648 #> 9 Kildare 3.169925 0.018723213 0.14926096 0.14688325 #> 10 Kilkenny 4.120105 0.105365819 1.40668493 2.15214600 #> 11 Laoghis 3.985449 0.001724096 0.01660985 0.01657177 #> 12 Leitrim 3.547872 0.109608339 1.18229964 1.66578026 #> 13 Limerick 5.347370 0.027585567 0.32820959 0.34241163 #> 14 Longford 5.351218 0.108368224 2.22687206 4.19385821 #> 15 Louth 8.096967 0.037745731 0.78968254 0.98878788 #> 16 Mayo 4.684091 0.105317102 1.75922892 2.94711915 #> 17 Meath 3.399289 0.020074178 0.15693992 0.15623206 #> 18 Monaghan 6.422179 0.053418031 0.94193428 1.24723730 #> 19 Offaly 3.401055 0.071432961 0.59871278 0.67858124 #> 20 Roscommon 3.349691 0.357114199 4.33885200 10.02517077 #> 21 Sligo 4.759210 -0.036185300 -0.60775394 -0.74635955 #> 22 Tipperary 3.029041 0.006482570 0.04683010 0.04657633 #> 23 Waterford 5.049095 0.093409563 1.61022194 2.62552879 #> 24 Westmeath 4.596009 0.080097979 1.05978192 1.45704611 #> 25 Wexford 4.921174 0.085478829 1.32647942 1.98902088 #> 26 Wicklow 4.513581 0.020437514 0.21417067 0.21406975 mean(e.locmor[,1]) #> [1] 0.3366057 sum(e.locmor[,1])/Szero(lw) #> [1] 0.3366057 lm.morantest(e.lm, lw) #> #> \tGlobal Moran I for regression residuals #> #> data: #> model: lm(formula = OWNCONS ~ ROADACC, data = eire) #> weights: lw #> #> Moran I statistic standard deviate = 3.2575, p-value = 0.0005619 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I Expectation Variance #> 0.33660565 -0.05877741 0.01473183 #> # note equality for mean() only when the sum of weights equals # the number of observations (thanks to Juergen Symanzik) hist(e.locmor[,\"Pr. (Sad)\"]) e.wlm <- lm(OWNCONS ~ ROADACC, data=eire, weights=RETSALE) e.locmorw1 <- summary(localmoran.sad(e.wlm, nb=eire.nb, resfun=weighted.residuals)) e.locmorw1 #> Local Morans I Stand. dev. (N) Pr. (N) Saddlepoint #> 1 Carlow 0.160490657 0.41009538 6.817360e-01 0.57729730 #> 2 Cavan -0.144663771 -0.27825575 1.219184e+00 -0.45305168 #> 3 Clare 0.301676582 0.59021701 5.550452e-01 0.78987327 #> 4 Cork 1.520488153 3.49016956 4.827142e-04 2.83665634 #> 5 Donegal -0.435899664 -0.44665946 1.344879e+00 -0.67136090 #> 6 Dublin -0.340222996 -0.60886675 1.457387e+00 -0.85658016 #> 7 Galway 1.469009037 3.64546192 2.669119e-04 2.82274510 #> 8 Kerry 0.268957279 0.49517211 6.204786e-01 0.66861012 #> 9 Kildare 0.002996577 0.12659200 8.992633e-01 0.09978249 #> 10 Kilkenny 0.497968801 1.20610829 2.277757e-01 1.34091379 #> 11 Laoghis -0.026328708 -0.01713904 1.013674e+00 -0.06511750 #> 12 Leitrim 0.277306386 0.80644537 4.199861e-01 1.01176491 #> 13 Limerick 0.263122939 0.67591893 4.990921e-01 0.87759628 #> 14 Longford 0.605211711 1.23874274 2.154408e-01 1.35375850 #> 15 Louth 0.359469683 0.53572990 5.921452e-01 0.73280188 #> 16 Mayo 1.742480472 3.68118786 2.321499e-04 3.01500163 #> 17 Meath -0.112171618 -0.26680698 1.210382e+00 -0.45470531 #> 18 Monaghan 0.241044892 0.46013751 6.454175e-01 0.64094159 #> 19 Offaly 0.129191178 0.40988983 6.818868e-01 0.57205532 #> 20 Roscommon 1.469671750 4.39927211 1.086146e-05 3.13215267 #> 21 Sligo 0.095559559 0.31036587 7.562827e-01 0.38503064 #> 22 Tipperary 0.088352646 0.39958273 6.894639e-01 0.52592105 #> 23 Waterford 1.212658861 2.69846035 6.966104e-03 2.29292584 #> 24 Westmeath 0.256165310 0.61222265 5.403905e-01 0.81620859 #> 25 Wexford 0.619197906 1.31967483 1.869436e-01 1.42553832 #> 26 Wicklow 0.006531073 0.13142161 8.954418e-01 0.10986725 #> Pr. (Sad) Expectation Variance Skewness Kurtosis Minimum #> 1 Carlow 0.563738639 -0.01840558 0.19029731 -0.1986977 6.709176 -5.665283 #> 2 Cavan 0.650511526 -0.02184465 0.19482455 -0.2329761 6.717975 -5.769371 #> 3 Clare 0.429601786 -0.02782578 0.31166901 -0.2346279 6.718435 -7.299407 #> 4 Cork 0.004558865 -0.07147410 0.20805228 -0.7280203 7.002789 -6.495227 #> 5 Donegal 0.501990650 -0.07638800 0.64784767 -0.4450323 6.803659 -10.931345 #> 6 Dublin 0.391676955 -0.11187469 0.14065367 -1.3324828 7.767845 -5.846924 #> 7 Galway 0.004761441 -0.04407925 0.17227545 -0.4973247 6.833103 -5.688263 #> 8 Kerry 0.503744214 -0.05644300 0.43184063 -0.4031537 6.782459 -8.859407 #> 9 Kildare 0.920517009 -0.04145378 0.12329287 -0.5519841 6.867423 -4.857131 #> 10 Kilkenny 0.179948446 -0.02321457 0.18672759 -0.2528322 6.723714 -5.669156 #> 11 Laoghis 0.948080445 -0.01882531 0.19166504 -0.2024943 6.710081 -5.689691 #> 12 Leitrim 0.311650473 -0.03314655 0.14819776 -0.4041387 6.782933 -5.190860 #> 13 Limerick 0.380162847 -0.04800976 0.21188592 -0.4885390 6.827925 -6.298874 #> 14 Longford 0.175813436 -0.01321709 0.24923967 -0.1247567 6.694960 -6.392250 #> 15 Louth 0.463679274 -0.02272663 0.50895713 -0.1500895 6.699098 -9.179410 #> 16 Mayo 0.002569779 -0.09458039 0.24904116 -0.8745463 7.144787 -7.272523 #> 17 Meath 0.649321260 -0.02548973 0.10555100 -0.3685280 6.766525 -4.353122 #> 18 Monaghan 0.521560632 -0.02333303 0.33012248 -0.1912612 6.707452 -7.451275 #> 19 Offaly 0.567284497 -0.01927989 0.13120470 -0.2505068 6.723017 -4.750083 #> 20 Roscommon 0.001735296 -0.02385522 0.11525625 -0.3302939 6.750604 -4.517676 #> 21 Sligo 0.700214717 -0.06927688 0.28207107 -0.6087587 6.906925 -7.416881 #> 22 Tipperary 0.598943063 -0.03719246 0.09871568 -0.5534442 6.868390 -4.347214 #> 23 Waterford 0.021852275 -0.04027429 0.21558757 -0.4070996 6.784366 -6.264083 #> 24 Westmeath 0.414380842 -0.01522814 0.19650786 -0.1618342 6.701275 -5.716689 #> 25 Wexford 0.154001651 -0.02786850 0.24041626 -0.2674357 6.728234 -6.450174 #> 26 Wicklow 0.912514660 -0.04751424 0.16911517 -0.5404006 6.859847 -5.677417 #> Maximum omega sad.r sad.u #> 1 Carlow 5.223549 0.033637462 0.38794383 0.41751442 #> 2 Cavan 5.245099 -0.022294725 -0.26091513 -0.27432856 #> 3 Clare 6.631589 0.035302524 0.54866959 0.62630505 #> 4 Cork 4.779848 0.134384022 2.56890121 5.11058941 #> 5 Donegal 9.098033 -0.017507303 -0.40402088 -0.45010348 #> 6 Dublin 3.161931 -0.040828131 -0.50710580 -0.60543071 #> 7 Galway 4.630361 0.138454493 2.55314856 5.08170760 #> 8 Kerry 7.504775 0.027195108 0.47167584 0.51758880 #> 9 Kildare 3.862240 0.014230854 0.12280697 0.12246022 #> 10 Kilkenny 5.112007 0.071351828 1.03314661 1.41988761 #> 11 Laoghis 5.237883 -0.001502568 -0.01645549 -0.01646868 #> 12 Leitrim 4.395343 0.066207108 0.74158109 0.90609823 #> 13 Limerick 5.146640 0.050265468 0.63703133 0.74253221 #> 14 Longford 6.075040 0.060534639 1.04112815 1.44165700 #> 15 Louth 8.633971 0.025231866 0.49793592 0.55971045 #> 16 Mayo 5.002594 0.135902733 2.75603129 5.62669411 #> 17 Meath 3.741368 -0.028724497 -0.24912602 -0.26221742 #> 18 Monaghan 6.891283 0.028042744 0.43280552 0.47360371 #> 19 Offaly 4.287365 0.040883462 0.38909358 0.41780262 #> 20 Roscommon 3.945151 0.180270100 2.87643937 6.00202551 #> 21 Sligo 5.754236 0.023145822 0.30299868 0.31062426 #> 22 Tipperary 3.454595 0.048932861 0.38768333 0.40902706 #> 23 Waterford 5.297500 0.101874758 1.99944904 3.59542986 #> 24 Westmeath 5.351214 0.044919886 0.56403221 0.65024353 #> 25 Wexford 5.781330 0.066083430 1.11524637 1.57637406 #> 26 Wicklow 4.537075 0.012609906 0.12748740 0.12720134 e.locmorw2 <- summary(localmoran.sad(e.wlm, nb=eire.nb, resfun=rstudent)) e.locmorw2 #> Local Morans I Stand. dev. (N) Pr. (N) Saddlepoint #> 1 Carlow 0.121997164 0.32185426 0.7475631028 0.45871930 #> 2 Cavan -0.110588620 -0.20105599 1.1593452023 -0.34808741 #> 3 Clare 0.308759283 0.60290381 0.5465726820 0.80379674 #> 4 Cork 1.404203115 3.23522979 0.0012154487 2.69598105 #> 5 Donegal -0.421182109 -0.42837428 1.3316213558 -0.65187732 #> 6 Dublin -0.443534307 -0.88433550 1.6234848706 -1.05167518 #> 7 Galway 1.376190254 3.42183495 0.0006220006 2.70663064 #> 8 Kerry 0.241623387 0.45357724 0.6501331373 0.61515126 #> 9 Kildare 0.008842913 0.14324202 0.8860990418 0.12690939 #> 10 Kilkenny 0.382893124 0.93980330 0.3473184643 1.12810394 #> 11 Laoghis -0.019904450 -0.00246494 1.0019667357 -0.04176107 #> 12 Leitrim 0.200483743 0.60688769 0.5439254449 0.80241456 #> 13 Limerick 0.238810092 0.62310059 0.5332184222 0.81824678 #> 14 Longford 0.466942853 0.96178354 0.3361583457 1.14088225 #> 15 Louth 0.271710988 0.41271732 0.6798137369 0.58520655 #> 16 Mayo 1.705850161 3.60778634 0.0003088206 2.97346461 #> 17 Meath -0.160603054 -0.41587901 1.3225014587 -0.63254531 #> 18 Monaghan 0.181378604 0.35629110 0.7216225742 0.50697175 #> 19 Offaly 0.107919508 0.35116431 0.7254650854 0.49312417 #> 20 Roscommon 1.249826037 3.75170355 0.0001756371 2.81402777 #> 21 Sligo 0.079431883 0.27999953 0.7794778655 0.33741411 #> 22 Tipperary 0.085153638 0.38940098 0.6969795442 0.51126046 #> 23 Waterford 1.022922345 2.28982205 0.0220316342 2.06385578 #> 24 Westmeath 0.201539331 0.48899468 0.6248454598 0.67791734 #> 25 Wexford 0.481114325 1.03805702 0.2992435100 1.21094348 #> 26 Wicklow -0.011694661 0.08710223 0.9305902563 0.03786608 #> Pr. (Sad) Expectation Variance Skewness Kurtosis Minimum #> 1 Carlow 0.646435751 -0.01840558 0.19029731 -0.1986977 6.709176 -5.665283 #> 2 Cavan 0.727774542 -0.02184465 0.19482455 -0.2329761 6.717975 -5.769371 #> 3 Clare 0.421514374 -0.02782578 0.31166901 -0.2346279 6.718435 -7.299407 #> 4 Cork 0.007018166 -0.07147410 0.20805228 -0.7280203 7.002789 -6.495227 #> 5 Donegal 0.514480318 -0.07638800 0.64784767 -0.4450323 6.803659 -10.931345 #> 6 Dublin 0.292948602 -0.11187469 0.14065367 -1.3324828 7.767845 -5.846924 #> 7 Galway 0.006796983 -0.04407925 0.17227545 -0.4973247 6.833103 -5.688263 #> 8 Kerry 0.538454834 -0.05644300 0.43184063 -0.4031537 6.782459 -8.859407 #> 9 Kildare 0.899012117 -0.04145378 0.12329287 -0.5519841 6.867423 -4.857131 #> 10 Kilkenny 0.259276027 -0.02321457 0.18672759 -0.2528322 6.723714 -5.669156 #> 11 Laoghis 0.966689166 -0.01882531 0.19166504 -0.2024943 6.710081 -5.689691 #> 12 Leitrim 0.422313193 -0.03314655 0.14819776 -0.4041387 6.782933 -5.190860 #> 13 Limerick 0.413216288 -0.04800976 0.21188592 -0.4885390 6.827925 -6.298874 #> 14 Longford 0.253918927 -0.01321709 0.24923967 -0.1247567 6.694960 -6.392250 #> 15 Louth 0.558408841 -0.02272663 0.50895713 -0.1500895 6.699098 -9.179410 #> 16 Mayo 0.002944584 -0.09458039 0.24904116 -0.8745463 7.144787 -7.272523 #> 17 Meath 0.527030613 -0.02548973 0.10555100 -0.3685280 6.766525 -4.353122 #> 18 Monaghan 0.612174643 -0.02333303 0.33012248 -0.1912612 6.707452 -7.451275 #> 19 Offaly 0.621924855 -0.01927989 0.13120470 -0.2505068 6.723017 -4.750083 #> 20 Roscommon 0.004892500 -0.02385522 0.11525625 -0.3302939 6.750604 -4.517676 #> 21 Sligo 0.735804747 -0.06927688 0.28207107 -0.6087587 6.906925 -7.416881 #> 22 Tipperary 0.609168686 -0.03719246 0.09871568 -0.5534442 6.868390 -4.347214 #> 23 Waterford 0.039031392 -0.04027429 0.21558757 -0.4070996 6.784366 -6.264083 #> 24 Westmeath 0.497824103 -0.01522814 0.19650786 -0.1618342 6.701275 -5.716689 #> 25 Wexford 0.225917068 -0.02786850 0.24041626 -0.2674357 6.728234 -6.450174 #> 26 Wicklow 0.969794461 -0.04751424 0.16911517 -0.5404006 6.859847 -5.677417 #> Maximum omega sad.r sad.u #> 1 Carlow 5.223549 0.0272472954 0.306852385 0.321490350 #> 2 Cavan 5.245099 -0.0166242430 -0.190223798 -0.196022741 #> 3 Clare 6.631589 0.0358559846 0.559584155 0.641527095 #> 4 Cork 4.779848 0.1283688794 2.421993662 4.702934834 #> 5 Donegal 9.098033 -0.0169574018 -0.388662370 -0.430528174 #> 6 Dublin 3.161931 -0.0507848831 -0.696824139 -0.892299501 #> 7 Galway 4.630361 0.1333224875 2.431707338 4.745166958 #> 8 Kerry 7.504775 0.0252982005 0.433626352 0.469138111 #> 9 Kildare 3.862240 0.0161278548 0.139072871 0.138837812 #> 10 Kilkenny 5.112007 0.0622219791 0.835166590 1.066654825 #> 11 Laoghis 5.237883 -0.0002164925 -0.002368023 -0.002368244 #> 12 Leitrim 4.395343 0.0543844388 0.571625643 0.652237768 #> 13 Limerick 5.146640 0.0473787285 0.590605630 0.675595582 #> 14 Longford 6.075040 0.0528365356 0.840671447 1.082014178 #> 15 Louth 8.633971 0.0204960239 0.389078238 0.419930705 #> 16 Mayo 5.002594 0.1340509166 2.712635049 5.503894365 #> 17 Meath 3.741368 -0.0415411327 -0.379736494 -0.417998694 #> 18 Monaghan 6.891283 0.0226076552 0.338579266 0.358443998 #> 19 Offaly 4.287365 0.0357600182 0.335019324 0.353243066 #> 20 Roscommon 3.945151 0.1623235556 2.543240406 5.063795948 #> 21 Sligo 5.754236 0.0209568244 0.273376649 0.278204612 #> 22 Tipperary 3.454595 0.0478130890 0.377982061 0.397511387 #> 23 Waterford 5.297500 0.0941811771 1.762051071 2.998984773 #> 24 Westmeath 5.351214 0.0379323563 0.457473561 0.506014991 #> 25 Wexford 5.781330 0.0582538352 0.911459483 1.197527949 #> 26 Wicklow 4.537075 0.0083101099 0.084281843 0.083952776 run <- FALSE if (requireNamespace(\"spatialreg\", quietly=TRUE)) run <- TRUE if (run) { e.errorsar <- spatialreg::errorsarlm(OWNCONS ~ ROADACC, data=eire, listw=lw) if (packageVersion(\"spatialreg\") < \"1.1.7\") spatialreg::print.sarlm(e.errorsar) else print(e.errorsar) } if (run) { lm.target <- lm(e.errorsar$tary ~ e.errorsar$tarX - 1) Omega <- tcrossprod(spatialreg::invIrW(lw, rho=e.errorsar$lambda)) e.clocmor <- summary(localmoran.sad(lm.target, nb=eire.nb, Omega=Omega)) e.clocmor } if (run) { hist(e.clocmor[,\"Pr. (Sad)\"]) }"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"Given two continuous numeric variables, calculate bivariate Local Moran's .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"","code":"localmoran_bv(x, y, listw, nsim = 199, scale = TRUE, alternative=\"two.sided\", iseed=1L, no_repeat_in_row=FALSE, zero.policy=attr(listw, \"zero.policy\"))"},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"x numeric vector length y. y numeric vector length x. listw listw object example created nb2listw(). nsim number simulations run. scale default TRUE. alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"two.sided\", \"less\". iseed default NULL, used set seed; output reproducible count CPU cores across computation distributed . no_repeat_in_row default FALSE, TRUE, sample conditionally row without replacements avoid duplicate values, https://github.com/r-spatial/spdep/issues/124 zero.policy default default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"data.frame containing two columns Ib p_sim containing local bivariate Moran's simulated p-values respectively.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"Bivariate Local Moran, like global counterpart, evaluates value x observation spatial neighbors' value y. value \\(I_i^B\\) xi * Wyi. , simpler words, local bivariate Moran result multiplying x spatial lag y. Formally defined \\( I_i^B= cx_i\\Sigma_j{w_{ij}y_j} \\)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"Anselin, Luc, Ibnu Syabri, Oleg Smirnov. 2002. “Visualizing Multivariate Spatial Correlation Dynamically Linked Windows.” New Tools Spatial Data Analysis: Proceedings Specialist Meeting, edited Luc Anselin Sergio Rey. University California, Santa Barbara: Center Spatially Integrated Social Science (CSISS).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"Josiah Parry josiah.parry@gmail.com","code":""},{"path":"https://r-spatial.github.io/spdep/reference/localmoran_bv.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute the Local Bivariate Moran's I Statistic — localmoran_bv","text":"","code":"# load columbus datay columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")) #> Reading layer `columbus' from data source #> `C:\\Users\\rzomor2\\AppData\\Local\\R\\win-library\\4.4\\spData\\shapes\\columbus.gpkg' #> using driver `GPKG' #> Simple feature collection with 49 features and 20 fields #> Geometry type: POLYGON #> Dimension: XY #> Bounding box: xmin: 5.874907 ymin: 10.78863 xmax: 11.28742 ymax: 14.74245 #> Projected CRS: Undefined Cartesian SRS with unknown unit nb <- poly2nb(columbus) listw <- nb2listw(nb) set.seed(1) (res <- localmoran_bv(columbus$CRIME, columbus$INC, listw, nsim = 499)) #> Ibvi E.Ibvi Var.Ibvi Z.Ibvi Pr(z != E(Ibvi)) #> [1,] -0.8578252210 -1.826370e-02 0.731541578 -0.98159654 3.262987e-01 #> [2,] 0.1802618568 2.554658e-02 0.334247968 0.26760782 7.890012e-01 #> [3,] 0.0118856298 7.791116e-03 0.017162929 0.03125407 9.750669e-01 #> [4,] -0.0163525887 -3.452848e-03 0.005852145 -0.16862558 8.660912e-01 #> [5,] -0.5037734606 1.811633e-02 0.101966376 -1.63436973 1.021812e-01 #> [6,] -0.0041841415 1.293651e-02 0.139142736 -0.04589760 9.633919e-01 #> [7,] 1.5201688711 -1.466392e-04 1.099034279 1.45020069 1.470026e-01 #> [8,] -0.2016456990 7.471406e-03 0.007231278 -2.45913301 1.392730e-02 #> [9,] 0.0297432891 1.600490e-03 0.009219518 0.29309821 7.694471e-01 #> [10,] -0.0374203146 1.218906e-03 0.001100110 -1.16495823 2.440359e-01 #> [11,] -1.2368494456 7.720869e-02 0.498286158 -1.86155199 6.266627e-02 #> [12,] -1.2010054212 4.055009e-02 0.266658169 -2.40430022 1.620346e-02 #> [13,] -0.5377131737 1.218864e-02 0.122363375 -1.57202494 1.159448e-01 #> [14,] -0.9879712511 3.048475e-02 0.320475271 -1.79905736 7.200961e-02 #> [15,] -0.6057303757 2.137030e-02 0.102916086 -1.95476986 5.061024e-02 #> [16,] -0.7878039284 1.378587e-02 0.161039891 -1.99749384 4.577156e-02 #> [17,] 0.1379508106 9.352179e-04 0.003351141 2.36686570 1.793944e-02 #> [18,] -0.3253226893 1.066349e-02 0.078469609 -1.19941831 2.303653e-01 #> [19,] -0.3888822685 -7.104732e-06 0.432305953 -0.59144532 5.542221e-01 #> [20,] -0.4544889957 1.367811e-01 0.355060554 -0.99228105 3.210604e-01 #> [21,] -0.0006014046 3.919068e-03 0.031597455 -0.02543067 9.797114e-01 #> [22,] -0.0068813684 -3.664201e-03 0.001242910 -0.09125440 9.272904e-01 #> [23,] -0.8788967496 1.189579e-02 0.289002627 -1.65701209 9.751703e-02 #> [24,] -0.1256865340 -3.048451e-03 0.004692164 -1.79035349 7.339710e-02 #> [25,] -0.9307459211 4.509269e-02 0.303474056 -1.77140234 7.649382e-02 #> [26,] -0.2252775788 1.039843e-02 0.019527743 -1.68651169 9.169728e-02 #> [27,] 0.1413018326 -1.409345e-02 0.236810168 0.31932848 7.494774e-01 #> [28,] -0.7804482928 3.200178e-02 0.184987862 -1.88897002 5.889585e-02 #> [29,] -0.7654416689 5.928648e-02 0.364667175 -1.36572255 1.720261e-01 #> [30,] -0.9074829015 7.597435e-03 0.737090639 -1.06585659 2.864885e-01 #> [31,] -0.5510119267 -1.377557e-03 0.388899970 -0.88136323 3.781213e-01 #> [32,] -1.9581476375 2.561515e-02 0.239115219 -4.05682367 4.974461e-05 #> [33,] 0.0907015890 3.048227e-02 0.043681309 0.28812970 7.732475e-01 #> [34,] -0.4297843082 2.130996e-02 0.104683121 -1.39421250 1.632534e-01 #> [35,] 0.1181174820 6.746380e-04 0.008393054 1.28193663 1.998649e-01 #> [36,] -0.9901007017 2.760845e-02 0.278368628 -1.92891697 5.374117e-02 #> [37,] -0.2195812498 -7.723065e-03 0.032151838 -1.18152344 2.373948e-01 #> [38,] -0.3096268627 3.401135e-02 0.205499338 -0.75804717 4.484227e-01 #> [39,] -0.6090192229 1.689079e-02 0.308320019 -1.12722610 2.596469e-01 #> [40,] -1.2709838927 6.528265e-02 0.216905961 -2.86917707 4.115413e-03 #> [41,] -1.3940681427 9.430182e-02 0.304439982 -2.69749131 6.986411e-03 #> [42,] -0.4820987026 3.961324e-02 0.632999863 -0.65573592 5.119941e-01 #> [43,] -0.0064402410 2.939096e-03 0.001385154 -0.25201308 8.010310e-01 #> [44,] 0.0761664412 2.162964e-02 0.054095662 0.23448142 8.146113e-01 #> [45,] -0.0560342555 7.788766e-03 0.029796273 -0.36973996 7.115763e-01 #> [46,] -0.8249832451 -2.301643e-02 0.673531467 -0.97718648 3.284768e-01 #> [47,] -0.8915318222 2.294960e-02 0.095247718 -2.96310881 3.045489e-03 #> [48,] -0.1282863305 -9.674295e-03 0.061579149 -0.47798241 6.326627e-01 #> [49,] 0.0094888641 -4.828535e-03 0.222107368 0.03037964 9.757643e-01 #> Pr(z != E(Ibvi)) Sim Pr(folded) Sim #> [1,] 0.324 0.162 #> [2,] 0.880 0.440 #> [3,] 0.976 0.488 #> [4,] 0.800 0.400 #> [5,] 0.112 0.056 #> [6,] 0.864 0.430 #> [7,] 0.096 0.048 #> [8,] 0.004 0.002 #> [9,] 0.852 0.426 #> [10,] 0.260 0.130 #> [11,] 0.056 0.028 #> [12,] 0.008 0.004 #> [13,] 0.084 0.042 #> [14,] 0.064 0.032 #> [15,] 0.052 0.026 #> [16,] 0.028 0.014 #> [17,] 0.028 0.014 #> [18,] 0.192 0.096 #> [19,] 0.608 0.304 #> [20,] 0.368 0.184 #> [21,] 0.936 0.468 #> [22,] 0.928 0.464 #> [23,] 0.120 0.060 #> [24,] 0.040 0.020 #> [25,] 0.044 0.022 #> [26,] 0.076 0.038 #> [27,] 0.736 0.368 #> [28,] 0.032 0.016 #> [29,] 0.140 0.070 #> [30,] 0.284 0.142 #> [31,] 0.408 0.204 #> [32,] 0.004 0.002 #> [33,] 0.724 0.362 #> [34,] 0.188 0.094 #> [35,] 0.216 0.108 #> [36,] 0.084 0.042 #> [37,] 0.232 0.116 #> [38,] 0.464 0.232 #> [39,] 0.268 0.134 #> [40,] 0.004 0.002 #> [41,] 0.020 0.010 #> [42,] 0.468 0.234 #> [43,] 0.884 0.442 #> [44,] 0.904 0.452 #> [45,] 0.672 0.336 #> [46,] 0.344 0.172 #> [47,] 0.012 0.006 #> [48,] 0.544 0.272 #> [49,] 0.896 0.448 #> attr(,\"quadr\") #> mean median pysal #> 1 Low-High Low-High Low-High #> 2 Low-Low Low-Low Low-Low #> 3 Low-Low Low-Low Low-Low #> 4 Low-High Low-High Low-High #> 5 High-Low High-Low High-Low #> 6 Low-Low Low-High Low-High #> 7 Low-Low Low-Low Low-Low #> 8 High-Low High-Low High-Low #> 9 Low-Low Low-Low Low-Low #> 10 Low-High Low-High Low-High #> 11 High-Low High-Low High-Low #> 12 High-Low High-Low High-Low #> 13 High-Low High-Low High-Low #> 14 High-Low High-Low High-Low #> 15 High-Low High-Low High-Low #> 16 High-Low High-Low High-Low #> 17 High-High High-High High-High #> 18 High-Low High-Low High-Low #> 19 High-Low High-Low High-Low #> 20 Low-High Low-High Low-High #> 21 High-Low High-High High-Low #> 22 Low-High Low-High Low-High #> 23 Low-High Low-High Low-High #> 24 High-Low High-Low High-Low #> 25 High-Low High-Low High-Low #> 26 High-Low High-Low High-Low #> 27 High-High High-High High-High #> 28 High-Low High-Low High-Low #> 29 High-Low High-Low High-Low #> 30 High-Low High-Low High-Low #> 31 Low-High Low-High Low-High #> 32 Low-High Low-High Low-High #> 33 High-High High-High High-High #> 34 Low-High Low-High Low-High #> 35 High-High High-High High-High #> 36 Low-High Low-High Low-High #> 37 High-Low High-Low High-Low #> 38 High-Low High-Low High-Low #> 39 Low-High Low-High Low-High #> 40 Low-High Low-High Low-High #> 41 Low-High Low-High Low-High #> 42 Low-High Low-High Low-High #> 43 High-Low High-Low High-Low #> 44 Low-Low Low-Low Low-Low #> 45 Low-High Low-High Low-High #> 46 Low-High Low-High Low-High #> 47 Low-High Low-High Low-High #> 48 Low-High Low-High Low-High #> 49 Low-Low Low-Low Low-Low #> attr(,\"class\") #> [1] \"localmoran\" \"matrix\" \"array\" #> attr(,\"ncpus\") #> [1] 1 columbus$hs <- hotspot(res, Prname=\"Pr(folded) Sim\", cutoff=0.05, quadrant.type=\"pysal\", p.adjust=\"none\") # \\donttest{ if (require(\"tmap\", quietly=TRUE)) { tmap4 <- packageVersion(\"tmap\") >= \"3.99\" if (tmap4) { tm_shape(columbus) + tm_polygons(fill=\"hs\", fill.scale=tm_scale(values=\"brewer.set3\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"top\"), frame=FALSE, item.r=0), lwd=0.01) } else { tm_shape(columbus) + tm_fill(\"hs\") } } # } moran.plot(x=columbus$CRIME, y=columbus$INC, listw=listw)"},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate the local bivariate join count — local_joincount_bv","title":"Calculate the local bivariate join count — local_joincount_bv","text":"bivariate join count (BJC) evaluates event occurrences predefined regions tests co-occurrence events deviates complete spatial randomness.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate the local bivariate join count — local_joincount_bv","text":"","code":"local_joincount_bv( x, z, listw, nsim = 199, alternative = \"two.sided\" )"},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate the local bivariate join count — local_joincount_bv","text":"x binary variable either numeric logical z binary variable either numeric logical length x listw listw object containing binary weights created, example, nb2listw(nb, style = \"B\") nsim number conditional permutation simulations alternative default \"greater\". One \"less\" \"greater\".","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Calculate the local bivariate join count — local_joincount_bv","text":"two cases evaluated bivariate join count. first -situ colocation (CLC) xi = 1 zi = 1. second general form bivariate join count (BJC) used -situ colocation. BJC case \"useful x z occur location, x z correspond two different values single categorical variable\" \"x z can co-locate, \" (Anselin Li, 2019). Whereas CLC case useful evaluating simultaneous occurrences events. local bivariate join count statistic requires binary weights list can generated nb2listw(nb, style = \"B\"). P-values reported regions match CLC BJC criteria. Others associated p-value. P-values estimated using conditional permutation approach. creates reference distribution observed statistic compared.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate the local bivariate join count — local_joincount_bv","text":"data.frame two columns join_count p_sim number rows equal length arguments x.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Calculate the local bivariate join count — local_joincount_bv","text":"Anselin, L., & Li, X. (2019). Operational Local Join Count Statistics Cluster Detection. Journal geographical systems, 21(2), 189–210. doi:10.1007/s10109-019-00299-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Calculate the local bivariate join count — local_joincount_bv","text":"Josiah Parry josiah.parry@gmail.com","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_bv.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate the local bivariate join count — local_joincount_bv","text":"","code":"data(\"oldcol\") listw <- nb2listw(COL.nb, style = \"B\") # Colocation case x <- COL.OLD[[\"CP\"]] z <- COL.OLD[[\"EW\"]] set.seed(1) res <- local_joincount_bv(x, z, listw) na.omit(res) #> join_count p_sim #> 9 2 0.480 #> 19 3 0.180 #> 20 4 0.020 #> 21 3 0.040 #> 22 3 0.060 #> 23 4 0.070 #> 24 5 0.005 #> 27 2 0.300 #> 28 3 0.050 #> 29 5 0.010 #> 30 5 0.010 #> 31 9 0.005 #> 32 4 0.090 #> 33 4 0.055 # no colocation case z <- 1 - x set.seed(1) res <- local_joincount_bv(x, z, listw) na.omit(res) #> join_count p_sim #> 9 2 0.065 #> 19 3 0.300 #> 20 1 0.015 #> 21 1 0.040 #> 22 1 0.045 #> 23 3 0.165 #> 24 1 0.000 #> 27 2 0.230 #> 28 1 0.050 #> 29 1 0.000 #> 36 1 0.000 #> 37 2 0.005 #> 38 2 0.185 #> 39 2 0.265 #> 40 1 0.005 #> 43 1 0.070"},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":null,"dir":"Reference","previous_headings":"","what":"Calculate the local univariate join count — local_joincount_uni","title":"Calculate the local univariate join count — local_joincount_uni","text":"univariate local join count statistic used identify clusters rarely occurring binary variables. binary variable interest occur less half time.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Calculate the local univariate join count — local_joincount_uni","text":"","code":"local_joincount_uni( fx, chosen, listw, alternative = \"two.sided\", nsim = 199, iseed = NULL, no_repeat_in_row=FALSE )"},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Calculate the local univariate join count — local_joincount_uni","text":"fx factor two levels; use ordered factor well understood. chosen scalar character containing level fx considered observed value (1). listw listw object containing binary weights created, example, nbwlistw(nb, style = \"B\") alternative default \"greater\". One \"less\" \"greater\". nsim number conditional permutation simulations iseed default NULL, used set seed; output reproducible count CPU cores across computation distributed no_repeat_in_row default FALSE, TRUE, sample conditionally row without replacements avoid duplicate values, https://github.com/r-spatial/spdep/issues/124","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Calculate the local univariate join count — local_joincount_uni","text":"data.frame two columns BB Pr() number rows equal length x.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Calculate the local univariate join count — local_joincount_uni","text":"local join count statistic requires binary weights list can generated nb2listw(nb, style = \"B\"). Additionally, ensure binary variable interest rarely occurring half observations. P-values estimated using conditional permutation approach. creates reference distribution observed statistic compared. see Geoda Glossary.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Calculate the local univariate join count — local_joincount_uni","text":"Anselin, L., & Li, X. (2019). Operational Local Join Count Statistics Cluster Detection. Journal geographical systems, 21(2), 189–210. doi:10.1007/s10109-019-00299-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Calculate the local univariate join count — local_joincount_uni","text":"Josiah Parry josiah.parry@gmail.com","code":""},{"path":"https://r-spatial.github.io/spdep/reference/local_joincount_uni.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Calculate the local univariate join count — local_joincount_uni","text":"","code":"data(oldcol) fx <- as.factor(ifelse(COL.OLD$CRIME < 35, \"low-crime\", \"high-crime\")) listw <- nb2listw(COL.nb, style = \"B\") set.seed(1) (res <- local_joincount_uni(fx, chosen = \"high-crime\", listw)) #> BB Pr(z != E(BBi)) #> 1 0 NA #> 2 0 NA #> 3 4 0.50 #> 4 0 NA #> 5 0 NA #> 6 0 NA #> 7 4 0.89 #> 8 0 NA #> 9 5 0.11 #> 10 0 NA #> 11 0 NA #> 12 0 NA #> 13 0 NA #> 14 0 NA #> 15 0 NA #> 16 0 NA #> 17 0 NA #> 18 0 NA #> 19 0 NA #> 20 3 0.55 #> 21 2 0.84 #> 22 3 0.30 #> 23 4 0.61 #> 24 5 0.12 #> 25 0 NA #> 26 0 NA #> 27 0 NA #> 28 0 NA #> 29 3 0.98 #> 30 5 0.09 #> 31 8 0.01 #> 32 7 0.02 #> 33 6 0.02 #> 34 5 0.04 #> 35 7 0.03 #> 36 8 0.02 #> 37 6 0.05 #> 38 5 0.04 #> 39 3 0.44 #> 40 5 0.14 #> 41 3 0.13 #> 42 5 0.05 #> 43 2 0.63 #> 44 0 NA #> 45 0 NA #> 46 0 NA #> 47 0 NA #> 48 0 NA #> 49 0 NA"},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":null,"dir":"Reference","previous_headings":"","what":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"function implements chi-square based test statistic local spatial heteroscedasticity (LOSH) proposed Ord & Getis (2012).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"","code":"LOSH.cs(x, listw, zero.policy = attr(listw, \"zero.policy\"), na.action = na.fail, p.adjust.method = \"none\", spChk = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass used, zero substituted NA values calculating spatial lag. (Note na.exclude work properly starting R 1.9.0, na.omit na.exclude assign wrong classes 1.8.*) p.adjust.method character string specifying probability value adjustment multiple tests, default \"none\"; see p.adjustSP. Note number multiple tests region taken number neighbours + 1 region, rather total number regions. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption()","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"test uses = 2 (see LOSH) chi-square based inference applicable exponents. function makes use LOSH calculations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"Hi LOSH statistic E.Hi expectation LOSH Var.Hi variance LOSH Z.Hi approximately chi-square distributed test statistics x_bar_i local spatially weighted mean values ei residuals local spatially weighted mean values Pr() p-values Hi obtained non-central Chi-square distribution \\(2/Var.Hi\\) degrees freedom","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"Ord, J. K., & Getis, . 2012. Local spatial heteroscedasticity (LOSH), Annals Regional Science, 48 (2), 529–539.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"René Westerholt rene.westerholt@tu-dortmund.de","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.cs.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Chi-square based test for local spatial heteroscedasticity — LOSH.cs","text":"","code":"data(boston, package=\"spData\") resLOSH <- LOSH.cs(boston.c$NOX, nb2listw(boston.soi)) hist(resLOSH[,\"Hi\"]) mean(resLOSH[,\"Hi\"]) #> [1] 0.9919329"},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":null,"dir":"Reference","previous_headings":"","what":"Local spatial heteroscedasticity — LOSH","title":"Local spatial heteroscedasticity — LOSH","text":"Local spatial heteroscedasticity calculated location based spatial weights object used. statistic : $$H_i = \\frac{\\sum_j^n w_{ij} \\cdot |e_j|^}{h_1 \\cdot \\sum_j^n w_{ij}}$$ $$e_j = x_j - \\bar{x}_j$$ $$\\bar{x}_j = \\frac{\\sum_k^n w_{jk} \\cdot x_k}{\\sum_k^n w_{jk}}$$ expectation variance given Ord & Getis (2012). exponent allows investigating different types mean dispersal.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Local spatial heteroscedasticity — LOSH","text":"","code":"LOSH(x, listw, a=2, var_hi=TRUE, zero.policy=attr(listw, \"zero.policy\"), na.action=na.fail, spChk=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Local spatial heteroscedasticity — LOSH","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw exponent applied local residuals; default value 2 leads measure heterogeneity spatial variance var_hi default TRUE, moments test statistics calculated location; FALSE, plain LOSH measures, \\(\\bar{x}_i\\) \\(e_i\\) calculated zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass used, zero substituted NA values calculating spatial lag. (Note na.exclude work properly starting R 1.9.0, na.omit na.exclude assign wrong classes 1.8.*) spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption()","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Local spatial heteroscedasticity — LOSH","text":"addition LOSH measure, values returned include local spatially weighted mean values \\(\\bar{x}_i\\) local residuals \\(e_i\\) estimated means. values facilitate interpretation LOSH values. , specified var_hi, statistical moments test statistics proposed Ord & Getis (2012) also calculated returned.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Local spatial heteroscedasticity — LOSH","text":"Hi LOSH statistic E.Hi (optional) expectation LOSH Var.Hi (optional) variance LOSH Z.Hi (optional) approximately Chi-square distributed test statistics x_bar_i local spatially weighted mean values ei residuals local spatially weighted mean values","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Local spatial heteroscedasticity — LOSH","text":"Ord, J. K., & Getis, . 2012. Local spatial heteroscedasticity (LOSH), Annals Regional Science, 48 (2), 529–539.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Local spatial heteroscedasticity — LOSH","text":"René Westerholt rene.westerholt@tu-dortmund.de","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Local spatial heteroscedasticity — LOSH","text":"","code":"data(boston, package=\"spData\") resLOSH <- LOSH(boston.c$NOX, nb2listw(boston.soi)) hist(resLOSH[,\"Hi\"]) mean(resLOSH[,\"Hi\"]) #> [1] 0.9919329"},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"function draws inferences local spatial heteroscedasticity (LOSH) means randomisation-based Monte-Carlo bootstrap proposed Xu et al. (2014).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"","code":"LOSH.mc(x, listw, a = 2, nsim = 99, zero.policy = attr(listw, \"zero.policy\"), na.action = na.fail, spChk = NULL, adjust.n = TRUE, p.adjust.method = \"none\")"},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw exponent applied local residuals; default value 2 leads measure heterogeneity spatial variance nsim number randomisations used bootstrap zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass used, zero substituted NA values calculating spatial lag. (Note na.exclude work properly starting R 1.9.0, na.omit na.exclude assign wrong classes 1.8.*) spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted p.adjust.method character string specifying probability value adjustment multiple tests, default \"none\"; see p.adjustSP. Note number multiple tests region taken number neighbours + 1 region, rather total number regions.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"test calculates LOSH (see LOSH) estimates pseudo p-values conditional bootstrap. Thereby, -th value location held fixed, whereas values permuted nsim times spatial units.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"Hi LOSH statistic E.Hi expectation LOSH Var.Hi variance LOSH Z.Hi approximately chi-square distributed test statistics x_bar_i local spatially weighted mean values ei residuals local spatially weighted mean values Pr() p-values Hi obtained conditional bootstrap distribution","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"Ord, J. K., & Getis, . 2012. Local spatial heteroscedasticity (LOSH), Annals Regional Science, 48 (2), 529–539; Xu, M., Mei, C. L., & Yan, N. 2014. note null distribution local spatial heteroscedasticity (LOSH) statistic. Annals Regional Science, 52 (3), 697–710.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"René Westerholt rene.westerholt@tu-dortmund.de","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/LOSH.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Bootstrapping-based test for local spatial heteroscedasticity — LOSH.mc","text":"","code":"data(columbus, package=\"spData\") resLOSH_mc <- LOSH.mc(columbus$CRIME, nb2listw(col.gal.nb), 2, 100) summary(resLOSH_mc) #> Hi x_bar_i ei Pr() #> Min. :0.03438 Min. :13.85 Min. : 0.0298 Min. :0.009901 #> 1st Qu.:0.23838 1st Qu.:24.71 1st Qu.: 7.0114 1st Qu.:0.118812 #> Median :0.66689 Median :35.90 Median : 52.1094 Median :0.673267 #> Mean :1.06592 Mean :34.88 Mean : 151.9232 Mean :0.551424 #> 3rd Qu.:1.59680 3rd Qu.:45.39 3rd Qu.: 105.0551 3rd Qu.:0.900990 #> Max. :4.68765 Max. :54.91 Max. :2455.2201 Max. :0.990099 resLOSH_cs <- LOSH.cs(columbus$CRIME, nb2listw(col.gal.nb)) summary(resLOSH_cs) #> Hi E.Hi Var.Hi Z.Hi #> Min. :0.03438 Min. :1 Min. :0.4972 Min. :0.04356 #> 1st Qu.:0.23838 1st Qu.:1 1st Qu.:0.9136 1st Qu.:0.35069 #> Median :0.66689 Median :1 Median :1.4342 Median :1.19175 #> Mean :1.06592 Mean :1 Mean :1.4758 Mean :1.89447 #> 3rd Qu.:1.59680 3rd Qu.:1 3rd Qu.:1.9547 3rd Qu.:2.65120 #> Max. :4.68765 Max. :1 Max. :2.9958 Max. :7.25681 #> x_bar_i ei Pr() #> Min. :13.85 Min. : 0.0298 Min. :0.0190 #> 1st Qu.:24.71 1st Qu.: 7.0114 1st Qu.:0.2050 #> Median :35.90 Median : 52.1094 Median :0.5264 #> Mean :34.88 Mean : 151.9232 Mean :0.4507 #> 3rd Qu.:45.39 3rd Qu.: 105.0551 3rd Qu.:0.6529 #> Max. :54.91 Max. :2455.2201 Max. :0.9540 plot(resLOSH_mc[,\"Pr()\"], resLOSH_cs[,\"Pr()\"])"},{"path":"https://r-spatial.github.io/spdep/reference/mat2listw.html","id":null,"dir":"Reference","previous_headings":"","what":"Convert a square spatial weights matrix to a weights list object — mat2listw","title":"Convert a square spatial weights matrix to a weights list object — mat2listw","text":"function converts square spatial weights matrix, optionally sparse matrix weights list object, optionally adding region IDs row names matrix, sequence numbers 1:nrow(x), given argument. style can imposed rebuilting weights list object internally.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mat2listw.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Convert a square spatial weights matrix to a weights list object — mat2listw","text":"","code":"mat2listw(x, row.names = NULL, style=NULL, zero.policy = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/mat2listw.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Convert a square spatial weights matrix to a weights list object — mat2listw","text":"x square non-negative matrix NAs representing spatial weights; may matrix class “sparseMatrix” row.names row names use region IDs style default NULL, missing, set \"M\" warning given; \"M\", passed nb2listw re-build object zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mat2listw.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Convert a square spatial weights matrix to a weights list object — mat2listw","text":"listw object following members: style \"M\", meaning matrix style, underlying style unknown, assigned style argument rebuilt object neighbours derived neighbours list weights weights neighbours derived matrix","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mat2listw.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Convert a square spatial weights matrix to a weights list object — mat2listw","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/mat2listw.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Convert a square spatial weights matrix to a weights list object — mat2listw","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col005 <- dnearneigh(st_coordinates(st_centroid(st_geometry(columbus), of_largest_polygon=TRUE)), 0, 0.5, as.character(columbus$NEIGNO)) #> Warning: neighbour object has 8 sub-graphs summary(col005) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 170 #> Percentage nonzero weights: 7.080383 #> Average number of links: 3.469388 #> 4 regions with no links: #> 1005, 1006, 1008, 1043 #> 8 disjoint connected subgraphs #> Link number distribution: #> #> 0 1 2 3 4 5 6 7 8 9 #> 4 11 5 8 3 9 2 2 3 2 #> 11 least connected regions: #> 1001 1007 1018 1010 1045 1044 1046 1047 1049 1048 1015 with 1 link #> 2 most connected regions: #> 1038 1036 with 9 links col005.w.mat <- nb2mat(col005, style=\"W\", zero.policy=TRUE) try(col005.w.b <- mat2listw(col005.w.mat, style=\"W\")) #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> Warning: neighbour object has 8 sub-graphs #> Error in nb2listw(res$neighbours, glist = res$weights, style = style, : #> Empty neighbour sets found (zero.policy: FALSE) col005.w.b <- mat2listw(col005.w.mat, style=\"W\", zero.policy=TRUE) #> Warning: neighbour object has 8 sub-graphs summary(col005.w.b$neighbours) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 170 #> Percentage nonzero weights: 7.080383 #> Average number of links: 3.469388 #> 4 regions with no links: #> 1005, 1006, 1008, 1043 #> 8 disjoint connected subgraphs #> Link number distribution: #> #> 0 1 2 3 4 5 6 7 8 9 #> 4 11 5 8 3 9 2 2 3 2 #> 11 least connected regions: #> 1001 1007 1018 1010 1045 1044 1046 1047 1049 1048 1015 with 1 link #> 2 most connected regions: #> 1038 1036 with 9 links diffnb(col005, col005.w.b$neighbours) #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 0 #> Percentage nonzero weights: 0 #> Average number of links: 0 #> 49 regions with no links: #> 1005, 1001, 1006, 1002, 1007, 1008, 1004, 1003, 1018, 1010, 1038, 1037, #> 1039, 1040, 1009, 1036, 1011, 1042, 1041, 1017, 1043, 1019, 1012, 1035, #> 1032, 1020, 1021, 1031, 1033, 1034, 1045, 1013, 1022, 1044, 1023, 1046, #> 1030, 1024, 1047, 1016, 1014, 1049, 1029, 1025, 1028, 1048, 1015, 1027, #> 1026 #> 49 disjoint connected subgraphs col005.w.mat.3T <- kronecker(diag(3), col005.w.mat) col005.w.b.3T <- mat2listw(col005.w.mat.3T, style=\"W\", zero.policy=TRUE) #> Warning: neighbour object has 24 sub-graphs summary(col005.w.b.3T$neighbours) #> Neighbour list object: #> Number of regions: 147 #> Number of nonzero links: 510 #> Percentage nonzero weights: 2.360128 #> Average number of links: 3.469388 #> 12 regions with no links: #> 1, 3, 6, 21, 50, 52, 55, 70, 99, 101, 104, 119 #> 24 disjoint connected subgraphs #> Link number distribution: #> #> 0 1 2 3 4 5 6 7 8 9 #> 12 33 15 24 9 27 6 6 9 6 #> 33 least connected regions: #> 2 5 9 10 31 34 36 39 42 46 47 51 54 58 59 80 83 85 88 91 95 96 100 103 107 108 129 132 134 137 140 144 145 with 1 link #> 6 most connected regions: #> 11 16 60 65 109 114 with 9 links run <- FALSE if (require(\"spatialreg\", quiet=TRUE)) run <- TRUE if (run) { W <- as(nb2listw(col005, style=\"W\", zero.policy=TRUE), \"CsparseMatrix\") try(col005.spM <- mat2listw(W)) col005.spM <- mat2listw(W, style=\"W\", zero.policy=TRUE) summary(col005.spM$neighbours) } if (run) { diffnb(col005, col005.spM$neighbours) } if (run && require(\"Matrix\", quiet=TRUE)) { IW <- kronecker(Diagonal(3), W) col005.spM.3T <- mat2listw(as(IW, \"CsparseMatrix\"), style=\"W\", zero.policy=TRUE) summary(col005.spM.3T$neighbours) }"},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute Moran's I — moran","title":"Compute Moran's I — moran","text":"simple function compute Moran's , called moran.test moran.mc; $$= \\frac{n}{\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}} \\frac{\\sum_{=1}^{n}\\sum_{j=1}^{n}w_{ij}(x_i-\\bar{x})(x_j-\\bar{x})}{\\sum_{=1}^{n}(x_i - \\bar{x})^2} $$","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute Moran's I — moran","text":"","code":"moran(x, listw, n, S0, zero.policy=attr(listw, \"zero.policy\"), NAOK=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute Moran's I — moran","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw n number zones S0 global sum weights zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA NAOK 'TRUE' 'NA' 'NaN' 'Inf' values x passed foreign function. 'FALSE', presence 'NA' 'NaN' 'Inf' values regarded error.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute Moran's I — moran","text":"list Moran's K sample kurtosis x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute Moran's I — moran","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 17.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute Moran's I — moran","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/moran.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute Moran's I — moran","text":"","code":"data(oldcol) col.W <- nb2listw(COL.nb, style=\"W\") crime <- COL.OLD$CRIME str(moran(crime, col.W, length(COL.nb), Szero(col.W))) #> List of 2 #> $ I: num 0.511 #> $ K: num 2.23 is.na(crime) <- sample(1:length(crime), 10) str(moran(crime, col.W, length(COL.nb), Szero(col.W), NAOK=TRUE)) #> Warning: NAs in lagged values #> List of 2 #> $ I: num 0.213 #> $ K: num 2.85"},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Permutation test for Moran's I statistic — moran.mc","title":"Permutation test for Moran's I statistic — moran.mc","text":"permutation test Moran's statistic calculated using nsim random permutations x given spatial weighting scheme, establish rank observed statistic relation nsim simulated values.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Permutation test for Moran's I statistic — moran.mc","text":"","code":"moran.mc(x, listw, nsim, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\", na.action=na.fail, spChk=NULL, return_boot=FALSE, adjust.n=TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Permutation test for Moran's I statistic — moran.mc","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw nsim number permutations zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"two.sided\", \"less\". na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass permitted meaningless permutation test. spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() return_boot return object class boot equivalent permutation bootstrap rather object class htest adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Permutation test for Moran's I statistic — moran.mc","text":"list class htest mc.sim containing following components: statistic value observed Moran's . parameter rank observed Moran's . p.value pseudo p-value test. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data, number simulations. res nsim simulated values statistic, final value observed statistic","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Permutation test for Moran's I statistic — moran.mc","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 63-5.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Permutation test for Moran's I statistic — moran.mc","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/moran.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Permutation test for Moran's I statistic — moran.mc","text":"","code":"data(oldcol) colw <- nb2listw(COL.nb, style=\"W\") nsim <- 99 set.seed(1234) sim1 <- moran.mc(COL.OLD$CRIME, listw=colw, nsim=nsim) sim1 #> #> \tMonte-Carlo simulation of Moran I #> #> data: COL.OLD$CRIME #> weights: colw #> number of simulations + 1: 100 #> #> statistic = 0.51095, observed rank = 100, p-value = 0.01 #> alternative hypothesis: greater #> mean(sim1$res[1:nsim]) #> [1] -0.003196117 var(sim1$res[1:nsim]) #> [1] 0.008543554 summary(sim1$res[1:nsim]) #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> -0.180085 -0.073721 -0.009528 -0.003196 0.063865 0.206779 colold.lags <- nblag(COL.nb, 3) set.seed(1234) sim2 <- moran.mc(COL.OLD$CRIME, nb2listw(colold.lags[[2]], style=\"W\"), nsim=nsim) summary(sim2$res[1:nsim]) #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> -0.15905 -0.07503 -0.01535 -0.02060 0.03305 0.13023 sim3 <- moran.mc(COL.OLD$CRIME, nb2listw(colold.lags[[3]], style=\"W\"), nsim=nsim) summary(sim3$res[1:nsim]) #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> -0.192986 -0.055468 -0.024154 -0.026327 0.004769 0.129996 crime <- COL.OLD$CRIME is.na(crime) <- sample(1:length(crime), 10) try(moran.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, na.action=na.fail)) #> Error in na.fail.default(x) : missing values in object moran.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE, na.action=na.omit) #> #> \tMonte-Carlo simulation of Moran I #> #> data: crime #> weights: nb2listw(COL.nb, style = \"W\") #> omitted: 5, 7, 9, 15, 19, 33, 40, 45, 47, 48 #> number of simulations + 1: 100 #> #> statistic = 0.42342, observed rank = 100, p-value = 0.01 #> alternative hypothesis: greater #> moran.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE, return_boot=TRUE, na.action=na.omit) #> NA observations omitted: 5, 7, 9, 15, 19, 33, 40, 45, 47, 48 #> #> DATA PERMUTATION #> #> #> Call: #> boot(data = x, statistic = moran_boot, R = nsim, sim = \"permutation\", #> listw = listw, n = n, S0 = S0, zero.policy = zero.policy, #> parallel = parallel, ncpus = ncpus, cl = cl) #> #> #> Bootstrap Statistics : #> original bias std. error #> t1* 0.4234221 -0.4429891 0.1293935 moran.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE, na.action=na.exclude) #> #> \tMonte-Carlo simulation of Moran I #> #> data: crime #> weights: nb2listw(COL.nb, style = \"W\") #> omitted: 5, 7, 9, 15, 19, 33, 40, 45, 47, 48 #> number of simulations + 1: 100 #> #> statistic = 0.42342, observed rank = 100, p-value = 0.01 #> alternative hypothesis: greater #> moran.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, zero.policy=TRUE, return_boot=TRUE, na.action=na.exclude) #> NA observations omitted: 5, 7, 9, 15, 19, 33, 40, 45, 47, 48 #> #> DATA PERMUTATION #> #> #> Call: #> boot(data = x, statistic = moran_boot, R = nsim, sim = \"permutation\", #> listw = listw, n = n, S0 = S0, zero.policy = zero.policy, #> parallel = parallel, ncpus = ncpus, cl = cl) #> #> #> Bootstrap Statistics : #> original bias std. error #> t1* 0.4234221 -0.4384413 0.1243937 try(moran.mc(crime, nb2listw(COL.nb, style=\"W\"), nsim=99, na.action=na.pass)) #> Error in moran.mc(crime, nb2listw(COL.nb, style = \"W\"), nsim = 99, na.action = na.pass) : #> na.pass not permitted"},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":null,"dir":"Reference","previous_headings":"","what":"Moran scatterplot — moran.plot","title":"Moran scatterplot — moran.plot","text":"plot spatial data spatially lagged values, augmented reporting summary influence measures linear relationship data lag. zero policy TRUE, observations also marked occur.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Moran scatterplot — moran.plot","text":"","code":"moran.plot(x, listw, y=NULL, zero.policy=attr(listw, \"zero.policy\"), spChk=NULL, labels=NULL, xlab=NULL, ylab=NULL, quiet=NULL, plot=TRUE, return_df=TRUE, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Moran scatterplot — moran.plot","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw y optional numeric vector length neighbours list listw bi-variate plot zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() labels character labels points high influence measures, set FALSE, labels plotted points large influence xlab label x axis ylab label x axis quiet default NULL, use !verbose global option value; TRUE, output summary influence object suppressed plot default TRUE, false, plotting suppressed return_df default TRUE, invisibly return data.frame object; FALSE invisibly return influence measures object ... graphical parameters par(..)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Moran scatterplot — moran.plot","text":"function returns data.frame object coordinates influence measures return_df TRUE, influence object influence.measures.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Moran scatterplot — moran.plot","text":"Anselin, L. 1996. Moran scatterplot ESDA tool assess local instability spatial association. pp. 111–125 M. M. Fischer, H. J. Scholten D. Unwin (eds) Spatial analytical perspectives GIS, London, Taylor Francis; Anselin, L. 1995. Local indicators spatial association, Geographical Analysis, 27, 93–115","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Moran scatterplot — moran.plot","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/moran.plot.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Moran scatterplot — moran.plot","text":"","code":"data(afcon, package=\"spData\") mp <- moran.plot(afcon$totcon, nb2listw(paper.nb), labels=as.character(afcon$name), pch=19) moran.plot(as.vector(scale(afcon$totcon)), nb2listw(paper.nb), labels=as.character(afcon$name), xlim=c(-2, 4), ylim=c(-2,4), pch=19) if (require(ggplot2, quietly=TRUE)) { xname <- attr(mp, \"xname\") ggplot(mp, aes(x=x, y=wx)) + geom_point(shape=1) + geom_smooth(formula=y ~ x, method=\"lm\") + geom_hline(yintercept=mean(mp$wx), lty=2) + geom_vline(xintercept=mean(mp$x), lty=2) + theme_minimal() + geom_point(data=mp[mp$is_inf,], aes(x=x, y=wx), shape=9) + geom_text(data=mp[mp$is_inf,], aes(x=x, y=wx, label=labels, vjust=1.5)) + xlab(xname) + ylab(paste0(\"Spatially lagged \", xname)) } columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")) #> Reading layer `columbus' from data source #> `C:\\Users\\rzomor2\\AppData\\Local\\R\\win-library\\4.4\\spData\\shapes\\columbus.gpkg' #> using driver `GPKG' #> Simple feature collection with 49 features and 20 fields #> Geometry type: POLYGON #> Dimension: XY #> Bounding box: xmin: 5.874907 ymin: 10.78863 xmax: 11.28742 ymax: 14.74245 #> Projected CRS: Undefined Cartesian SRS with unknown unit nb <- poly2nb(columbus) listw <- nb2listw(nb) moran.plot(x=columbus$CRIME, y=columbus$INC, listw=listw) moran.plot(x=columbus$INC, y=columbus$CRIME, listw=listw)"},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":null,"dir":"Reference","previous_headings":"","what":"Moran's I test for spatial autocorrelation — moran.test","title":"Moran's I test for spatial autocorrelation — moran.test","text":"Moran's test spatial autocorrelation using spatial weights matrix weights list form. assumptions underlying test sensitive form graph neighbour relationships factors, results may checked moran.mc permutations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Moran's I test for spatial autocorrelation — moran.test","text":"","code":"moran.test(x, listw, randomisation=TRUE, zero.policy=attr(listw, \"zero.policy\"), alternative=\"greater\", rank = FALSE, na.action=na.fail, spChk=NULL, adjust.n=TRUE, drop.EI2=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Moran's I test for spatial autocorrelation — moran.test","text":"x numeric vector length neighbours list listw listw listw object created example nb2listw randomisation variance calculated assumption randomisation, FALSE normality zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one greater (default), less two.sided. rank logical value - default FALSE continuous variables, TRUE, uses adaptation Moran's ranks suggested Cliff Ord (1981, p. 46) na.action function (default na.fail), can also na.omit na.exclude - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. na.pass used, zero substituted NA values calculating spatial lag spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted drop.EI2 default FALSE, TRUE, emulate CrimeStat <= 4.02","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Moran's I test for spatial autocorrelation — moran.test","text":"list class htest containing following components: statistic value standard deviate Moran's . p.value p-value test. estimate value observed Moran's , expectation variance method assumption. alternative character string describing alternative hypothesis. method character string giving assumption used calculating standard deviate. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Moran's I test for spatial autocorrelation — moran.test","text":"Var() taken Cliff Ord (1969, p. 28), Goodchild's CATMOG 47 (1986), see also Upton & Fingleton (1985) p. 171; agrees SpaceStat, see Tutorial workbook Chapter 22; VI second crude moment minus square first crude moment. derivation test (Cliff Ord, 1981, p. 18) assumes weights matrix symmetric. inherently non-symmetric matrices, k-nearest neighbour matrices, listw2U() can used make matrix symmetric.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Moran's I test for spatial autocorrelation — moran.test","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 21; Bivand RS, Wong DWS 2018 Comparing implementations global local indicators spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Moran's I test for spatial autocorrelation — moran.test","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/moran.test.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Moran's I test for spatial autocorrelation — moran.test","text":"","code":"data(oldcol) coords.OLD <- cbind(COL.OLD$X, COL.OLD$Y) moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"W\")) #> #> \tMoran I test under randomisation #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.nb, style = \"W\") #> #> Moran I statistic standard deviate = 5.6341, p-value = 8.797e-09 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.510951264 -0.020833333 0.008908762 #> moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"B\")) #> #> \tMoran I test under randomisation #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.nb, style = \"B\") #> #> Moran I statistic standard deviate = 6.2116, p-value = 2.622e-10 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.52063815 -0.02083333 0.00759872 #> moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"C\")) #> #> \tMoran I test under randomisation #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.nb, style = \"C\") #> #> Moran I statistic standard deviate = 6.2116, p-value = 2.622e-10 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.52063815 -0.02083333 0.00759872 #> moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"S\")) #> #> \tMoran I test under randomisation #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.nb, style = \"S\") #> #> Moran I statistic standard deviate = 5.9786, p-value = 1.125e-09 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.512957470 -0.020833333 0.007971504 #> moran.test(COL.OLD$CRIME, nb2listw(COL.nb, style=\"W\"), randomisation=FALSE) #> #> \tMoran I test under normality #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.nb, style = \"W\") #> #> Moran I statistic standard deviate = 5.6754, p-value = 6.92e-09 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.510951264 -0.020833333 0.008779831 #> colold.lags <- nblag(COL.nb, 3) moran.test(COL.OLD$CRIME, nb2listw(colold.lags[[2]], style=\"W\")) #> #> \tMoran I test under randomisation #> #> data: COL.OLD$CRIME #> weights: nb2listw(colold.lags[[2]], style = \"W\") #> #> Moran I statistic standard deviate = 2.6076, p-value = 0.004559 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.168485742 -0.020833333 0.005271314 #> moran.test(COL.OLD$CRIME, nb2listw(colold.lags[[3]], style=\"W\")) #> #> \tMoran I test under randomisation #> #> data: COL.OLD$CRIME #> weights: nb2listw(colold.lags[[3]], style = \"W\") #> #> Moran I statistic standard deviate = -1.7896, p-value = 0.9632 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> -0.138930745 -0.020833333 0.004354683 #> print(is.symmetric.nb(COL.nb)) #> [1] TRUE COL.k4.nb <- knn2nb(knearneigh(coords.OLD, 4)) print(is.symmetric.nb(COL.k4.nb)) #> [1] FALSE moran.test(COL.OLD$CRIME, nb2listw(COL.k4.nb, style=\"W\")) #> #> \tMoran I test under randomisation #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.k4.nb, style = \"W\") #> #> Moran I statistic standard deviate = 7.2183, p-value = 2.632e-13 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.624933667 -0.020833333 0.008003503 #> moran.test(COL.OLD$CRIME, nb2listw(COL.k4.nb, style=\"W\"), randomisation=FALSE) #> #> \tMoran I test under normality #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.k4.nb, style = \"W\") #> #> Moran I statistic standard deviate = 7.2711, p-value = 1.782e-13 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.624933667 -0.020833333 0.007887613 #> cat(\"Note: non-symmetric weights matrix, use listw2U()\") #> Note: non-symmetric weights matrix, use listw2U() moran.test(COL.OLD$CRIME, listw2U(nb2listw(COL.k4.nb, style=\"W\"))) #> #> \tMoran I test under randomisation #> #> data: COL.OLD$CRIME #> weights: listw2U(nb2listw(COL.k4.nb, style = \"W\")) #> #> Moran I statistic standard deviate = 7.2183, p-value = 2.632e-13 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.624933667 -0.020833333 0.008003503 #> moran.test(COL.OLD$CRIME, listw2U(nb2listw(COL.k4.nb, style=\"W\")), randomisation=FALSE) #> #> \tMoran I test under normality #> #> data: COL.OLD$CRIME #> weights: listw2U(nb2listw(COL.k4.nb, style = \"W\")) #> #> Moran I statistic standard deviate = 7.2711, p-value = 1.782e-13 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.624933667 -0.020833333 0.007887613 #> ranks <- rank(COL.OLD$CRIME) names(ranks) <- rownames(COL.OLD) moran.test(ranks, nb2listw(COL.nb, style=\"W\"), rank=TRUE) #> #> \tMoran I test under randomisation #> #> data: ranks using rank correction #> weights: nb2listw(COL.nb, style = \"W\") #> #> Moran I statistic standard deviate = 6.3815, p-value = 8.766e-11 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.584333495 -0.020833333 0.008992923 #> crime <- COL.OLD$CRIME is.na(crime) <- sample(1:length(crime), 10) res <- try(moran.test(crime, nb2listw(COL.nb, style=\"W\"), na.action=na.fail)) #> Error in na.fail.default(x) : missing values in object moran.test(crime, nb2listw(COL.nb, style=\"W\"), zero.policy=TRUE, na.action=na.omit) #> Warning: subsetting caused increase in subgraph count #> #> \tMoran I test under randomisation #> #> data: crime #> weights: nb2listw(COL.nb, style = \"W\") #> omitted: 2, 6, 10, 18, 21, 28, 29, 38, 40, 45 #> #> Moran I statistic standard deviate = 4.4356, p-value = 4.591e-06 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.52990879 -0.02631579 0.01572539 #> moran.test(crime, nb2listw(COL.nb, style=\"W\"), zero.policy=TRUE, na.action=na.exclude) #> Warning: subsetting caused increase in subgraph count #> #> \tMoran I test under randomisation #> #> data: crime #> weights: nb2listw(COL.nb, style = \"W\") #> omitted: 2, 6, 10, 18, 21, 28, 29, 38, 40, 45 #> #> Moran I statistic standard deviate = 4.4356, p-value = 4.591e-06 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.52990879 -0.02631579 0.01572539 #> moran.test(crime, nb2listw(COL.nb, style=\"W\"), na.action=na.pass) #> Warning: NAs in lagged values #> #> \tMoran I test under randomisation #> #> data: crime #> weights: nb2listw(COL.nb, style = \"W\") #> #> Moran I statistic standard deviate = 3.5517, p-value = 0.0001914 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.312720923 -0.020833333 0.008819955 #> columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col_geoms <- st_geometry(columbus) col_geoms[1] <- st_buffer(col_geoms[1], dist=-0.05) st_geometry(columbus) <- col_geoms (nb1 <- poly2nb(columbus)) #> Warning: some observations have no neighbours; #> if this seems unexpected, try increasing the snap argument. #> Warning: neighbour object has 2 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 232 #> Percentage nonzero weights: 9.662641 #> Average number of links: 4.734694 #> 1 region with no links: #> 1 #> 2 disjoint connected subgraphs try(lw <- nb2listw(nb1, style=\"W\")) #> Error in nb2listw(nb1, style = \"W\") : #> Empty neighbour sets found (zero.policy: FALSE) (lw <- nb2listw(nb1, style=\"W\", zero.policy=TRUE)) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 232 #> Percentage nonzero weights: 9.662641 #> Average number of links: 4.734694 #> 1 region with no links: #> 1 #> 2 disjoint connected subgraphs #> #> Weights style: W #> Weights constants summary: #> n nn S0 S1 S2 #> W 48 2304 48 22.23035 199.8188 moran.test(COL.OLD$CRIME, lw) #> #> \tMoran I test under randomisation #> #> data: COL.OLD$CRIME #> weights: lw #> n reduced by no-neighbour observations #> #> Moran I statistic standard deviate = 2.7707, p-value = 0.002797 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.23901261 -0.02127660 0.00882535 #>"},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute the Global Bivariate Moran's I — moran_bv","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"Given two continuous numeric variables, calculate bivariate Moran's . See details .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"","code":"moran_bv(x, y, listw, nsim = 499, scale = TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"x numeric vector length y. y numeric vector length x. listw listw object example created nb2listw(). nsim number simulations run. scale default TRUE.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"object class \"boot\", observed statistic component t0.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"Global Bivariate Moran defined \\( I_B = \\frac{\\Sigma_i(\\Sigma_j{w_{ij}y_j\\times x_i})}{\\Sigma_i{x_i^2}} \\) important note measure autocorrelation X spatial lag Y. , resultant measure may overestimate amount spatial autocorrelation may product inherent correlation X Y. output object class \"boot\", plots confidence intervals available using appropriate methods.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"Wartenberg, D. (1985), Multivariate Spatial Correlation: Method Exploratory Geographical Analysis. Geographical Analysis, 17: 263-283. doi:10.1111/j.1538-4632.1985.tb00849.x","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"Josiah Parry josiah.parry@gmail.com","code":""},{"path":"https://r-spatial.github.io/spdep/reference/moran_bv.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute the Global Bivariate Moran's I — moran_bv","text":"","code":"data(boston, package = \"spData\") x <- boston.c$CRIM y <- boston.c$NOX listw <- nb2listw(boston.soi) set.seed(1) res_xy <- moran_bv(x, y, listw, nsim=499) res_xy$t0 #> [1] 0.4082073 boot::boot.ci(res_xy, conf=c(0.99, 0.95, 0.9), type=\"basic\") #> BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS #> Based on 499 bootstrap replicates #> #> CALL : #> boot::boot.ci(boot.out = res_xy, conf = c(0.99, 0.95, 0.9), type = \"basic\") #> #> Intervals : #> Level Basic #> 99% ( 0.7443, 0.8789 ) #> 95% ( 0.7639, 0.8673 ) #> 90% ( 0.7739, 0.8615 ) #> Calculations and Intervals on Original Scale #> Some basic intervals may be unstable plot(res_xy) set.seed(1) lee_xy <- lee.mc(x, y, listw, nsim=499, return_boot=TRUE) lee_xy$t0 #> [1] 0.3993476 boot::boot.ci(lee_xy, conf=c(0.99, 0.95, 0.9), type=\"basic\") #> BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS #> Based on 499 bootstrap replicates #> #> CALL : #> boot::boot.ci(boot.out = lee_xy, conf = c(0.99, 0.95, 0.9), type = \"basic\") #> #> Intervals : #> Level Basic #> 99% ( 0.6363, 0.7236 ) #> 95% ( 0.6538, 0.7131 ) #> 90% ( 0.6584, 0.7098 ) #> Calculations and Intervals on Original Scale #> Some basic intervals may be unstable plot(lee_xy) set.seed(1) res_yx <- moran_bv(y, x, listw, nsim=499) res_yx$t0 #> [1] 0.4029821 boot::boot.ci(res_yx, conf=c(0.99, 0.95, 0.9), type=\"basic\") #> BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS #> Based on 499 bootstrap replicates #> #> CALL : #> boot::boot.ci(boot.out = res_yx, conf = c(0.99, 0.95, 0.9), type = \"basic\") #> #> Intervals : #> Level Basic #> 99% ( 0.7301, 0.8729 ) #> 95% ( 0.7574, 0.8584 ) #> 90% ( 0.7664, 0.8541 ) #> Calculations and Intervals on Original Scale #> Some basic intervals may be unstable plot(res_yx) set.seed(1) lee_yx <- lee.mc(y, x, listw, nsim=499, return_boot=TRUE) lee_yx$t0 #> [1] 0.3993476 boot::boot.ci(lee_yx, conf=c(0.99, 0.95, 0.9), type=\"basic\") #> BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS #> Based on 499 bootstrap replicates #> #> CALL : #> boot::boot.ci(boot.out = lee_yx, conf = c(0.99, 0.95, 0.9), type = \"basic\") #> #> Intervals : #> Level Basic #> 99% ( 0.6363, 0.7236 ) #> 95% ( 0.6538, 0.7131 ) #> 90% ( 0.6584, 0.7098 ) #> Calculations and Intervals on Original Scale #> Some basic intervals may be unstable plot(lee_yx)"},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":null,"dir":"Reference","previous_headings":"","what":"Find the minimal spanning tree — mstree","title":"Find the minimal spanning tree — mstree","text":"minimal spanning tree connected graph n nodes n-1 edges. smaller class possible partitions graph pruning edges high dissimilarity. one edge removed, graph partioned two unconnected subgraphs. function implements algorithm due Prim (1987).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Find the minimal spanning tree — mstree","text":"","code":"mstree(nbw, ini = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Find the minimal spanning tree — mstree","text":"nbw object listw class returned nb2listw function. See help details. ini initial node minimal spanning tree.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Find the minimal spanning tree — mstree","text":"minimum spanning tree algorithm. Input connected graph. Begin empty set nodes. Add arbitrary note set. nodes set, find minimum cost edge connecting node set node set add node set. set edges minimum spanning tree.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Find the minimal spanning tree — mstree","text":"matrix n-1 rows tree columns. row two nodes cost, . e. edge cost.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Find the minimal spanning tree — mstree","text":"R. C. Prim (1957) Shortest connection networks generalisations. : Bell System Technical Journal, 36, pp. 1389-1401","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Find the minimal spanning tree — mstree","text":"Renato M. Assuncao Elias T. Krainski","code":""},{"path":"https://r-spatial.github.io/spdep/reference/mstree.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Find the minimal spanning tree — mstree","text":"","code":"### loading data GDAL37 <- numeric_version(unname(sf::sf_extSoftVersion()[\"GDAL\"]), strict=FALSE) (GDAL37 <- ifelse(is.na(GDAL37), FALSE, GDAL37 >= \"3.7.0\")) #> [1] TRUE file <- \"etc/shapes/bhicv.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) { bh <- st_read(zipfile) } else { td <- tempdir() bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE) target <- unzip(zipfile, files=bn, exdir=td) bh <- st_read(target) } #> Reading layer `bhicv' from data source #> `C:\\Users\\rzomor2\\AppData\\Local\\Temp\\RtmpErQTm3\\temp_libpath1a5cde63ff3\\spdep\\etc\\shapes\\bhicv.gpkg.zip' #> using driver `GPKG' #> Simple feature collection with 98 features and 8 fields #> Geometry type: POLYGON #> Dimension: XY #> Bounding box: xmin: -45.02175 ymin: -20.93007 xmax: -42.50321 ymax: -18.08342 #> Geodetic CRS: Corrego Alegre 1970-72 ### data padronized dpad <- data.frame(scale(as.data.frame(bh)[,5:8])) ### neighboorhod list bh.nb <- poly2nb(bh) ### calculing costs lcosts <- nbcosts(bh.nb, dpad) ### making listw nb.w <- nb2listw(bh.nb, lcosts, style=\"B\") ### find a minimum spanning tree system.time(mst.bh <- mstree(nb.w,5)) #> user system elapsed #> 0 0 0 dim(mst.bh) #> [1] 97 3 head(mst.bh) #> [,1] [,2] [,3] #> [1,] 5 12 1.2951120 #> [2,] 12 13 0.6141101 #> [3,] 13 11 0.7913745 #> [4,] 13 6 0.9775650 #> [5,] 11 31 0.9965625 #> [6,] 31 39 0.6915158 tail(mst.bh) #> [,1] [,2] [,3] #> [92,] 89 90 2.5743702 #> [93,] 26 56 2.6235317 #> [94,] 86 87 2.6471303 #> [95,] 87 72 0.7874461 #> [96,] 49 36 2.8743677 #> [97,] 24 25 3.4675168 ### the mstree plot par(mar=c(0,0,0,0)) plot(st_geometry(bh), border=gray(.5)) plot(mst.bh, st_coordinates(st_centroid(bh)), col=2, cex.lab=.6, cex.circles=0.035, fg=\"blue\", add=TRUE) #> Warning: st_centroid assumes attributes are constant over geometries"},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":null,"dir":"Reference","previous_headings":"","what":"Block up neighbour list for location-less observations — nb2blocknb","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"function blocks neighbour list known spatial locations create new neighbour list multiple location-less observations know belong spatial locations, using identification tags locations key.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"","code":"nb2blocknb(nb=NULL, ID, row.names = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"nb object class nb list integer vectors containing neighbour region number ids; null, nb object neighbours created length unique(.character(ID)) ID identification tags locations location-less observations; sort(unique(.character(ID))) must identical sort(.character(attr(nb, \"region.id\"))); length row.names provided. row.names character vector observation ids added neighbours list attribute region.id, default seq(1, nrow(x)); length ID provided.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"Assume list unique locations, neighbour list can build , create input neighbour list. needs \"unfolded\", observations belonging unique location observation neighbours, observations belonging location neighbours unique location question also observation neighbours, finally removing observation (neighbour). scenario also arises say post codes available, post codes contain multiple observations, known belong specific post code, located within (given post code locations known).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"function returns object class nb list integer vectors containing neighbour observation number ids.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nb2blocknb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Block up neighbour list for location-less observations — nb2blocknb","text":"","code":"if (FALSE) { # \\dontrun{ data(boston, package=\"spData\") summary(as.vector(table(boston.c$TOWN))) townaggr <- aggregate(boston.utm, list(town=boston.c$TOWN), mean) block.rel <- graph2nb(relativeneigh(as.matrix(townaggr[,2:3])), as.character(townaggr[,1]), sym=TRUE) block.rel print(is.symmetric.nb(block.rel)) plot(block.rel, as.matrix(townaggr[,2:3])) points(boston.utm, pch=18, col=\"lightgreen\") block.nb <- nb2blocknb(block.rel, as.character(boston.c$TOWN)) block.nb print(is.symmetric.nb(block.nb)) plot(block.nb, boston.utm) points(boston.utm, pch=18, col=\"lightgreen\") n.comp.nb(block.nb)$nc moran.test(boston.c$CMEDV, nb2listw(boston.soi)) moran.test(boston.c$CMEDV, nb2listw(block.nb)) block.nb <- nb2blocknb(NULL, as.character(boston.c$TOWN)) block.nb print(is.symmetric.nb(block.nb)) plot(block.nb, boston.utm) n.comp.nb(block.nb)$nc moran.test(boston.c$CMEDV, nb2listw(block.nb, zero.policy=TRUE), zero.policy=TRUE) } # }"},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":null,"dir":"Reference","previous_headings":"","what":"Output spatial neighbours for INLA — nb2INLA","title":"Output spatial neighbours for INLA — nb2INLA","text":"Output spatial neighbours INLA","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Output spatial neighbours for INLA — nb2INLA","text":"","code":"nb2INLA(file, nb)"},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Output spatial neighbours for INLA — nb2INLA","text":"file file adjacency matrix stored nb object class nb","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Output spatial neighbours for INLA — nb2INLA","text":"Nothing returned file created representation adjacency matrix required INLA spatial models.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Output spatial neighbours for INLA — nb2INLA","text":"http://www.r-inla.org","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Output spatial neighbours for INLA — nb2INLA","text":"Virgilio Gomez-Rubio","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2INLA.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Output spatial neighbours for INLA — nb2INLA","text":"","code":"col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) td <- tempdir() x <- nb2INLA(paste(td, \"columbus-INLA.adj\", sep=\"/\"), col.gal.nb) readLines(paste(td, \"columbus-INLA.adj\", sep=\"/\"), n=10) #> [1] \"49\" \"1 2 2 3\" #> [3] \"2 3 1 3 4\" \"3 4 1 2 4 5\" #> [5] \"4 4 2 3 5 8\" \"5 7 3 4 6 8 9 11 15\" #> [7] \"6 2 5 9\" \"7 4 8 12 13 14\" #> [9] \"8 6 4 5 7 11 12 13\" \"9 8 5 6 10 15 20 22 25 26\""},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":null,"dir":"Reference","previous_headings":"","what":"Use vector files for import and export of weights — nb2lines","title":"Use vector files for import and export of weights — nb2lines","text":"Use vector files import export weights, storing spatial entity coordinates arcs, entity indices data frame.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Use vector files for import and export of weights — nb2lines","text":"","code":"nb2lines(nb, wts, coords, proj4string=NULL, as_sf=FALSE) listw2lines(listw, coords, proj4string=NULL, as_sf=FALSE) df2sn(df, i=\"i\", i_ID=\"i_ID\", j=\"j\", wt=\"wt\")"},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Use vector files for import and export of weights — nb2lines","text":"nb neighbour object class nb wts list general weights corresponding neighbours coords matrix region point coordinates, Spatial object (points polygons), sfc object (points polygons) proj4string default NULL; coords Spatial sf object, value used, otherwise value converted appropriately as_sf output object Spatial sf format, default FALSE, set TRUE coords sfc object FALSE Spatial object listw listw object spatial weights df data frame read shapefile, derived output nb2lines character name column df entity index i_ID character name column df entity region ID j character name column df entity index wt character name column df weights","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Use vector files for import and export of weights — nb2lines","text":"neighbour weights objects may retrieved converting specified columns data slot SpatialLinesDataFrame object spatial.neighbour object, converted weights list object.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Use vector files for import and export of weights — nb2lines","text":"nb2lines listw2lines return SpatialLinesDataFrame object sf object; data frame contains indices neighbour links weights. df2sn converts data retrieved reading data df back spatial.neighbour object.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Use vector files for import and export of weights — nb2lines","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Use vector files for import and export of weights — nb2lines","text":"Original idea due Gidske Leknes Andersen, Department Biology, University Bergen, Norway","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nb2lines.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Use vector files for import and export of weights — nb2lines","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) res <- listw2lines(nb2listw(col.gal.nb), st_geometry(columbus)) summary(res) #> i j i_ID j_ID #> Min. : 1.00 Min. : 1.00 Length:230 Length:230 #> 1st Qu.:13.00 1st Qu.:13.00 Class :character Class :character #> Median :24.00 Median :24.00 Mode :character Mode :character #> Mean :24.19 Mean :24.19 #> 3rd Qu.:35.00 3rd Qu.:35.00 #> Max. :49.00 Max. :49.00 #> wt geometry #> Min. :0.1000 LINESTRING:230 #> 1st Qu.:0.1429 epsg:NA : 0 #> Median :0.1667 #> Mean :0.2130 #> 3rd Qu.:0.2500 #> Max. :0.5000 tf <- paste0(tempfile(), \".gpkg\") st_write(res, dsn=tf, driver=\"GPKG\") #> Writing layer `file32024c0802' to data source #> `C:\\Users\\rzomor2\\AppData\\Local\\Temp\\RtmpqWMtxS\\file32024c0802.gpkg' using driver `GPKG' #> Writing 230 features with 5 fields and geometry type Line String. inMap <- st_read(tf) #> Reading layer `file32024c0802' from data source #> `C:\\Users\\rzomor2\\AppData\\Local\\Temp\\RtmpqWMtxS\\file32024c0802.gpkg' #> using driver `GPKG' #> Simple feature collection with 230 features and 5 fields #> Geometry type: LINESTRING #> Dimension: XY #> Bounding box: xmin: 6.165913 ymin: 11.04088 xmax: 10.96206 ymax: 14.43766 #> Projected CRS: Undefined Cartesian SRS with unknown unit summary(inMap) #> i j i_ID j_ID #> Min. : 1.00 Min. : 1.00 Length:230 Length:230 #> 1st Qu.:13.00 1st Qu.:13.00 Class :character Class :character #> Median :24.00 Median :24.00 Mode :character Mode :character #> Mean :24.19 Mean :24.19 #> 3rd Qu.:35.00 3rd Qu.:35.00 #> Max. :49.00 Max. :49.00 #> wt geom #> Min. :0.1000 LINESTRING:230 #> 1st Qu.:0.1429 epsg:NA : 0 #> Median :0.1667 #> Mean :0.2130 #> 3rd Qu.:0.2500 #> Max. :0.5000 diffnb(sn2listw(df2sn(as.data.frame(inMap)))$neighbours, col.gal.nb) #> Warning: style is M (missing); style should be set to a valid value #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 0 #> Percentage nonzero weights: 0 #> Average number of links: 0 #> 49 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 #> 49 disjoint connected subgraphs res1 <- listw2lines(nb2listw(col.gal.nb), as(columbus, \"Spatial\")) summary(res1) #> Object of class SpatialLinesDataFrame #> Coordinates: #> min max #> x 6.221943 10.95359 #> y 11.010031 14.36908 #> Is projected: TRUE #> proj4string : [NA] #> Data attributes: #> i j i_ID j_ID #> Min. : 1.00 Min. : 1.00 Length:230 Length:230 #> 1st Qu.:13.00 1st Qu.:13.00 Class :character Class :character #> Median :24.00 Median :24.00 Mode :character Mode :character #> Mean :24.19 Mean :24.19 #> 3rd Qu.:35.00 3rd Qu.:35.00 #> Max. :49.00 Max. :49.00 #> wt #> Min. :0.1000 #> 1st Qu.:0.1429 #> Median :0.1667 #> Mean :0.2130 #> 3rd Qu.:0.2500 #> Max. :0.5000"},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial weights for neighbours lists — nb2listw","title":"Spatial weights for neighbours lists — nb2listw","text":"nb2listw function supplements neighbours list spatial weights chosen coding scheme. can..simmed helper function checks whether spatial weights object similar symmetric can transformed yield real eigenvalues Cholesky decomposition. helper function listw2U() constructs weights list object corresponding sparse matrix \\(\\frac{1}{2} ( \\mathbf{W} + \\mathbf{W}'\\).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial weights for neighbours lists — nb2listw","text":"","code":"nb2listw(neighbours, glist=NULL, style=\"W\", zero.policy=NULL) listw2U(listw)"},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial weights for neighbours lists — nb2listw","text":"neighbours object class nb glist list general weights corresponding neighbours style style can take values “W”, “B”, “C”, “U”, “minmax” “S” zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors listw listw object created example nb2listw","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Spatial weights for neighbours lists — nb2listw","text":"Starting binary neighbours list, regions either listed neighbours absent (thus set neighbours definition), function adds weights list values given coding scheme style chosen. B basic binary coding, W row standardised (sums links n), C globally standardised (sums links n), U equal C divided number neighbours (sums links unity), S variance-stabilizing coding scheme proposed Tiefelsdorf et al. 1999, p. 167-168 (sums links n). zero policy set TRUE, weights vectors zero length inserted regions without neighbour neighbours list. turn generate lag values zero, equivalent sum products zero row t(rep(0, length=length(neighbours))) %*% x, arbitraty numerical vector x length length(neighbours). spatially lagged value x zero-neighbour region zero, may (may ) sensible choice. sum glist vector one observations zero, warning message issued. consequence later operations -neighbour observations present zero.policy argument set true. “minmax” style based Kelejian Prucha (2010), divides weights minimum maximum row sums maximum column sums input weights. similar C U styles; also available Stata.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial weights for neighbours lists — nb2listw","text":"listw object following members: style one W, B, C, U, S, minmax neighbours input neighbours list weights weights neighbours chosen style, attributes set report type relationships (binary general, general form glist argument), style attributes: region.id character, neighbour object call function call zero.policy logical; value zero.policy object created","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Spatial weights for neighbours lists — nb2listw","text":"Tiefelsdorf, M., Griffith, D. ., Boots, B. 1999 variance-stabilizing coding scheme spatial link matrices, Environment Planning , 31, pp. 165–180; Kelejian, H. H., . R. Prucha. 2010. Specification estimation spatial autoregressive models autoregressive heteroskedastic disturbances. Journal Econometrics, 157: pp. 53–67.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial weights for neighbours lists — nb2listw","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nb2listw.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial weights for neighbours lists — nb2listw","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries cards <- card(col.gal.nb) col.w <- nb2listw(col.gal.nb) plot(cards, unlist(lapply(col.w$weights, sum)),xlim=c(0,10), ylim=c(0,10), xlab=\"number of links\", ylab=\"row sums of weights\") col.b <- nb2listw(col.gal.nb, style=\"B\") points(cards, unlist(lapply(col.b$weights, sum)), col=\"red\") col.c <- nb2listw(col.gal.nb, style=\"C\") points(cards, unlist(lapply(col.c$weights, sum)), col=\"green\") col.u <- nb2listw(col.gal.nb, style=\"U\") points(cards, unlist(lapply(col.u$weights, sum)), col=\"orange\") col.s <- nb2listw(col.gal.nb, style=\"S\") points(cards, unlist(lapply(col.s$weights, sum)), col=\"blue\") legend(x=c(0, 1), y=c(7, 9), legend=c(\"W\", \"B\", \"C\", \"U\", \"S\"), bty=\"n\", col=c(\"black\", \"red\", \"green\", \"orange\", \"blue\"), pch=rep(1,5), cex=0.8, y.intersp=2.5) summary(nb2listw(col.gal.nb, style=\"minmax\")) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> Link number distribution: #> #> 2 3 4 5 6 7 8 9 10 #> 7 7 13 4 9 6 1 1 1 #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links #> #> Weights style: minmax #> Weights constants summary: #> n nn S0 S1 S2 #> minmax 49 2401 23 4.6 50.48 dlist <- nbdists(col.gal.nb, coords) dlist <- lapply(dlist, function(x) 1/x) col.w.d <- nb2listw(col.gal.nb, glist=dlist) summary(unlist(col.w$weights)) #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> 0.1000 0.1429 0.1667 0.2130 0.2500 0.5000 summary(unlist(col.w.d$weights)) #> Min. 1st Qu. Median Mean 3rd Qu. Max. #> 0.06977 0.13114 0.17710 0.21304 0.27124 0.67178 # introducing other conditions into weights - only earlier sales count # see http://sal.uiuc.edu/pipermail/openspace/2005-October/000610.html data(baltimore, package=\"spData\") set.seed(211) dates <- sample(1:500, nrow(baltimore), replace=TRUE) nb_15nn <- knn2nb(knearneigh(cbind(baltimore$X, baltimore$Y), k=15)) glist <- vector(mode=\"list\", length=length(nb_15nn)) for (i in seq(along=nb_15nn)) glist[[i]] <- ifelse(dates[i] > dates[nb_15nn[[i]]], 1, 0) listw_15nn_dates <- nb2listw(nb_15nn, glist=glist, style=\"B\") #> Warning: zero sum general weights which(lag(listw_15nn_dates, baltimore$PRICE) == 0.0) #> [1] 1 22 29 35 66 80 99 117 147 155 169 195 197 200 which(sapply(glist, sum) == 0) #> [1] 1 22 29 35 66 80 99 117 147 155 169 195 197 200 ex <- which(sapply(glist, sum) == 0)[1] dates[ex] #> [1] 28 dates[nb_15nn[[ex]]] #> [1] 395 247 275 179 142 484 111 239 369 199 294 251 448 390 229"},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":null,"dir":"Reference","previous_headings":"","what":"Distance-based spatial weights for neighbours lists — nb2listwdist","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"nb2listwdist function supplements neighbours list spatial weights chosen types distance modelling coding scheme. offered coding schemes parallel nb2listw function, three distance-based types weights available: inverse distance weighting (IDW), double-power distance weights, exponential distance decay. can..simmed helper function checks whether spatial weights object similar symmetric can transformed yield real eigenvalues Cholesky decomposition.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"","code":"nb2listwdist(neighbours, x, type=\"idw\", style=\"raw\", alpha = 1, dmax = NULL, longlat = NULL, zero.policy=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"neighbours object class nb x sp sf, sfc object type default “idw”; intended type distance modelling, can take values “idw”, “exp”, “dpd” style default “raw”; style can take values “raw”, “W”, “B”, “C”, “U”, “minmax”, “S” alpha default 0; parameter controlling distance modelling, see “Details” dmax default NULL, maximum distance threshold required type “dpd” optional types longlat default NULL; TRUE point coordinates longitude-latitude decimal degrees, case distances measured metres; x SpatialPoints object, value taken object , overrides argument NULL; distances measured map units FALSE NULL zero.policy default NULL; use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"Starting binary neighbours list, regions either listed neighbours absent (thus set neighbours definition), function adds distance-based weights list. Three types distance weight calculations based pairwise distances \\(d_{ij}\\) possible, controlled parameter “alpha” (\\(\\alpha\\) ): $$\\textrm{idw: } w_{ij} = d_{ij}^{-\\alpha},$$ $$\\textrm{exp: } w_{ij} = \\exp(-\\alpha \\cdot d_{ij}),$$ $$\\textrm{dpd: } w_{ij} = \\left[1 - \\left(d_{ij}/d_{\\textrm{max}}\\right)^{\\alpha}\\right]^{\\alpha},$$ latter leads \\(w_{ij} = 0\\) \\(d_{ij} > d_{\\textrm{max}}\\). Note IDW weights show extreme behaviour close 0 can take value infinity. cases, infinite values replaced largest finite weight present weights list. default coding scheme “raw”, outputs raw distance-based weights without applying kind normalisation. addition, coding scheme styles also available nb2listw function can chosen. B basic binary coding, W row standardised (sums links n), C globally standardised (sums links n), U equal C divided number neighbours (sums links unity), S variance-stabilising coding scheme proposed Tiefelsdorf et al. 1999, p. 167-168 (sums links n). “minmax” style based Kelejian Prucha (2010), divides weights minimum maximum row sums maximum column sums input weights. similar C U styles; also available Stata. zero.policy set TRUE, weights vectors zero length inserted regions without neighbour neighbours list. turn generate lag values zero, equivalent sum products zero row t(rep(0, length=length(neighbours))) %*% x, arbitraty numerical vector x length length(neighbours). spatially lagged value x zero-neighbour region zero, may (may ) sensible choice.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"listw object following members: style one W, B, C, U, S, minmax type one idw, exp, dpd neighbours input neighbours list weights weights neighbours chosen style, attributes set report type relationships (binary general, general form glist argument), style ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"Tiefelsdorf, M., Griffith, D. ., Boots, B. 1999 variance-stabilizing coding scheme spatial link matrices, Environment Planning , 31, pp. 165–180; Kelejian, H. H., . R. Prucha. 2010. Specification estimation spatial autoregressive models autoregressive heteroskedastic disturbances. Journal Econometrics, 157: pp. 53–67.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"Rene Westerholt rene.westerholt@tu-dortmund.de","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nb2listwdist.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Distance-based spatial weights for neighbours lists — nb2listwdist","text":"","code":"# World examples data(world, package=\"spData\") # neighbours on distance interval [0, 1000] kilometres # suppressWarnings(st_crs(world) <- \"+proj=longlat\") # for older PROJ pts <- st_centroid(st_transform(world, 3857)) #> Warning: st_centroid assumes attributes are constant over geometries nb_world <- dnearneigh(pts, 0, 1000000) #> Warning: neighbour object has 46 sub-graphs # Moran's I (life expectancy) with IDW with alpha = 2, no coding scheme world_weights <- nb2listwdist(nb_world, as(pts, \"Spatial\"), type = \"idw\", alpha = 2, zero.policy = TRUE) moran.test(world$lifeExp, world_weights, zero.policy = TRUE, na.action = na.pass) #> Warning: NAs in lagged values #> #> \tMoran I test under randomisation #> #> data: world$lifeExp #> weights: world_weights #> n reduced by no-neighbour observations #> #> Moran I statistic standard deviate = 2.7769, p-value = 0.002744 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.473883371 -0.007042254 0.029994057 #> if (FALSE) { # \\dontrun{ # Moran's I (life expectancy) with IDW with alpha = 2, no coding scheme world_weights <- nb2listwdist(nb_world, pts, type = \"idw\", alpha = 2, zero.policy = TRUE) moran.test(world$lifeExp, world_weights, zero.policy = TRUE, na.action = na.pass) # Moran's I (life expectancy), DPD, alpha = 2, dmax = 1000 km, no coding scheme world_weights <- nb2listwdist(nb_world, pts, type = \"dpd\", dmax = 1000000, alpha = 2, zero.policy = TRUE) moran.test(world$lifeExp, world_weights, zero.policy = TRUE, na.action = na.pass) # Boston examples data(boston, package=\"spData\") boston_coords <- data.frame(x = boston.utm[,1], y = boston.utm[,2]) boston.geoms <- st_as_sf(boston_coords, coords = c(\"x\", \"y\"), remove = FALSE) nb_boston <- dnearneigh(boston.geoms, 0, 3) # Moran's I (crime) with exp weights with alpha = 2, no coding scheme boston_weights <- nb2listwdist(nb_boston, boston.geoms, type = \"exp\", alpha = 2, style=\"raw\", zero.policy = TRUE) moran.test(boston.c$CRIM, boston_weights, zero.policy = TRUE, na.action = na.pass) # Moran's I (crime) with idw weights with alpha = 2, coding scheme = W boston_weights <- nb2listwdist(nb_boston, boston.geoms, type = \"idw\", alpha = 2, style=\"W\", zero.policy = TRUE) moran.test(boston.c$CRIM, boston_weights, zero.policy = TRUE, na.action = na.pass) } # }"},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial weights matrices for neighbours lists — nb2mat","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"function generates weights matrix neighbours list spatial weights chosen coding scheme.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"","code":"nb2mat(neighbours, glist=NULL, style=\"W\", zero.policy=NULL) listw2mat(listw)"},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"neighbours object class nb glist list general weights corresponding neighbours style style can take values W, B, C, S zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors listw listw object example nb2listw","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"Starting binary neighbours list, regions either listed neighbours absent (thus set neighbours definition), function creates n n weights matrix values given coding scheme style chosen. B basic binary coding, W row standardised, C globally standardised, S variance-stabilizing coding scheme proposed Tiefelsdorf et al. 1999, p. 167-168. function leaves matrix rows zero regions zero neighbours fore zero.policy TRUE. turn generate lag values zero, equivalent sum products zero row t(rep(0, length=length(neighbours))) %*% x, arbitraty numerical vector x length length(neighbours). spatially lagged value x zero-neighbour region zero, may (may ) sensible choice.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"n n matrix, n=length(neighbours)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"Tiefelsdorf, M., Griffith, D. ., Boots, B. 1999 variance-stabilizing coding scheme spatial link matrices, Environment Planning , 31, pp. 165-180.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nb2mat.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial weights matrices for neighbours lists — nb2mat","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col005 <- dnearneigh(st_coordinates(st_centroid(st_geometry(columbus), of_largest_polygon=TRUE)), 0, 0.5, as.character(columbus$NEIGNO)) #> Warning: neighbour object has 8 sub-graphs summary(col005) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 170 #> Percentage nonzero weights: 7.080383 #> Average number of links: 3.469388 #> 4 regions with no links: #> 1005, 1006, 1008, 1043 #> 8 disjoint connected subgraphs #> Link number distribution: #> #> 0 1 2 3 4 5 6 7 8 9 #> 4 11 5 8 3 9 2 2 3 2 #> 11 least connected regions: #> 1001 1007 1018 1010 1045 1044 1046 1047 1049 1048 1015 with 1 link #> 2 most connected regions: #> 1038 1036 with 9 links col005.w.mat <- nb2mat(col005, style=\"B\", zero.policy=TRUE) table(round(rowSums(col005.w.mat))) #> #> 0 1 2 3 4 5 6 7 8 9 #> 4 11 5 8 3 9 2 2 3 2"},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":null,"dir":"Reference","previous_headings":"","what":"Output spatial weights for WinBUGS — nb2WB","title":"Output spatial weights for WinBUGS — nb2WB","text":"Output spatial weights WinBUGS","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Output spatial weights for WinBUGS — nb2WB","text":"","code":"nb2WB(nb) listw2WB(listw)"},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Output spatial weights for WinBUGS — nb2WB","text":"nb object class nb listw listw object example nb2listw","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Output spatial weights for WinBUGS — nb2WB","text":"list suitable convering using dput WinBUGS","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Output spatial weights for WinBUGS — nb2WB","text":"http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/geobugs12manual.pdf","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Output spatial weights for WinBUGS — nb2WB","text":"Virgilio Gomez-Rubio","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nb2WB.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Output spatial weights for WinBUGS — nb2WB","text":"","code":"col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) x <- nb2WB(col.gal.nb) dput(x, control=NULL) #> list(c(2, 3, 1, 3, 4, 1, 2, 4, 5, 2, 3, 5, 8, 3, 4, 6, 8, 9, #> 11, 15, 5, 9, 8, 12, 13, 14, 4, 5, 7, 11, 12, 13, 5, 6, 10, 15, #> 20, 22, 25, 26, 9, 17, 20, 22, 5, 8, 12, 15, 16, 7, 8, 11, 13, #> 14, 16, 7, 8, 12, 14, 7, 12, 13, 16, 18, 19, 5, 9, 11, 16, 25, #> 26, 11, 12, 14, 15, 18, 24, 25, 10, 20, 23, 14, 16, 19, 24, 14, #> 18, 24, 9, 10, 17, 22, 23, 27, 32, 33, 35, 40, 24, 30, 34, 9, #> 10, 20, 26, 27, 28, 17, 20, 32, 16, 18, 19, 21, 25, 29, 30, 9, #> 15, 16, 24, 26, 28, 29, 9, 15, 22, 25, 28, 29, 20, 22, 28, 33, #> 22, 25, 26, 27, 29, 33, 35, 37, 38, 24, 25, 26, 28, 30, 37, 38, #> 21, 24, 29, 37, 34, 36, 20, 23, 40, 41, 20, 27, 28, 35, 21, 31, #> 36, 42, 20, 28, 33, 38, 40, 43, 44, 31, 34, 39, 42, 46, 28, 29, #> 30, 38, 43, 45, 28, 29, 35, 37, 43, 44, 36, 46, 20, 32, 35, 41, #> 47, 32, 40, 47, 34, 36, 35, 37, 38, 44, 45, 48, 35, 38, 43, 48, #> 49, 37, 43, 48, 49, 36, 39, 40, 41, 43, 44, 45, 49, 44, 45, 48 #> ), c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, #> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, #> 1), c(2, 3, 4, 4, 7, 2, 4, 6, 8, 4, 5, 6, 4, 6, 6, 7, 3, 4, 3, #> 10, 3, 6, 3, 7, 7, 6, 4, 9, 7, 4, 2, 4, 4, 4, 7, 5, 6, 6, 2, #> 5, 3, 2, 6, 5, 4, 2, 2, 4, 3)) x <- listw2WB(nb2listw(col.gal.nb)) dput(x, control=NULL) #> list(c(2, 3, 1, 3, 4, 1, 2, 4, 5, 2, 3, 5, 8, 3, 4, 6, 8, 9, #> 11, 15, 5, 9, 8, 12, 13, 14, 4, 5, 7, 11, 12, 13, 5, 6, 10, 15, #> 20, 22, 25, 26, 9, 17, 20, 22, 5, 8, 12, 15, 16, 7, 8, 11, 13, #> 14, 16, 7, 8, 12, 14, 7, 12, 13, 16, 18, 19, 5, 9, 11, 16, 25, #> 26, 11, 12, 14, 15, 18, 24, 25, 10, 20, 23, 14, 16, 19, 24, 14, #> 18, 24, 9, 10, 17, 22, 23, 27, 32, 33, 35, 40, 24, 30, 34, 9, #> 10, 20, 26, 27, 28, 17, 20, 32, 16, 18, 19, 21, 25, 29, 30, 9, #> 15, 16, 24, 26, 28, 29, 9, 15, 22, 25, 28, 29, 20, 22, 28, 33, #> 22, 25, 26, 27, 29, 33, 35, 37, 38, 24, 25, 26, 28, 30, 37, 38, #> 21, 24, 29, 37, 34, 36, 20, 23, 40, 41, 20, 27, 28, 35, 21, 31, #> 36, 42, 20, 28, 33, 38, 40, 43, 44, 31, 34, 39, 42, 46, 28, 29, #> 30, 38, 43, 45, 28, 29, 35, 37, 43, 44, 36, 46, 20, 32, 35, 41, #> 47, 32, 40, 47, 34, 36, 35, 37, 38, 44, 45, 48, 35, 38, 43, 48, #> 49, 37, 43, 48, 49, 36, 39, 40, 41, 43, 44, 45, 49, 44, 45, 48 #> ), c(0.5, 0.5, 0.333333333333333, 0.333333333333333, 0.333333333333333, #> 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.142857142857143, #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.142857142857143, #> 0.142857142857143, 0.142857142857143, 0.5, 0.5, 0.25, 0.25, 0.25, #> 0.25, 0.166666666666667, 0.166666666666667, 0.166666666666667, #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.125, #> 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.25, 0.25, #> 0.25, 0.25, 0.2, 0.2, 0.2, 0.2, 0.2, 0.166666666666667, 0.166666666666667, #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667, #> 0.25, 0.25, 0.25, 0.25, 0.166666666666667, 0.166666666666667, #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667, #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667, #> 0.166666666666667, 0.166666666666667, 0.142857142857143, 0.142857142857143, #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.142857142857143, #> 0.142857142857143, 0.333333333333333, 0.333333333333333, 0.333333333333333, #> 0.25, 0.25, 0.25, 0.25, 0.333333333333333, 0.333333333333333, #> 0.333333333333333, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, #> 0.1, 0.333333333333333, 0.333333333333333, 0.333333333333333, #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667, #> 0.166666666666667, 0.166666666666667, 0.333333333333333, 0.333333333333333, #> 0.333333333333333, 0.142857142857143, 0.142857142857143, 0.142857142857143, #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.142857142857143, #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.142857142857143, #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.166666666666667, #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667, #> 0.166666666666667, 0.25, 0.25, 0.25, 0.25, 0.111111111111111, #> 0.111111111111111, 0.111111111111111, 0.111111111111111, 0.111111111111111, #> 0.111111111111111, 0.111111111111111, 0.111111111111111, 0.111111111111111, #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.142857142857143, #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.25, #> 0.25, 0.25, 0.25, 0.5, 0.5, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, #> 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.142857142857143, 0.142857142857143, #> 0.142857142857143, 0.142857142857143, 0.142857142857143, 0.142857142857143, #> 0.142857142857143, 0.2, 0.2, 0.2, 0.2, 0.2, 0.166666666666667, #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667, #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667, #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.5, #> 0.5, 0.2, 0.2, 0.2, 0.2, 0.2, 0.333333333333333, 0.333333333333333, #> 0.333333333333333, 0.5, 0.5, 0.166666666666667, 0.166666666666667, #> 0.166666666666667, 0.166666666666667, 0.166666666666667, 0.166666666666667, #> 0.2, 0.2, 0.2, 0.2, 0.2, 0.25, 0.25, 0.25, 0.25, 0.5, 0.5, 0.5, #> 0.5, 0.25, 0.25, 0.25, 0.25, 0.333333333333333, 0.333333333333333, #> 0.333333333333333), c(2, 3, 4, 4, 7, 2, 4, 6, 8, 4, 5, 6, 4, #> 6, 6, 7, 3, 4, 3, 10, 3, 6, 3, 7, 7, 6, 4, 9, 7, 4, 2, 4, 4, #> 4, 7, 5, 6, 6, 2, 5, 3, 2, 6, 5, 4, 2, 2, 4, 3))"},{"path":"https://r-spatial.github.io/spdep/reference/nbcosts.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute cost of edges — nbcosts","title":"Compute cost of edges — nbcosts","text":"cost edge distance nodes. function compute distance using data.frame observations vector node.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbcosts.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute cost of edges — nbcosts","text":"","code":"nbcost(data, id, id.neigh, method = c(\"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\", \"minkowski\", \"mahalanobis\"), p = 2, cov, inverted = FALSE) nbcosts(nb, data, method = c(\"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\", \"minkowski\", \"mahalanobis\"), p = 2, cov, inverted = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/nbcosts.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute cost of edges — nbcosts","text":"nb object nb class. See poly2nb details. data matrix observations nodes. id Node index compute cost id.neigh Idex neighbours nodes node id method Character function declare distance method. method character, method must \"mahalanobis\" \"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\" \"minkowisk\". method one \"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\" \"minkowisk\", see dist details, function used compute distance. method=\"mahalanobis\", mahalanobis distance computed neighbour areas. method function, function used compute distance. p power Minkowski distance. cov covariance matrix used compute mahalanobis distance. inverted logical. 'TRUE', 'cov' supposed contain inverse covariance matrix.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbcosts.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute cost of edges — nbcosts","text":"object nbdist class. See nbdists details.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbcosts.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Compute cost of edges — nbcosts","text":"neighbours must connected graph.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbcosts.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute cost of edges — nbcosts","text":"Elias T. Krainski Renato M. Assuncao","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nbdists.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial link distance measures — nbdists","title":"Spatial link distance measures — nbdists","text":"Given list spatial neighbour links (neighbours list object type nb), function returns Euclidean distances along links list form neighbours list. longlat = TRUE, Great Circle distances used.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbdists.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial link distance measures — nbdists","text":"","code":"nbdists(nb, coords, longlat = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/nbdists.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial link distance measures — nbdists","text":"nb object class nb coords matrix point coordinates, object inheriting SpatialPoints \"sf\" \"sfc\" object; \"sf\" \"sfc\" object geometries geographical coordinates (sf::st_is_longlat(x) == TRUE sf::sf_use_s2() == TRUE), s2 used find distances https://github.com/r-spatial/s2/issues/125 longlat TRUE point coordinates longitude-latitude decimal degrees, case distances measured kilometers; coords SpatialPoints object, value taken object ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbdists.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial link distance measures — nbdists","text":"list class nbdist","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nbdists.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial link distance measures — nbdists","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nbdists.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial link distance measures — nbdists","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries dlist <- nbdists(col.gal.nb, coords) dlist <- lapply(dlist, function(x) 1/x) stem(unlist(dlist)) #> #> The decimal point is at the | #> #> 1 | 1111112222223333334444444444 #> 1 | 555555556666667777777777888888888899999999999999999999 #> 2 | 00000000111111111111111122222222222222333333333333334444 #> 2 | 55555555556666666666666677777777888888999999 #> 3 | 0000111111222233334444 #> 3 | 77779999 #> 4 | 223344 #> 4 | 77 #> 5 | 001144 #> 5 | #> 6 | #> 6 | 99 #> 7 | #> 7 | 88 #>"},{"path":"https://r-spatial.github.io/spdep/reference/nblag.html","id":null,"dir":"Reference","previous_headings":"","what":"Higher order neighbours lists — nblag","title":"Higher order neighbours lists — nblag","text":"function creates higher order neighbour lists, higher order neighbours lags links graph described input neighbours list. refuse lag neighbours lists attribute self.included set TRUE. nblag_cumul cumulates neighbour lists single neighbour list (“nb” object).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nblag.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Higher order neighbours lists — nblag","text":"","code":"nblag(neighbours, maxlag) nblag_cumul(nblags)"},{"path":"https://r-spatial.github.io/spdep/reference/nblag.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Higher order neighbours lists — nblag","text":"neighbours input neighbours list class nb maxlag maximum lag constructed nblags list neighbour lists output nblag","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nblag.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Higher order neighbours lists — nblag","text":"returns list lagged neighbours lists class nb","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nblag.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Higher order neighbours lists — nblag","text":"Roger Bivand Roger.Bivand@nhh.Giovanni Millo","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nblag.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Higher order neighbours lists — nblag","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries summary(col.gal.nb, coords) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> Link number distribution: #> #> 2 3 4 5 6 7 8 9 10 #> 7 7 13 4 9 6 1 1 1 #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links col.lags <- nblag(col.gal.nb, 2) print(col.lags) #> [[1]] #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> #> [[2]] #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 406 #> Percentage nonzero weights: 16.90962 #> Average number of links: 8.285714 #> #> attr(,\"call\") #> nblag(neighbours = col.gal.nb, maxlag = 2) summary(col.lags[[2]], coords) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 406 #> Percentage nonzero weights: 16.90962 #> Average number of links: 8.285714 #> Link number distribution: #> #> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 #> 1 2 5 4 2 3 5 4 2 3 7 3 4 1 1 1 1 #> 1 least connected region: #> 36 with 1 link #> 1 most connected region: #> 25 with 17 links plot(st_geometry(columbus), border=\"grey\") plot(col.gal.nb, coords, add=TRUE) title(main=\"GAL order 1 (black) and 2 (red) links\") plot(col.lags[[2]], coords, add=TRUE, col=\"red\", lty=2) cuml <- nblag_cumul(col.lags) cuml #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 636 #> Percentage nonzero weights: 26.48896 #> Average number of links: 12.97959 run <- FALSE if (require(igraph, quietly=TRUE) && require(spatialreg, quietly=TRUE)) run <- TRUE if (run) { W <- as(nb2listw(col.gal.nb), \"CsparseMatrix\") G <- graph_from_adjacency_matrix(W, mode=\"directed\", weight=\"W\") D <- diameter(G) nbs <- nblag(col.gal.nb, maxlag=D) n <- length(col.gal.nb) lmat <- lapply(nbs, nb2mat, style=\"B\", zero.policy=TRUE) mat <- matrix(0, n, n) for (i in seq(along=lmat)) mat = mat + i*lmat[[i]] G2 <- distances(G) print(all.equal(G2, mat, check.attributes=FALSE)) }"},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":null,"dir":"Reference","previous_headings":"","what":"Set operations on neighborhood objects — nb.set.operations","title":"Set operations on neighborhood objects — nb.set.operations","text":"Performs set operations neighbors list objects union, intersection, (asymmetric!) difference complement; note 1.3-9, setdiff.nb behaves like setdiff, ordering objects compared matters - (asymmetric!) difference.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Set operations on neighborhood objects — nb.set.operations","text":"","code":"intersect.nb(nb.obj1,nb.obj2) union.nb(nb.obj1,nb.obj2) setdiff.nb(nb.obj1,nb.obj2) complement.nb(nb.obj)"},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Set operations on neighborhood objects — nb.set.operations","text":"nb.obj neighbor list created neighborhood list funtions nb.obj1 neighbor list created neighborhood list funtions nb.obj2 neighbor list created neighborhood list funtions","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Set operations on neighborhood objects — nb.set.operations","text":"functions perform set operations element neighborlist. arguments must neighbor lists created spatial objects, checked region.id attributes required identical.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Set operations on neighborhood objects — nb.set.operations","text":"new neighborlist created set operations input neighbor list(s)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Set operations on neighborhood objects — nb.set.operations","text":"Nicholas Lewin-Koh nikko@hailmail.net","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/nboperations.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Set operations on neighborhood objects — nb.set.operations","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries col.tri.nb <- tri2nb(coords) oldpar <- par(mfrow=c(1,2)) if (require(\"dbscan\", quietly=TRUE)) { col.soi.nb <- graph2nb(soi.graph(col.tri.nb, coords)) plot(st_geometry(columbus), border=\"grey\") plot(col.soi.nb, coords, add=TRUE) title(main=\"Sphere of Influence Graph\", cex.main=0.7) plot(st_geometry(columbus), border=\"grey\") plot(complement.nb(col.soi.nb), coords, add=TRUE) title(main=\"Complement of Sphere of Influence Graph\", cex.main=0.7) } par(mfrow=c(2,2)) col2 <- droplinks(col.gal.nb, 21) #> Warning: some observations have no neighbours #> Warning: neighbour object has 3 sub-graphs plot(intersect.nb(col.gal.nb, col2), coords) #> Warning: neighbour object has 3 sub-graphs title(main=\"Intersect\", cex.main=0.7) plot(union.nb(col.gal.nb, col2), coords) title(main=\"Union\", cex.main=0.7) plot(setdiff.nb(col.gal.nb, col2), coords) #> Warning: neighbour object has 46 sub-graphs title(main=\"Set diff\", cex.main=0.7) par(oldpar)"},{"path":"https://r-spatial.github.io/spdep/reference/p.adjustSP.html","id":null,"dir":"Reference","previous_headings":"","what":"Adjust local association measures' p-values — p.adjustSP","title":"Adjust local association measures' p-values — p.adjustSP","text":"Make adjustment local association measures' p-values based number neighbours (+1) region, rather total number regions.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/p.adjustSP.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Adjust local association measures' p-values — p.adjustSP","text":"","code":"p.adjustSP(p, nb, method = \"none\")"},{"path":"https://r-spatial.github.io/spdep/reference/p.adjustSP.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Adjust local association measures' p-values — p.adjustSP","text":"p vector p-values nb list neighbours class nb method correction method defined p.adjust: \"adjustment methods include Bonferroni correction ('\"bonferroni\"') p-values multiplied number comparisons. Four less conservative corrections also included Holm (1979) ('holm'), Hochberg (1988) ('hochberg'), Hommel (1988) ('hommel') Benjamini & Hochberg (1995) ('fdr'), respectively. pass-option ('none') also included.\"","code":""},{"path":"https://r-spatial.github.io/spdep/reference/p.adjustSP.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Adjust local association measures' p-values — p.adjustSP","text":"vector corrected p-values using number neighbours + 1.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/p.adjustSP.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Adjust local association measures' p-values — p.adjustSP","text":"Danlin Yu Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/p.adjustSP.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Adjust local association measures' p-values — p.adjustSP","text":"","code":"data(afcon, package=\"spData\") oid <- order(afcon$id) resG <- as.vector(localG(afcon$totcon, nb2listw(include.self(paper.nb)))) non <- format.pval(pnorm(2*(abs(resG)), lower.tail=FALSE), 2) bon <- format.pval(p.adjustSP(pnorm(2*(abs(resG)), lower.tail=FALSE), paper.nb, \"bonferroni\"), 2) tot <- format.pval(p.adjust(pnorm(2*(abs(resG)), lower.tail=FALSE), \"bonferroni\", n=length(resG)), 2) data.frame(resG, non, bon, tot, row.names=afcon$name)[oid,] #> resG non bon tot #> THE GAMBIA -0.98383592 0.02455 0.04911 1.0000 #> MALI -1.69893391 0.00034 0.00272 0.0143 #> SENEGAL -1.46321911 0.00171 0.00857 0.0720 #> BENIN -1.30139679 0.00462 0.02312 0.1942 #> MAURITANIA -0.60496775 0.11315 0.56576 1.0000 #> NIGER -1.04877003 0.01797 0.14378 0.7549 #> IVORY COAST -1.41712454 0.00230 0.01378 0.0965 #> GUINEA -1.44888005 0.00188 0.01128 0.0789 #> BURKINA FASO -1.75085492 0.00023 0.00162 0.0097 #> LIBERIA -1.04053617 0.01871 0.07485 0.7860 #> SIERRA LEONE -0.87032623 0.04087 0.12262 1.0000 #> GHANA -1.10269327 0.01371 0.05485 0.5760 #> TOGO -0.99053008 0.02379 0.09517 0.9993 #> CAMEROON -1.13328519 0.01171 0.07025 0.4917 #> NIGERIA -1.17261672 0.00951 0.04754 0.3993 #> GABON -0.78935857 0.05720 0.17160 1.0000 #> CENTRAL AFRICAN REPUBLIC 1.17349763 0.00946 0.05678 0.3974 #> CHAD 0.46259185 0.17744 1.00000 1.0000 #> CONGO -0.20253005 0.34272 1.00000 1.0000 #> ZAIRE 2.02270432 2.6e-05 0.00026 0.0011 #> ANGOLA 1.23450728 0.00677 0.02710 0.2845 #> UGANDA 3.33600851 1.3e-11 7.6e-11 5.3e-10 #> KENYA 3.50301896 1.2e-12 7.4e-12 5.1e-11 #> TANZANIA 1.09843592 0.01401 0.12613 0.5886 #> BURUNDI 0.77417084 0.06077 0.24308 1.0000 #> RWANDA 1.45720776 0.00178 0.00891 0.0748 #> SOMALIA 1.18316273 0.00898 0.02695 0.3773 #> ETHIOPIA 2.62720027 7.4e-08 3.0e-07 3.1e-06 #> ZAMBIA 0.75273285 0.06610 0.59492 1.0000 #> ZIMBABWE -0.19956472 0.34490 1.00000 1.0000 #> MALAWI 0.21195283 0.33582 1.00000 1.0000 #> MOZAMBIQUE -0.28761679 0.28257 1.00000 1.0000 #> SOUTH AFRICA -0.86814954 0.04126 0.33004 1.0000 #> LESOTHO -0.29841469 0.27531 0.55062 1.0000 #> BOTSWANA 0.04090396 0.46740 1.00000 1.0000 #> SWAZILAND -0.65938417 0.09362 0.28087 1.0000 #> MOROCCO 0.02191606 0.48252 1.00000 1.0000 #> ALGERIA -0.36307938 0.23387 1.00000 1.0000 #> TUNISIA 0.57910139 0.12339 0.37017 1.0000 #> LIBYA 2.55272169 1.7e-07 1.2e-06 6.9e-06 #> SUDAN 4.03925235 3.3e-16 3.0e-15 1.4e-14 #> EGYPT 4.42133637 < 2e-16 < 2e-16 < 2e-16"},{"path":"https://r-spatial.github.io/spdep/reference/plot.mst.html","id":null,"dir":"Reference","previous_headings":"","what":"Plot the Minimum Spanning Tree — plot.mst","title":"Plot the Minimum Spanning Tree — plot.mst","text":"function plots MST, nodes circles edges segments.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/plot.mst.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Plot the Minimum Spanning Tree — plot.mst","text":"","code":"# S3 method for class 'mst' plot(x, coords, label.areas = NULL, cex.circles = 1, cex.labels = 1, add=FALSE, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/plot.mst.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Plot the Minimum Spanning Tree — plot.mst","text":"x Object mst class. coords two column matrix coordinates nodes. label.areas vector labels nodes cex.circles length circles plot. cex.labels length nodes labels ploted. add default FALSE, create new plot ... arguments passed plotting functions.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/plot.mst.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Plot the Minimum Spanning Tree — plot.mst","text":"Elias T. Krainski Renato M. Assuncao","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/plot.mst.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Plot the Minimum Spanning Tree — plot.mst","text":"","code":"### see example in mstree function documentation"},{"path":"https://r-spatial.github.io/spdep/reference/plot.nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Plot a neighbours list — plot.nb","title":"Plot a neighbours list — plot.nb","text":"function plot neighbours list given point coordinates represent region two dimensions; plot.listw wrapper passes neighbours component plot.nb.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/plot.nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Plot a neighbours list — plot.nb","text":"","code":"# S3 method for class 'nb' plot(x, coords, col=\"black\", points=TRUE, add=FALSE, arrows=FALSE, length=0.1, xlim=NULL, ylim=NULL, ...) # S3 method for class 'listw' plot(x, coords, col=\"black\", points=TRUE, add=FALSE, arrows=FALSE, length=0.1, xlim=NULL, ylim=NULL, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/plot.nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Plot a neighbours list — plot.nb","text":"x object class nb (plot.listw) class listw coords matrix region point coordinates, Spatial object (points polygons), sfc object (points polygons) col plotting colour points (logical) add points plot add (logical) add existing plot arrows (logical) draw arrowheads asymmetric neighbours length length plot inches arrow heads drawn asymmetric neighbours lists xlim, ylim plot window bounds ... graphical parameters par(..)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/plot.nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Plot a neighbours list — plot.nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/plot.nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Plot a neighbours list — plot.nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) plot(col.gal.nb, st_geometry(columbus)) title(main=\"GAL order 1 links with first nearest neighbours in red\", cex.main=0.6) plot(col.gal.nb, as(columbus, \"Spatial\")) title(main=\"GAL order 1 links with first nearest neighbours in red\", cex.main=0.6) coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE) col.knn <- knearneigh(coords, k=1) plot(knn2nb(col.knn), coords, add=TRUE, col=\"red\", length=0.08) #> Warning: neighbour object has 13 sub-graphs"},{"path":"https://r-spatial.github.io/spdep/reference/plot.skater.html","id":null,"dir":"Reference","previous_headings":"","what":"Plot the object of skater class — plot.skater","title":"Plot the object of skater class — plot.skater","text":"function displays results skater function. subgraphs plotted different colours.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/plot.skater.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Plot the object of skater class — plot.skater","text":"","code":"# S3 method for class 'skater' plot(x, coords, label.areas = NULL, groups.colors, cex.circles = 1, cex.labels = 1, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/plot.skater.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Plot the object of skater class — plot.skater","text":"x object skater class. coords matrix two colums coordinates nodes. label.areas vector labels nodes. groups.colors vector colors groups ou sub-graphs. cex.circles length circles represent nodes. cex.labels length labels nodes. ... arguments passed plotting funcitons.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/plot.skater.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Plot the object of skater class — plot.skater","text":"Elias T. Krainski Renato M. Assuncao","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/plot.skater.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Plot the object of skater class — plot.skater","text":"","code":"### see example in the skater function documentation"},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Construct neighbours list from polygon list — poly2nb","title":"Construct neighbours list from polygon list — poly2nb","text":"function builds neighbours list based regions contiguous boundaries, sharing one boundary point. current function part interpreted may run slowly many regions detailed boundaries, 0.2-16 fail lack memory single polygons built many border coordinates.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Construct neighbours list from polygon list — poly2nb","text":"","code":"poly2nb(pl, row.names = NULL, snap=NULL, queen=TRUE, useC=TRUE, foundInBox=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Construct neighbours list from polygon list — poly2nb","text":"pl list polygons class extending SpatialPolygons, sf sfc object containing non-empty (multi-)polygon objects row.names character vector region ids added neighbours list attribute region.id, default seq(1, nrow(x)); pl row.names, used instead default sequence. snap boundary points less snap distance apart considered indicate contiguity; used find candidate actual neighbours planar geometries, actual neighbours spherical geometries, spherical spatial indexing injects fuzzyness. set, SpatialPolygons objects, default sqrt(.Machine$double.eps), value also used sf objects coordinate reference system. sf objects defined coordinate reference system, default value 1e-7 geographical coordinates (approximately 10mm), 10mm projected coordinates metre units, converted 10mm distance units coordinates. conversion fail, snap reverts sqrt(.Machine$double.eps). queen TRUE, single shared boundary point meets contiguity condition, FALSE, one shared point required; note one shared boundary point necessarily mean shared boundary line useC default TRUE, work loop C, may set false revert R code calling two C functions n*k work loop, k average number candidate neighbours foundInBox default NULL using R code st_intersects() generate candidate neighbours (using snap= geometries spherical); NULL (legacy purposes) list length (n-1) integer vectors candidate neighbours (j > ) (created poly_findInBoxGEOS function rgeos clean polygons)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Construct neighbours list from polygon list — poly2nb","text":"neighbours list class nb. See card details “nb” objects.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Construct neighbours list from polygon list — poly2nb","text":"0.5-8, function includes faster bounding box indexing improvements contributed Micah Altman. cluster provided using set.ClusterOption, used finding candidate bounding box overlaps exact testing contiguity. 1.1-7, sf polygons included start end points, erroneously report queen neighbourhood rook present, see https://github.com/r-spatial/spdep/issues/50. 1.1-9 sf 1.0-0, s2 used bounding box indexing internally pl geographical coordinates. topology engine s2 differs use GEOS planar coordinates sf, output differences may expected. Since treating spherical geometries planar also questionable, clear whether spherical contiguous polygon neighbours simply follow neighbours found treating geometries planar https://github.com/r-spatial/s2/issues/125#issuecomment-864403372. However, current advice necessarily use s2 finding contiguity neighbours, least check output.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Construct neighbours list from polygon list — poly2nb","text":"Roger Bivand Roger.Bivand@nhh.contributions Micah Altman","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/poly2nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Construct neighbours list from polygon list — poly2nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(st_geometry(columbus))) xx <- poly2nb(as(columbus, \"Spatial\")) dxx <- diffnb(xx, col.gal.nb) #> Warning: neighbour object has 46 sub-graphs plot(st_geometry(columbus), border=\"grey\") plot(col.gal.nb, coords, add=TRUE) plot(dxx, coords, add=TRUE, col=\"red\") title(main=paste(\"Differences (red) in Columbus GAL weights (black)\", \"and polygon generated queen weights\", sep=\"\\n\"), cex.main=0.6) # poly2nb with sf sfc_MULTIPOLYGON objects sf_xx <- poly2nb(columbus) diffnb(sf_xx, xx) #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 0 #> Percentage nonzero weights: 0 #> Average number of links: 0 #> 49 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 #> 49 disjoint connected subgraphs sfc_xx <- poly2nb(st_geometry(columbus)) diffnb(sfc_xx, xx) #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 0 #> Percentage nonzero weights: 0 #> Average number of links: 0 #> 49 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 #> 49 disjoint connected subgraphs xxx <- poly2nb(as(columbus, \"Spatial\"), queen=FALSE) dxxx <- diffnb(xxx, col.gal.nb) #> Warning: neighbour object has 34 sub-graphs plot(st_geometry(columbus), border = \"grey\") plot(col.gal.nb, coords, add = TRUE) plot(dxxx, coords, add = TRUE, col = \"red\") title(main=paste(\"Differences (red) in Columbus GAL weights (black)\", \"and polygon generated rook weights\", sep=\"\\n\"), cex.main=0.6) cards <- card(xx) maxconts <- which(cards == max(cards)) if(length(maxconts) > 1) maxconts <- maxconts[1] fg <- rep(\"grey\", length(cards)) fg[maxconts] <- \"red\" fg[xx[[maxconts]]] <- \"green\" plot(st_geometry(columbus), col=fg) title(main=\"Region with largest number of contiguities\", cex.main=0.6) nc.sids <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\")[1], quiet=TRUE) system.time(xxnb <- poly2nb(nc.sids)) #> user system elapsed #> 0.02 0.00 0.05 system.time(xxnb <- poly2nb(as(nc.sids, \"Spatial\"))) #> user system elapsed #> 0.03 0.00 0.06 plot(st_geometry(nc.sids)) plot(xxnb, st_coordinates(st_centroid(nc.sids)), add=TRUE, col=\"blue\") #> Warning: st_centroid assumes attributes are constant over geometries sq <- st_polygon(list(rbind(c(0,0), c(1,0), c(1,1), c(0,1), c(0,0)))) sq2 <- sq + c(0,1) sq3 <- sq + c(1,0) sq4 <- sq + c(1,1) gm <- st_sfc(list(sq, sq2, sq3, sq4)) df <- st_as_sf(data.frame(gm, id=1:4)) plot(st_geometry(df)) text(st_coordinates(st_centroid(gm)), as.character(df$id)) unclass(poly2nb(df, queen = FALSE)) #> [[1]] #> [1] 2 3 #> #> [[2]] #> [1] 1 4 #> #> [[3]] #> [1] 1 4 #> #> [[4]] #> [1] 2 3 #> #> attr(,\"region.id\") #> [1] \"1\" \"2\" \"3\" \"4\" #> attr(,\"call\") #> poly2nb(pl = df, queen = FALSE) #> attr(,\"type\") #> [1] \"rook\" #> attr(,\"snap\") #> [1] 1.490116e-08 #> attr(,\"sym\") #> [1] TRUE #> attr(,\"ncomp\") #> attr(,\"ncomp\")$nc #> [1] 1 #> #> attr(,\"ncomp\")$comp.id #> [1] 1 1 1 1 #> col_geoms <- st_geometry(columbus) col_geoms[1] <- st_buffer(col_geoms[1], dist=-0.05) st_geometry(columbus) <- col_geoms poly2nb(columbus) #> Warning: some observations have no neighbours; #> if this seems unexpected, try increasing the snap argument. #> Warning: neighbour object has 2 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 232 #> Percentage nonzero weights: 9.662641 #> Average number of links: 4.734694 #> 1 region with no links: #> 1 #> 2 disjoint connected subgraphs"},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":null,"dir":"Reference","previous_headings":"","what":"Probability mapping for rates — probmap","title":"Probability mapping for rates — probmap","text":"function returns data frame rates counts populations risk crude rates, expected counts cases, relative risks, Poisson probabilities.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Probability mapping for rates — probmap","text":"","code":"probmap(n, x, row.names=NULL, alternative=\"less\")"},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Probability mapping for rates — probmap","text":"n numeric vector counts cases x numeric vector populations risk row.names row names passed output data frame alternative default “less”, may set “greater”","code":""},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Probability mapping for rates — probmap","text":"function returns data frame, rates may mapped class intervals chosen. class intervals used examples mostly taken referenced source.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Probability mapping for rates — probmap","text":"raw raw (crude) rates expCount expected counts cases assuming global rate relRisk relative risks: ratio observed expected counts cases multiplied 100 pmap Poisson probability map values: probablility getting “extreme” count actually observed - one-tailed, default alternative observed “less” expected","code":""},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Probability mapping for rates — probmap","text":"Bailey T, Gatrell (1995) Interactive Spatial Data Analysis, Harlow: Longman, pp. 300–303.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Probability mapping for rates — probmap","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/probmap.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Probability mapping for rates — probmap","text":"","code":"auckland <- st_read(system.file(\"shapes/auckland.gpkg\", package=\"spData\")[1], quiet=TRUE) res <- probmap(auckland$M77_85, 9*auckland$Und5_81) rt <- sum(auckland$M77_85)/sum(9*auckland$Und5_81) ppois_pmap <- numeric(length(auckland$Und5_81)) for (i in seq(along=ppois_pmap)) { ppois_pmap[i] <- poisson.test(auckland$M77_85[i], r=rt, T=(9*auckland$Und5_81[i]), alternative=\"less\")$p.value all.equal(ppois_pmap, res$pmap) } res$id <- 1:nrow(res) auckland$id <- res$id <- 1:nrow(res) auckland_res <- merge(auckland, res, by=\"id\") plot(auckland_res[, \"raw\"], main=\"Crude (raw) estimates\") plot(auckland_res[, \"relRisk\"], main=\"Standardised mortality ratios\") plot(auckland_res[, \"pmap\"], main=\"Poisson probabilities\", breaks=c(0, 0.05, 0.1, 0.5, 0.9, 0.95, 1))"},{"path":"https://r-spatial.github.io/spdep/reference/prunecost.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute cost of prune each edge — prunecost","title":"Compute cost of prune each edge — prunecost","text":"edge dropped, MST pruned. generate two subgraphs. , makes tree graphs tree dissimilarity values computed, one graph. dissimilarity sum sqared differences observactions nodes mean vector observations graph. dissimilarity original graph sum dissimilarity subgraphs returned.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/prunecost.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute cost of prune each edge — prunecost","text":"","code":"prunecost(edges, data, method = c(\"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\", \"minkowski\", \"mahalanobis\"), p = 2, cov, inverted = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/prunecost.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute cost of prune each edge — prunecost","text":"edges matrix 2 colums row one edge data data.frame observations nodes. method Character function declare distance method. method character, method must \"mahalanobis\" \"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\" \"minkowisk\". method one \"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\" \"minkowisk\", see dist details, function used compute distance. method=\"mahalanobis\", mahalanobis distance computed neighbour areas. method function, function used compute distance. p power Minkowski distance. cov covariance matrix used compute mahalanobis distance. inverted logical. 'TRUE', 'cov' supposed contain inverse covariance matrix.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/prunecost.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute cost of prune each edge — prunecost","text":"vector differences dissimilarity nodes dissimilarity sum subgraphs obtained pruning one edge time.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/prunecost.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute cost of prune each edge — prunecost","text":"Elias T. Krainski Renato M. Assuncao","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/prunecost.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute cost of prune each edge — prunecost","text":"","code":"d <- data.frame(a=-2:2, b=runif(5)) e <- matrix(c(1,2, 2,3, 3,4, 4,5), ncol=2, byrow=TRUE) sum(sweep(d, 2, colMeans(d))^2) #> [1] 10.35574 prunecost(e, d) #> [1] 2.138259 2.875555 2.820048 2.169740"},{"path":"https://r-spatial.github.io/spdep/reference/prunemst.html","id":null,"dir":"Reference","previous_headings":"","what":"Prune a Minimun Spanning Tree — prunemst","title":"Prune a Minimun Spanning Tree — prunemst","text":"function deletes first edge makes two subsets edges. subset Minimun Spanning Treee.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/prunemst.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Prune a Minimun Spanning Tree — prunemst","text":"","code":"prunemst(edges, only.nodes = TRUE)"},{"path":"https://r-spatial.github.io/spdep/reference/prunemst.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Prune a Minimun Spanning Tree — prunemst","text":"edges matrix two colums row one edge .nodes .nodes=FALSE, return edges nodes MST resulted. .nodes=TRUE, return two sets nodes. Defalt TRUE","code":""},{"path":"https://r-spatial.github.io/spdep/reference/prunemst.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Prune a Minimun Spanning Tree — prunemst","text":"list length two. .nodes=TRUE element vector nodes. .nodes=FALSE element list nodes edges.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/prunemst.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Prune a Minimun Spanning Tree — prunemst","text":"Elias T. Krainski Renato M. Assuncao","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/prunemst.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Prune a Minimun Spanning Tree — prunemst","text":"","code":"e <- matrix(c(2,3, 1,2, 3,4, 4,5), ncol=2, byrow=TRUE) e #> [,1] [,2] #> [1,] 2 3 #> [2,] 1 2 #> [3,] 3 4 #> [4,] 4 5 prunemst(e) #> $node1 #> [1] 2 1 #> #> $node2 #> [1] 3 4 5 #> prunemst(e, only.nodes=FALSE) #> [[1]] #> [[1]]$node #> [1] 2 1 #> #> [[1]]$edge #> [,1] [,2] #> [1,] 1 2 #> #> #> [[2]] #> [[2]]$node #> [1] 3 4 5 #> #> [[2]]$edge #> [,1] [,2] #> [1,] 3 4 #> [2,] 4 5 #> #>"},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":null,"dir":"Reference","previous_headings":"","what":"Read a GAL lattice file into a neighbours list — read.gal","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"function read.gal() reads GAL lattice file neighbours list spatial analysis. read old new style (GeoDa) GAL files. function read.geoda helper file reading comma separated value data files, calling read.csv().","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"","code":"read.gal(file, region.id=NULL, override.id=FALSE) read.geoda(file, row.names=NULL, skip=0)"},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"file name file GAL lattice data region.id region IDs specified order coerse neighbours list order numbering region.id override.id override given (NULL) region.id, collecting region.id numbering order GAL file. row.names row.names read.csv(), typically character string naming column file used skip skip number lines, read.csv()","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"Luc Anselin (2003): Spatial Analysis Laboratory, Department Agricultural Consumer Economics, University Illinois, Urbana-Champaign, now dead link: http://www.csiss.org/gispopsci/workshops/2011/PSU/readings/W15_Anselin2007.pdf; Luc Anselin (2003) GeoDa 0.9 User's Guide, pp. 80–81, Spatial Analysis Laboratory, Department Agricultural Consumer Economics, University Illinois, Urbana-Champaign, http://geodacenter.github.io/docs/geoda093.pdf; GAL - Geographical Algorithms Library, University Newcastle","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"function read.gal() returns object class nb list integer vectors containing neighbour region number ids. function read.geoda returns data frame, issues warning returned object one column.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"Example data originally downloaded now dead link: http://sal.agecon.uiuc.edu/weights/zips/us48.zip","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/read.gal.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Read a GAL lattice file into a neighbours list — read.gal","text":"","code":"us48.fipsno <- read.geoda(system.file(\"etc/weights/us48.txt\", package=\"spdep\")[1]) us48.q <- read.gal(system.file(\"etc/weights/us48_q.GAL\", package=\"spdep\")[1], us48.fipsno$Fipsno) us48.r <- read.gal(system.file(\"etc/weights/us48_rk.GAL\", package=\"spdep\")[1], us48.fipsno$Fipsno) data(state) if (as.numeric(paste(version$major, version$minor, sep=\"\")) < 19) { m50.48 <- match(us48.fipsno$\"State.name\", state.name) } else { m50.48 <- match(us48.fipsno$\"State_name\", state.name) } plot(us48.q, as.matrix(as.data.frame(state.center))[m50.48,]) plot(diffnb(us48.r, us48.q), as.matrix(as.data.frame(state.center))[m50.48,], add=TRUE, col=\"red\") #> Warning: neighbour object has 46 sub-graphs title(main=\"Differences between rook and queen criteria imported neighbours lists\")"},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Read and write spatial neighbour files — read.gwt2nb","title":"Read and write spatial neighbour files — read.gwt2nb","text":"\"gwt\" functions read write GeoDa GWT files (example file baltk4.GWT downloaded site given reference), \"dat\" functions read write Matlab sparse matrix files used James LeSage's Spatial Econometrics Toolbox (example file wmat.dat downloaded site given reference). body files headers three columns separated white space, third column must numeric locale reading platform (correct decimal separator).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Read and write spatial neighbour files — read.gwt2nb","text":"","code":"read.gwt2nb(file, region.id=NULL) write.sn2gwt(sn, file, shpfile=NULL, ind=NULL, useInd=FALSE, legacy=FALSE) read.dat2listw(file) write.sn2dat(sn, file) read.swmdbf2listw(fn, region.id=NULL, style=NULL, zero.policy=NULL) read_swm_dbf(fn) write.swmdbf(listw, file, ind, region.id = attr(listw, \"region.id\")) write_swm_dbf(listw, file, ind, region.id = attr(listw, \"region.id\")) write.sn2DBF(sn, file)"},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Read and write spatial neighbour files — read.gwt2nb","text":"file, fn name file weights data region.id character vector region IDs - ArcGIS SWM DBFs, values must character integers (numbers starting zero) listw listw object sn spatial.neighbour object shpfile character string: given Shapefile name taken GWT file dataset ind character string: region id indicator field name useInd default FALSE, TRUE, write region.id attribute ID key tags output file (use OpenGeoDa depend shapefile field named ind argument matching exported tags) legacy default FALSE; TRUE, header single field number observations style default NULL, missing, set \"M\" warning given; \"M\", passed nb2listw re-build object zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Read and write spatial neighbour files — read.gwt2nb","text":"Attempts honour region.id argument given reading GWT SWM/DBF files. region IDs given region.id= match origins destinations GWT file, error warning thrown, considered carefully. read_swm_dbf simplified interface read.swmdbf2listw -neighbour observations present, advised region.id= given read.swmdbf2listw; function read correctly minimum maximum IDs present observations neighbours without region.id= set, reading using read.swmdbf2listw fail minimum maximum ID observations neighbours region.id= given.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Read and write spatial neighbour files — read.gwt2nb","text":"read.gwt2nb returns neighbour \"nb\" object generalised weights stored list element called \"dlist\" \"GeoDa\" attribute; read.swmdbf2listw returns \"listw\" object read DBF file exported ArcGIS SWM object.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Read and write spatial neighbour files — read.gwt2nb","text":"Luc Anselin (2003) GeoDa 0.9 User's Guide, pp. 80–81, Spatial Analysis Laboratory, Department Agricultural Consumer Economics, University Illinois, Urbana-Champaign, http://geodacenter.github.io/docs/geoda093.pdf; also material formerly spatial-econometrics.com/data/contents.html","code":""},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Read and write spatial neighbour files — read.gwt2nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/read.gwt2nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Read and write spatial neighbour files — read.gwt2nb","text":"","code":"data(baltimore, package=\"spData\") STATION <- baltimore$STATION gwt1 <- read.gwt2nb(system.file(\"weights/baltk4.GWT\", package=\"spData\")[1], STATION) #> Warning: 102, 115, 208 are not destinations cat(paste(\"Neighbours list symmetry;\", is.symmetric.nb(gwt1, FALSE, TRUE), \"\\n\")) #> Neighbours list symmetry; FALSE listw1 <- nb2listw(gwt1, style=\"B\", glist=attr(gwt1, \"GeoDa\")$dist) tmpGWT <- tempfile() write.sn2gwt(listw2sn(listw1), tmpGWT) gwt2 <- read.gwt2nb(tmpGWT, STATION) #> Warning: 102, 115, 208 are not destinations cat(paste(\"Neighbours list symmetry;\", is.symmetric.nb(gwt2, FALSE, TRUE), \"\\n\")) #> Neighbours list symmetry; FALSE diffnb(gwt1, gwt2) #> Warning: neighbour object has 211 sub-graphs #> Neighbour list object: #> Number of regions: 211 #> Number of nonzero links: 0 #> Percentage nonzero weights: 0 #> Average number of links: 0 #> 211 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, #> 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, #> 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, #> 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, #> 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, #> 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, #> 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, #> 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, #> 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, #> 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, #> 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, #> 206, 207, 208, 209, 210, 211 #> 211 disjoint connected subgraphs data(oldcol) tmpMAT <- tempfile() COL.W <- nb2listw(COL.nb) write.sn2dat(listw2sn(COL.W), tmpMAT) listwmat1 <- read.dat2listw(tmpMAT) #> Warning: style is M (missing); style should be set to a valid value diffnb(listwmat1$neighbours, COL.nb, verbose=TRUE) #> Warning: region.id differ; using ids of first list #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 0 #> Percentage nonzero weights: 0 #> Average number of links: 0 #> 49 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 #> 49 disjoint connected subgraphs listwmat2 <- read.dat2listw(system.file(\"etc/weights/wmat.dat\", package=\"spdep\")[1]) #> Warning: style is M (missing); style should be set to a valid value diffnb(listwmat1$neighbours, listwmat2$neighbours, verbose=TRUE) #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 0 #> Percentage nonzero weights: 0 #> Average number of links: 0 #> 49 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 #> 49 disjoint connected subgraphs run <- FALSE if (require(\"foreign\", quietly=TRUE)) run <- TRUE if (run) { nc_sf <- sf::st_read(system.file(\"gpkg/nc.gpkg\", package=\"sf\")[1]) nc_sf$UniqueID <- 1:nrow(nc_sf) fn <- system.file(\"etc/misc/nc_contiguity_unique_id.dbf\", package=\"spdep\")[1] nc1 <- read.swmdbf2listw(fn, style=\"B\") nc1 } #> Reading layer `nc.gpkg' from data source #> `C:\\Users\\rzomor2\\AppData\\Local\\R\\win-library\\4.4\\sf\\gpkg\\nc.gpkg' #> using driver `GPKG' #> Simple feature collection with 100 features and 14 fields #> Geometry type: MULTIPOLYGON #> Dimension: XY #> Bounding box: xmin: -84.32385 ymin: 33.88199 xmax: -75.45698 ymax: 36.58965 #> Geodetic CRS: NAD27 #> Warning: region.id not given, c(MYID, NID) range is 1:100 #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 100 #> Number of nonzero links: 490 #> Percentage nonzero weights: 4.9 #> Average number of links: 4.9 #> #> Weights style: B #> Weights constants summary: #> n nn S0 S1 S2 #> B 100 10000 490 980 10696 if (run) { nc1a <- read.swmdbf2listw(fn, region.id=as.character(nc_sf$UniqueID), style=\"B\") all.equal(nc1, nc1a) } #> [1] TRUE if (run) { fn <- system.file(\"etc/misc/nc_contiguity_unique_id_islands.dbf\", package=\"spdep\")[1] try(nc1i <- read.swmdbf2listw(fn, style=\"B\")) nc1i <- read.swmdbf2listw(fn, style=\"B\", zero.policy=TRUE) nc1ia <- read.swmdbf2listw(fn, region.id=as.character(nc_sf$UniqueID), style=\"B\", zero.policy=TRUE) nc1ia } #> Warning: region.id not given, c(MYID, NID) range is 1:100 #> Warning: 81 is not an origin #> Error in read.swmdbf2listw(fn, style = \"B\") : #> Error in sn2listw(df1, style = style, zero.policy = zero.policy) : #> no-neighbour observations found, set zero.policy to TRUE #> #> Warning: region.id not given, c(MYID, NID) range is 1:100 #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 100 #> Number of nonzero links: 487 #> Percentage nonzero weights: 4.87 #> Average number of links: 4.87 #> 1 region with no links: #> 81 #> Non-symmetric neighbours list #> #> Weights style: B #> Weights constants summary: #> n nn S0 S1 S2 #> B 99 9801 487 971 10632 if (run) { all.equal(nc1i, nc1ia) } #> [1] TRUE if (run) { GDAL37 <- numeric_version(unname(sf::sf_extSoftVersion()[\"GDAL\"]), strict=FALSE) (GDAL37 <- ifelse(is.na(GDAL37), FALSE, GDAL37 >= \"3.7.0\")) file <- \"etc/shapes/california.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) { cal <- st_read(zipfile) } else { td <- tempdir() bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE) target <- unzip(zipfile, files=bn, exdir=td) cal <- st_read(target) } fn <- system.file(\"etc/misc/contiguity_myid.dbf\", package=\"spdep\")[1] cal1 <- read.swmdbf2listw(fn, style=\"B\") cal1a <- read.swmdbf2listw(fn, region.id=as.character(cal$MYID), style=\"B\") all.equal(cal1, cal1a) } #> Reading layer `california' from data source #> `C:\\Users\\rzomor2\\AppData\\Local\\Temp\\RtmpErQTm3\\temp_libpath1a5cde63ff3\\spdep\\etc\\shapes\\california.gpkg.zip' #> using driver `GPKG' #> Simple feature collection with 58 features and 2 fields #> Geometry type: MULTIPOLYGON #> Dimension: XY #> Bounding box: xmin: -13847330 ymin: 3810869 xmax: -12704360 ymax: 5132708 #> Projected CRS: World_Mercator #> Warning: region.id not given, c(MYID, NID) range is 158:215 #> [1] TRUE if (run) { fn <- system.file(\"etc/misc/contiguity_unique_id.dbf\", package=\"spdep\")[1] cal2 <- read.swmdbf2listw(fn, style=\"B\") cal2a <- read.swmdbf2listw(fn, region.id=as.character(cal$UniqueID), style=\"B\") all.equal(cal2, cal2a) } #> Warning: region.id not given, c(MYID, NID) range is 1:58 #> [1] TRUE if (run) { fn <- system.file(\"etc/misc/contiguity_unique_id_islands.dbf\", package=\"spdep\")[1] try(cal3i <- read.swmdbf2listw(fn, style=\"B\")) cal3i <- read.swmdbf2listw(fn, style=\"B\", zero.policy=TRUE) cal3ia <- read.swmdbf2listw(fn, region.id=as.character(cal$UniqueID), style=\"B\", zero.policy=TRUE) all.equal(cal3i, cal3ia) } #> Warning: region.id not given, c(MYID, NID) range is 1:58 #> Warning: 21, 38 are not origins #> Error in read.swmdbf2listw(fn, style = \"B\") : #> Error in sn2listw(df1, style = style, zero.policy = zero.policy) : #> no-neighbour observations found, set zero.policy to TRUE #> #> Warning: region.id not given, c(MYID, NID) range is 1:58 #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> [1] TRUE if (run) { cal1a_1n_nb <- cal1a$neighbours cal1a_1n_nb <- droplinks(cal1a_1n_nb, drop=c(\"158\", \"180\", \"215\"), sym=TRUE) cal1a_1n <- nb2listw(cal1a_1n_nb, style=\"B\", zero.policy=TRUE) cal1a_1n_sn <- listw2sn(cal1a_1n) file <- tempfile(fileext=\".dbf\") write.sn2DBF(cal1a_1n_sn, file) cal1a_1n_rt <- read.swmdbf2listw(file, region.id=as.character(cal$MYID), style=\"B\", zero.policy=TRUE) all.equal(cal1a_1n$neighbours, cal1a_1n_rt$neighbours) } #> Warning: some observations have no neighbours #> Warning: neighbour object has 4 sub-graphs #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> Warning: neighbour object has 4 sub-graphs #> [1] TRUE if (run) { all.equal(cal1a_1n$weights, cal1a_1n_rt$weights, check.attributes=FALSE) } #> [1] TRUE if (run) { cal1_1n_rt <- read.swmdbf2listw(file, style=\"B\", zero.policy=TRUE) all(isTRUE(all.equal(cal1a_1n$neighbours, cal1_1n_rt$neighbours))) } #> Warning: region.id not given, c(MYID, NID) range is 159:214 #> Warning: no-neighbour observations found, set zero.policy to TRUE; #> this warning will soon become an error #> Warning: neighbour object has 2 sub-graphs #> [1] FALSE if (run) { all(isTRUE(all.equal(cal1a_1n$weights, cal1_1n_rt$weights))) } #> [1] FALSE"},{"path":"https://r-spatial.github.io/spdep/reference/rotation.html","id":null,"dir":"Reference","previous_headings":"","what":"Rotate a set of point by a certain angle — Rotation","title":"Rotate a set of point by a certain angle — Rotation","text":"Rotate set XY coordinates angle (radians)","code":""},{"path":"https://r-spatial.github.io/spdep/reference/rotation.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Rotate a set of point by a certain angle — Rotation","text":"","code":"Rotation(xy, angle)"},{"path":"https://r-spatial.github.io/spdep/reference/rotation.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Rotate a set of point by a certain angle — Rotation","text":"xy 2-columns matrix data frame containing set X Y coordinates. angle Numeric. scalar giving angle points rotated. angle radians.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/rotation.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Rotate a set of point by a certain angle — Rotation","text":"2-columns matrix size xy giving rotated coordinates.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/rotation.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Rotate a set of point by a certain angle — Rotation","text":"F. Guillaume Blanchet","code":""},{"path":"https://r-spatial.github.io/spdep/reference/rotation.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Rotate a set of point by a certain angle — Rotation","text":"","code":"set.seed(1) ### Create a set of coordinates coords <- cbind(runif(20), runif(20)) ### Create a series of angles rad <- seq(0, pi, l=20) opar <- par(mfrow=c(5,4), mar=c(3,3,1,1)) for(i in rad){ coords.rot <- Rotation(coords, i) plot(coords.rot, xlab=\"\", ylab=\"\") } par(opar) ### Rotate the coordinates by an angle of 90 degrees coords.90 <- Rotation(coords, 90*pi/180) coords.90 #> [,1] [,2] #> [1,] -0.93470523 0.26550866 #> [2,] -0.21214252 0.37212390 #> [3,] -0.65167377 0.57285336 #> [4,] -0.12555510 0.90820779 #> [5,] -0.26722067 0.20168193 #> [6,] -0.38611409 0.89838968 #> [7,] -0.01339033 0.94467527 #> [8,] -0.38238796 0.66079779 #> [9,] -0.86969085 0.62911404 #> [10,] -0.34034900 0.06178627 #> [11,] -0.48208012 0.20597457 #> [12,] -0.59956583 0.17655675 #> [13,] -0.49354131 0.68702285 #> [14,] -0.18621760 0.38410372 #> [15,] -0.82737332 0.76984142 #> [16,] -0.66846674 0.49769924 #> [17,] -0.79423986 0.71761851 #> [18,] -0.10794363 0.99190609 #> [19,] -0.72371095 0.38003518 #> [20,] -0.41127443 0.77744522 plot(coords, xlim=range(rbind(coords.90,coords)[,1]), ylim=range(rbind(coords.90,coords)[,2]), asp=1) points(coords.90, pch=19)"},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":null,"dir":"Reference","previous_headings":"","what":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"Rao's score adjusted Rao's score tests linear hypotheses applied fitted linear model examine whether either spatially lagged dependent variable lag spatially lagged independent variable(s) WX included model, (SDM). Adjusted tests provided lag WX adapting presence , joint test . joint test equal unadjusted one plus adjusted . addition, draft tests added Koley (2024, section 6) spatial Durbin error models examine whether either spatially lagged error err spatially lagged independent variable(s) WX included model, (SDEM); orthogonality, adjusted tests required. spatial lags categorical variables poorly understood, version 1.3-11 warnings given categorical variables included Durbin term.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"","code":"SD.RStests(model, listw, zero.policy = attr(listw, \"zero.policy\"), test = \"SDM\", Durbin = TRUE) have_factor_preds_mf(mf) warn_factor_preds(x)"},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"model object class lm returned lm listw listw object created example nb2listw, expected row-standardised (W-style) zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA test test=“SDM” computes SDM tests, character vector tests requested chosen SDM_RSlag, SDM_adjRSlag, SDM_RSWX, SDM_adjRSWX, SDM_Joint, test=“SDEM” computes SDEM tests, character vector tests requested chosen SDEM_RSerr, SDEM_RSWX, SDEM_Joint; test=“” computes tests Durbin default TRUE Durbin models including WX; TRUE, full spatial Durbin model; formula object, subset explanatory variables lag mf model.frame object x object created have_factor_preds_mf","code":""},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"list class LMtestlist htest objects, : statistic value Lagrange Multiplier test. parameter number degrees freedom p.value p-value test. method character string giving method used. data.name character string giving name(s) data.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"Malabika Koley Anil K. Bera (2024) use, use spatial Durbin model? – question, Spatial Economic Analysis, 19:1, 30-56, doi:10.1080/17421772.2023.2256810 ; Malabika Koley (2024) Specification testing spatial econometric models, Ph.D. dissertation, University Illinois Urbana-Champaign, pp. 78-118, 148-156; https://hdl.handle.net/2142/124329.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"Roger Bivand Roger.Bivand@nhh., Malabika Koley Anil K. Bera","code":""},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"results example agree Table 3, p. 22 Koley Bera (2024).","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/SD.RStests.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Rao's score and adjusted Rao's score tests of linear hypotheses for spatial Durbin and spatial Durbin error models — SD.RStests","text":"","code":"columbus <- sf::st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1]) #> Reading layer `columbus' from data source #> `C:\\Users\\rzomor2\\AppData\\Local\\R\\win-library\\4.4\\spData\\shapes\\columbus.gpkg' #> using driver `GPKG' #> Simple feature collection with 49 features and 20 fields #> Geometry type: POLYGON #> Dimension: XY #> Bounding box: xmin: 5.874907 ymin: 10.78863 xmax: 11.28742 ymax: 14.74245 #> Projected CRS: Undefined Cartesian SRS with unknown unit col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) col.listw <- nb2listw(col.gal.nb, style=\"W\") columbus$fEW <- factor(columbus$EW) columbus$fDISCBD <- ordered(cut(columbus$DISCBD, c(0, 1.5, 3, 4.5, 6))) f <- formula(CRIME ~ INC + HOVAL + fDISCBD + fEW) lm_obj <- lm(f, data=columbus) summary(lm.RStests(lm_obj, col.listw, test=\"all\")) #> \tRao's score (a.k.a Lagrange multiplier) diagnostics for spatial #> \tdependence #> data: #> model: lm(formula = f, data = columbus) #> test weights: col.listw #> #> statistic parameter p.value #> RSerr 0.047443 1 0.8276 #> RSlag 0.718623 1 0.3966 #> adjRSerr 0.721842 1 0.3955 #> adjRSlag 1.393021 1 0.2379 #> SARMA 1.440465 2 0.4866 res <- SD.RStests(lm_obj, col.listw, test=\"SDM\") #> Warning: use of spatially lagged factors (categorical variables) #> fDISCBD, fEW #> is not well-understood #> Warning: In addition variable: #> fDISCBD #> is ordered (ordinal) with polynomial contrasts. summary(res) #> \tRao's score test spatial Durbin diagnostics #> data: #> model: lm(formula = f, data = columbus) #> weights: col.listw #> #> statistic parameter p.value #> SDM_RSlag 0.718623 1 0.39660 #> SDM_adjRSlag 0.047443 1 0.82757 #> SDM_RSWX 12.904287 6 0.04458 * #> SDM_adjRSWX 12.233108 6 0.05697 . #> SDM_Joint 12.951730 7 0.07329 . #> --- #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 all.equal(unname(res$SDM_Joint$statistic), unname(res$SDM_RSlag$statistic + res$SDM_adjRSWX$statistic)) #> [1] TRUE all.equal(unname(res$SDM_Joint$statistic), unname(res$SDM_adjRSlag$statistic + res$SDM_RSWX$statistic)) #> [1] TRUE res <- SD.RStests(lm_obj, col.listw, test=\"SDEM\") #> Warning: use of spatially lagged factors (categorical variables) #> fDISCBD, fEW #> is not well-understood #> Warning: In addition variable: #> fDISCBD #> is ordered (ordinal) with polynomial contrasts. summary(res) #> \tRao's score test spatial Durbin diagnostics #> data: #> model: lm(formula = f, data = columbus) #> weights: col.listw #> #> statistic parameter p.value #> SDEM_RSerr 0.047443 1 0.82757 #> SDEM_RSWX 12.904287 6 0.04458 * #> SDEM_Joint 12.951730 7 0.07329 . #> --- #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 all.equal(unname(res$SDEM_Joint$statistic), unname(res$SDEM_RSerr$statistic + res$SDEM_RSWX$statistic)) #> [1] TRUE summary(SD.RStests(lm_obj, nb2listw(col.gal.nb, style=\"C\"), test=\"all\")) #> Warning: Spatial weights matrix not row standardized #> Warning: use of spatially lagged factors (categorical variables) #> fDISCBD, fEW #> is not well-understood #> Warning: In addition variable: #> fDISCBD #> is ordered (ordinal) with polynomial contrasts. #> \tRao's score test spatial Durbin diagnostics #> data: #> model: lm(formula = f, data = columbus) #> weights: nb2listw(col.gal.nb, style = \"C\") #> #> statistic parameter p.value #> SDM_RSlag 1.3907611 1 0.23828 #> SDM_adjRSlag 0.0030013 1 0.95631 #> SDM_RSWX 12.2469692 7 0.09272 . #> SDM_adjRSWX 10.8592093 7 0.14488 #> SDM_Joint 12.2499705 8 0.14039 #> SDEM_RSerr 0.0030013 1 0.95631 #> SDEM_RSWX 12.2469692 7 0.09272 . #> SDEM_Joint 12.2499705 8 0.14039 #> --- #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 summary(SD.RStests(lm_obj, col.listw, test=\"all\", Durbin= ~ INC)) #> \tRao's score test spatial Durbin diagnostics #> data: #> model: lm(formula = f, data = columbus) #> weights: col.listw #> Durbin: ~ INC #> #> statistic parameter p.value #> SDM_RSlag 0.718623 1 0.3966 #> SDM_adjRSlag 0.269636 1 0.6036 #> SDM_RSWX 0.726478 1 0.3940 #> SDM_adjRSWX 0.277492 1 0.5984 #> SDM_Joint 0.996114 2 0.6077 #> SDEM_RSerr 0.047443 1 0.8276 #> SDEM_RSWX 0.726478 1 0.3940 #> SDEM_Joint 0.773922 2 0.6791 lm_obj0 <- lm(I(scale(CRIME)) ~ 0 + I(scale(INC)) + I(scale(HOVAL)), data=columbus) summary(SD.RStests(lm_obj0, col.listw, test=\"all\")) #> \tRao's score test spatial Durbin diagnostics #> data: #> model: lm(formula = I(scale(CRIME)) ~ 0 + I(scale(INC)) + #> I(scale(HOVAL)), data = columbus) #> weights: col.listw #> #> statistic parameter p.value #> SDM_RSlag 7.8250 1 0.005153 ** #> SDM_adjRSlag 4.6111 1 0.031765 * #> SDM_RSWX 6.0609 2 0.048295 * #> SDM_adjRSWX 2.8470 2 0.240873 #> SDM_Joint 10.6720 3 0.013638 * #> SDEM_RSerr 4.6111 1 0.031765 * #> SDEM_RSWX 6.0609 2 0.048295 * #> SDEM_Joint 10.6720 3 0.013638 * #> --- #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 columbusNA <- columbus columbusNA$HOVAL[15] <- NA lm_objNA <- lm(CRIME ~ INC + HOVAL, data=columbusNA) summary(SD.RStests(lm_objNA, col.listw, test=\"all\")) #> \tRao's score test spatial Durbin diagnostics #> data: #> model: lm(formula = CRIME ~ INC + HOVAL, data = columbusNA) #> weights: col.listw #> #> statistic parameter p.value #> SDM_RSlag 7.6010 1 0.005834 ** #> SDM_adjRSlag 4.4716 1 0.034463 * #> SDM_RSWX 6.0812 2 0.047807 * #> SDM_adjRSWX 2.9518 2 0.228576 #> SDM_Joint 10.5527 3 0.014407 * #> SDEM_RSerr 4.4716 1 0.034463 * #> SDEM_RSWX 6.0812 2 0.047807 * #> SDEM_Joint 10.5527 3 0.014407 * #> --- #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1"},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":null,"dir":"Reference","previous_headings":"","what":"Options for parallel support — set.mcOption","title":"Options for parallel support — set.mcOption","text":"Provides support use parallel computation parallel package.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Options for parallel support — set.mcOption","text":"","code":"set.mcOption(value) get.mcOption() set.coresOption(value) get.coresOption() set.ClusterOption(cl) get.ClusterOption()"},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Options for parallel support — set.mcOption","text":"value valid replacement value cl cluster object created makeCluster parallel","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Options for parallel support — set.mcOption","text":"Options spdep package held environment local package namespace exported. Option values set retrieved pairs access functions, get set. mc option set default FALSE Windows systems, fork R session; default TRUE systems, may set FALSE. mc FALSE, Cluster option used: mc FALSE Cluster option NULL parallel computing done, Cluster option passed “cluster” object created parallel snow package access without passed argument. cores option set NULL default, can used store number cores use integer. cores NULL, facilities parallel package used.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Options for parallel support — set.mcOption","text":"option access functions return current settings, assignment functions usually return previous value option.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Options for parallel support — set.mcOption","text":"extended example shown documentation aple.mc, including treatment seeding RNG multicore/cluster.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Options for parallel support — set.mcOption","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.mcOption.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Options for parallel support — set.mcOption","text":"","code":"ls(envir=spdep:::.spdepOptions) #> [1] \"cluster\" \"cores\" \"listw_is_CsparseMatrix\" #> [4] \"mc\" \"nb_subgraphs_N+E\" \"report_nb_noneighs\" #> [7] \"report_nb_subgraphs\" \"rlecuyerSeed\" \"spChkID\" #> [10] \"verbose\" \"zeroPolicy\" if (require(parallel, quietly=TRUE)) { nc <- max(2L, detectCores(logical=FALSE), na.rm = TRUE)-1L nc # set nc to 1L here if (nc > 1L) nc <- 1L #nc <- ifelse(nc > 2L, 2L, nc) coresOpt <- get.coresOption() coresOpt if (!is.na(nc)) { invisible(set.coresOption(nc)) print(exists(\"moran.mc\")) if(.Platform$OS.type == \"windows\") { # forking not permitted on Windows - start cluster print(get.mcOption()) cl <- makeCluster(get.coresOption()) print(clusterEvalQ(cl, exists(\"moran.mc\"))) set.ClusterOption(cl) clusterEvalQ(get.ClusterOption(), library(spdep)) print(clusterEvalQ(cl, exists(\"moran.mc\"))) clusterEvalQ(get.ClusterOption(), detach(package:spdep)) set.ClusterOption(NULL) print(clusterEvalQ(cl, exists(\"moran.mc\"))) stopCluster(cl) } else { mcOpt <- get.mcOption() print(mcOpt) print(mclapply(1:get.coresOption(), function(i) exists(\"moran.mc\"), mc.cores=get.coresOption())) invisible(set.mcOption(FALSE)) cl <- makeCluster(nc) print(clusterEvalQ(cl, exists(\"moran.mc\"))) set.ClusterOption(cl) clusterEvalQ(get.ClusterOption(), library(spdep)) print(clusterEvalQ(cl, exists(\"moran.mc\"))) clusterEvalQ(get.ClusterOption(), detach(package:spdep)) set.ClusterOption(NULL) print(clusterEvalQ(cl, exists(\"moran.mc\"))) stopCluster(cl) invisible(set.mcOption(mcOpt)) } invisible(set.coresOption(coresOpt)) } } #> [1] TRUE #> [1] FALSE #> [[1]] #> [1] FALSE #> #> [[1]] #> [1] TRUE #> #> [[1]] #> [1] FALSE #>"},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":null,"dir":"Reference","previous_headings":"","what":"Control checking of spatial object IDs — set.spChkOption","title":"Control checking of spatial object IDs — set.spChkOption","text":"Provides support checking mutual integrity spatial neighbour weights spatial data; similar mechanisms used passing global verbose zero.policy options, causing functions creating neighbour objects warn multiple subgraphs.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Control checking of spatial object IDs — set.spChkOption","text":"","code":"set.spChkOption(check) get.spChkOption() chkIDs(x, listw) spNamedVec(var, data) set.VerboseOption(check) get.VerboseOption() set.ZeroPolicyOption(check) get.ZeroPolicyOption() set.SubgraphOption(check) get.SubgraphOption() set.SubgraphCeiling(value) get.SubgraphCeiling() set.NoNeighbourOption(check) get.NoNeighbourOption() set.listw_is_CsparseMatrix_Option(check) get.listw_is_CsparseMatrix_Option()"},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Control checking of spatial object IDs — set.spChkOption","text":"check logical value, TRUE FALSE value integer value, initialised 100000L, sum numbers nodes edges neighbour graph x vector length, two-dimensional array, data frame number rows neighbours list listw listw listw object nb object inheriting \"nb\" var character string integer value column selected data two-dimensional array data frame containing var","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Control checking of spatial object IDs — set.spChkOption","text":"Analysis functions spChk argument default set NULL, call get.spChkOption() get global spatial option whether check — initialised FALSE, consequently break anything. can changed TRUE using set.spChkOption(TRUE), spChk argument can assigned analysis functions. spNamedVec() provided ensure rownames passed single columns taken two-dimensional arrays data frames.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Control checking of spatial object IDs — set.spChkOption","text":"set.spChkOption() returns old logical value, get.spChkOption() returns current logical value, chkIDs() returns logical value test lack difference. spNamedVec() returns selected column names set row names object extracted.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Control checking of spatial object IDs — set.spChkOption","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Control checking of spatial object IDs — set.spChkOption","text":"motivation mechanism provided observation spatial objects map attribute data values need linked uniquely, avoid spurious results. reordering legacy Columbus data set used earlier publications available download Spacestat website just one example common problem.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/set.spChkOption.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Control checking of spatial object IDs — set.spChkOption","text":"","code":"data(oldcol) rownames(COL.OLD) #> [1] \"1001\" \"1002\" \"1003\" \"1004\" \"1005\" \"1006\" \"1007\" \"1008\" \"1009\" \"1010\" #> [11] \"1011\" \"1012\" \"1013\" \"1014\" \"1015\" \"1016\" \"1017\" \"1018\" \"1019\" \"1020\" #> [21] \"1021\" \"1022\" \"1023\" \"1024\" \"1025\" \"1026\" \"1027\" \"1028\" \"1029\" \"1030\" #> [31] \"1031\" \"1032\" \"1033\" \"1034\" \"1035\" \"1036\" \"1037\" \"1038\" \"1039\" \"1040\" #> [41] \"1041\" \"1042\" \"1043\" \"1044\" \"1045\" \"1046\" \"1047\" \"1048\" \"1049\" data(columbus, package=\"spData\") rownames(columbus) #> [1] \"1005\" \"1001\" \"1006\" \"1002\" \"1007\" \"1008\" \"1004\" \"1003\" \"1018\" \"1010\" #> [11] \"1038\" \"1037\" \"1039\" \"1040\" \"1009\" \"1036\" \"1011\" \"1042\" \"1041\" \"1017\" #> [21] \"1043\" \"1019\" \"1012\" \"1035\" \"1032\" \"1020\" \"1021\" \"1031\" \"1033\" \"1034\" #> [31] \"1045\" \"1013\" \"1022\" \"1044\" \"1023\" \"1046\" \"1030\" \"1024\" \"1047\" \"1016\" #> [41] \"1014\" \"1049\" \"1029\" \"1025\" \"1028\" \"1048\" \"1015\" \"1027\" \"1026\" get.spChkOption() #> [1] FALSE oldChk <- set.spChkOption(TRUE) get.spChkOption() #> [1] TRUE chkIDs(COL.OLD, nb2listw(COL.nb)) #> [1] TRUE chkIDs(columbus, nb2listw(col.gal.nb)) #> [1] TRUE chkIDs(columbus, nb2listw(COL.nb)) #> [1] FALSE tmp <- try(moran.test(spNamedVec(\"CRIME\", COL.OLD), nb2listw(COL.nb))) tmp <- try(moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(col.gal.nb))) tmp <- try(moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(COL.nb))) #> Error in moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(COL.nb)) : #> Check of data and weights ID integrity failed set.spChkOption(FALSE) get.spChkOption() #> [1] FALSE moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(COL.nb)) #> #> \tMoran I test under randomisation #> #> data: spNamedVec(\"CRIME\", columbus) #> weights: nb2listw(COL.nb) #> #> Moran I statistic standard deviate = 3.8402, p-value = 6.147e-05 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic Expectation Variance #> 0.341628707 -0.020833333 0.008908762 #> tmp <- try(moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(COL.nb), spChk=TRUE), silent=TRUE) set.spChkOption(oldChk) get.spChkOption() #> [1] FALSE"},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"function implements SKATER procedure spatial clustering analysis. procedure essentialy begins edges set, data set number cuts. output object 'skater' class valid input .","code":""},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"","code":"skater(edges, data, ncuts, crit, vec.crit, method = c(\"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\", \"minkowski\", \"mahalanobis\"), p = 2, cov, inverted = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"edges matrix 2 colums row edge data data.frame data observed nodes. ncuts number cuts crit scalar two dimensional vector criteria groups. Examples: limits group size limits population size. scalar, minimum criteria groups. vec.crit vector evaluating criteria. method Character function declare distance method. method character, method must \"mahalanobis\" \"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\" \"minkowisk\". method one \"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\" \"minkowski\", see dist details, function used compute distance. method=\"mahalanobis\", mahalanobis distance computed neighbour areas. method function, function used compute distance. p power Minkowski distance. cov covariance matrix used compute mahalanobis distance. inverted logical. 'TRUE', 'cov' supposed contain inverse covariance matrix.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"object skater class : groups vector length equal number nodes. position identifies group node edges.groups list length equal number groups element set edges .prune vector identifying groups candidates partition. candidates vector identifying groups candidates partition. ssto total dissimilarity step edge removal.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"Assuncao, R.M., Lage J.P., Reis, E.. (2002). Analise de conglomerados espaciais via arvore geradora minima. Revista Brasileira de Estatistica, 62, 1-23. Assuncao, R. M, Neves, M. C., Camara, G. Freitas, C. da C. (2006). Efficient regionalization techniques socio-economic geographical units using minimum spanning trees. International Journal Geographical Information Science Vol. 20, . 7, August 2006, 797-811","code":""},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"Renato M. Assuncao Elias T. Krainski","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/skater.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial 'K'luster Analysis by Tree Edge Removal — skater","text":"","code":"### loading data GDAL37 <- numeric_version(unname(sf::sf_extSoftVersion()[\"GDAL\"]), strict=FALSE) (GDAL37 <- ifelse(is.na(GDAL37), FALSE, GDAL37 >= \"3.7.0\")) #> [1] TRUE file <- \"etc/shapes/bhicv.gpkg.zip\" zipfile <- system.file(file, package=\"spdep\") if (GDAL37) { bh <- st_read(zipfile) } else { td <- tempdir() bn <- sub(\".zip\", \"\", basename(file), fixed=TRUE) target <- unzip(zipfile, files=bn, exdir=td) bh <- st_read(target) } #> Reading layer `bhicv' from data source #> `C:\\Users\\rzomor2\\AppData\\Local\\Temp\\RtmpErQTm3\\temp_libpath1a5cde63ff3\\spdep\\etc\\shapes\\bhicv.gpkg.zip' #> using driver `GPKG' #> Simple feature collection with 98 features and 8 fields #> Geometry type: POLYGON #> Dimension: XY #> Bounding box: xmin: -45.02175 ymin: -20.93007 xmax: -42.50321 ymax: -18.08342 #> Geodetic CRS: Corrego Alegre 1970-72 ### data standardized dim(bh) #> [1] 98 9 dpad <- data.frame(scale(as.data.frame(bh)[,5:8])) ### neighboorhod list bh.nb <- poly2nb(bh) bh.nb #> Neighbour list object: #> Number of regions: 98 #> Number of nonzero links: 508 #> Percentage nonzero weights: 5.289463 #> Average number of links: 5.183673 ### calculating costs lcosts <- nbcosts(bh.nb, dpad) head(lcosts) #> [[1]] #> [1] 1.5418355 2.5253558 1.4738620 1.8462822 1.7089412 1.5613667 1.0279919 #> [8] 0.6334314 1.9029531 2.5816759 #> #> [[2]] #> [1] 1.0847913 1.7723275 0.7940341 #> #> [[3]] #> [1] 1.257984 2.634043 0.847224 1.807124 #> #> [[4]] #> [1] 1.2579836 1.0548805 0.7862035 #> #> [[5]] #> [1] 1.541835 1.295112 2.206320 #> #> [[6]] #> [1] 0.9981915 1.3801441 1.5225548 1.3606678 0.9775650 #> ### making listw nb.w <- nb2listw(bh.nb, lcosts, style=\"B\") nb.w #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 98 #> Number of nonzero links: 508 #> Percentage nonzero weights: 5.289463 #> Average number of links: 5.183673 #> #> Weights style: B #> Weights constants summary: #> n nn S0 S1 S2 #> B 98 9604 1027.424 5192.868 55983.97 ### find a minimum spanning tree mst.bh <- mstree(nb.w,5) str(mst.bh) #> 'mst' num [1:97, 1:3] 5 12 13 13 11 31 39 40 31 40 ... ### the mstree plot par(mar=c(0,0,0,0)) plot(st_geometry(bh), border=gray(.5)) pts <- st_coordinates(st_centroid(bh)) #> Warning: st_centroid assumes attributes are constant over geometries plot(mst.bh, pts, col=2, cex.lab=.6, cex.circles=0.035, fg=\"blue\", add=TRUE) ### three groups with no restriction res1 <- spdep::skater(edges=mst.bh[,1:2], data=dpad, ncuts=2) ### groups size table(res1$groups) #> #> 1 2 3 #> 18 23 57 ### the skater plot opar <- par(mar=c(0,0,0,0)) plot(res1, pts, cex.circles=0.035, cex.lab=.7) ### the skater plot, using other colors plot(res1, pts, cex.circles=0.035, cex.lab=.7, groups.colors=heat.colors(length(res1$ed))) ### the Spatial Polygons plot plot(st_geometry(bh), col=heat.colors(length(res1$edg))[res1$groups]) #par(opar) ### EXPERT OPTIONS ### more one partition res1b <- spdep::skater(res1, dpad, 1) ### length groups frequency table(res1$groups) #> #> 1 2 3 #> 18 23 57 table(res1b$groups) #> #> 1 2 3 4 #> 18 23 55 2 ### thee groups with minimum population res2 <- spdep::skater(mst.bh[,1:2], dpad, 2, 200000, bh$Pop) table(res2$groups) #> #> 1 2 3 #> 22 37 39 ### thee groups with minimun number of areas res3 <- spdep::skater(mst.bh[,1:2], dpad, 2, 3, rep(1,nrow(bh))) table(res3$groups) #> #> 1 2 3 #> 18 23 57 ### thee groups with minimun and maximun number of areas res4 <- spdep::skater(mst.bh[,1:2], dpad, 2, c(20,50), rep(1,nrow(bh))) table(res4$groups) #> #> 1 2 3 #> 50 24 24 ### if I want to get groups with 20 to 40 elements res5 <- spdep::skater(mst.bh[,1:2], dpad, 2, c(20,40), rep(1,nrow(bh))) ## DON'T MAKE DIVISIONS table(res5$groups) #> #> 1 #> 98 ### In this MST don't have groups with this restrictions ### In this case, first I do one division ### with the minimun criteria res5a <- spdep::skater(mst.bh[,1:2], dpad, 1, 20, rep(1,nrow(bh))) table(res5a$groups) #> #> 1 2 #> 75 23 ### and do more one division with the full criteria res5b <- spdep::skater(res5a, dpad, 1, c(20, 40), rep(1,nrow(bh))) table(res5b$groups) #> #> 1 2 3 #> 22 23 53 ### and do more one division with the full criteria res5c <- spdep::skater(res5b, dpad, 1, c(20, 40), rep(1,nrow(bh))) table(res5c$groups) #> #> 1 2 3 4 #> 22 23 33 20 ### It don't have another divison with this criteria res5d <- spdep::skater(res5c, dpad, 1, c(20, 40), rep(1,nrow(bh))) table(res5d$groups) #> #> 1 2 3 4 #> 22 23 33 20 if (FALSE) { # \\dontrun{ data(boston, package=\"spData\") bh.nb <- boston.soi dpad <- data.frame(scale(boston.c[,c(7:10)])) ### calculating costs system.time(lcosts <- nbcosts(bh.nb, dpad)) ### making listw nb.w <- nb2listw(bh.nb, lcosts, style=\"B\") ### find a minimum spanning tree mst.bh <- mstree(nb.w,5) ### three groups with no restriction system.time(res1 <- spdep::skater(mst.bh[,1:2], dpad, 2)) library(parallel) nc <- max(2L, detectCores(logical=FALSE), na.rm = TRUE)-1L # set nc to 1L here if (nc > 1L) nc <- 1L coresOpt <- get.coresOption() invisible(set.coresOption(nc)) if(!get.mcOption()) { # no-op, \"snow\" parallel calculation not available cl <- makeCluster(get.coresOption()) set.ClusterOption(cl) } ### calculating costs system.time(plcosts <- nbcosts(bh.nb, dpad)) all.equal(lcosts, plcosts, check.attributes=FALSE) ### making listw pnb.w <- nb2listw(bh.nb, plcosts, style=\"B\") ### find a minimum spanning tree pmst.bh <- mstree(pnb.w,5) ### three groups with no restriction system.time(pres1 <- spdep::skater(pmst.bh[,1:2], dpad, 2)) if(!get.mcOption()) { set.ClusterOption(NULL) stopCluster(cl) } all.equal(res1, pres1, check.attributes=FALSE) invisible(set.coresOption(coresOpt)) } # }"},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial correlogram — sp.correlogram","title":"Spatial correlogram — sp.correlogram","text":"Spatial correlograms Moran's autocorrelation coefficient, print plot helper functions.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial correlogram — sp.correlogram","text":"","code":"sp.correlogram(neighbours, var, order = 1, method = \"corr\", style = \"W\", randomisation = TRUE, zero.policy = NULL, spChk=NULL) # S3 method for class 'spcor' plot(x, main, ylab, ylim, ...) # S3 method for class 'spcor' print(x, p.adj.method=\"none\", ...)"},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial correlogram — sp.correlogram","text":"neighbours object class nb var numeric vector order maximum lag order method \"corr\" correlation, \"\" Moran's , \"C\" Geary's C style style can take values W, B, C, S randomisation variance C calculated assumption randomisation, FALSE normality zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() x object sp.correlogram() class spcor p.adj.method correction method p.adjust main overall title plot ylab title y axis ylim y limits plot ... arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Spatial correlogram — sp.correlogram","text":"print function also calculates standard deviates Moran's Geary's C two-sided probability value, optionally using p.adjust correct nymber lags. plot function plots bar estimated Moran's , Geary's C value +/- twice square root variance (previous releases , twice). table includes count included observations brackets lag order. Care needs shown interpreting results remaining included observations lag order increases.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial correlogram — sp.correlogram","text":"returns list class spcor: res \"corr\" vector values; \"\", matrix estimates \"\", expectations, variances method \"\" \"corr\" cardnos list tables neighbour cardinalities lag orders used var variable name","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Spatial correlogram — sp.correlogram","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, pp. 118–122, Martin, R. L., Oeppen, J. E. 1975 identification regional forecasting models using space-time correlation functions, Transactions Institute British Geographers, 66, 95–118.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial correlogram — sp.correlogram","text":"Roger Bivand, Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/sp.correlogram.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial correlogram — sp.correlogram","text":"","code":"nc.sids <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\")[1], quiet=TRUE) rn <- as.character(nc.sids$FIPS) ncCC89_nb <- read.gal(system.file(\"weights/ncCC89.gal\", package=\"spData\")[1], region.id=rn) #> Warning: neighbour object has 3 sub-graphs ft.SID74 <- sqrt(1000)*(sqrt(nc.sids$SID74/nc.sids$BIR74) + sqrt((nc.sids$SID74+1)/nc.sids$BIR74)) tr.SIDS74 <- ft.SID74*sqrt(nc.sids$BIR74) cspc <- sp.correlogram(ncCC89_nb, tr.SIDS74, order=8, method=\"corr\", zero.policy=TRUE) #> Warning: lag 1 neighbour object has 3 sub-graphs #> Warning: lag 2 neighbour object has 3 sub-graphs #> Warning: lag 3 neighbour object has 3 sub-graphs #> Warning: lag 4 neighbour object has 3 sub-graphs #> Warning: lag 5 neighbour object has 3 sub-graphs #> Warning: lag 6 neighbour object has 3 sub-graphs #> Warning: lag 7 neighbour object has 3 sub-graphs #> Warning: lag 8 neighbour object has 3 sub-graphs print(cspc) #> Spatial correlogram for tr.SIDS74 #> method: Spatial autocorrelation #> 1 2 3 4 5 6 #> 0.38193491 0.47679881 0.11740653 0.09935901 0.27819159 0.30153012 #> 7 8 #> -0.05150923 0.05283813 plot(cspc) Ispc <- sp.correlogram(ncCC89_nb, tr.SIDS74, order=8, method=\"I\", zero.policy=TRUE) #> Warning: lag 1 neighbour object has 3 sub-graphs #> Warning: lag 2 neighbour object has 3 sub-graphs #> Warning: lag 3 neighbour object has 3 sub-graphs #> Warning: lag 4 neighbour object has 3 sub-graphs #> Warning: lag 5 neighbour object has 3 sub-graphs #> Warning: lag 6 neighbour object has 3 sub-graphs #> Warning: lag 7 neighbour object has 3 sub-graphs #> Warning: lag 8 neighbour object has 3 sub-graphs print(Ispc) #> Spatial correlogram for tr.SIDS74 #> method: Moran's I #> estimate expectation variance standard deviate Pr(I) two sided #> 1 (98) 0.2311685 -0.0103093 0.0055378 3.2450 0.0011747 ** #> 2 (98) 0.2246930 -0.0103093 0.0037817 3.8214 0.0001327 *** #> 3 (98) 0.0193576 -0.0103093 0.0029386 0.5473 0.5841914 #> 4 (98) 0.0042255 -0.0103093 0.0024974 0.2908 0.7711687 #> 5 (98) 0.0875548 -0.0103093 0.0022875 2.0462 0.0407386 * #> 6 (98) 0.0758362 -0.0103093 0.0021583 1.8543 0.0637011 . #> 7 (98) -0.0752243 -0.0103093 0.0022282 -1.3752 0.1690654 #> 8 (98) -0.0261063 -0.0103093 0.0025211 -0.3146 0.7530514 #> --- #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 print(Ispc, \"bonferroni\") #> Spatial correlogram for tr.SIDS74 #> method: Moran's I #> estimate expectation variance standard deviate Pr(I) two sided #> 1 (98) 0.2311685 -0.0103093 0.0055378 3.2450 0.009397 ** #> 2 (98) 0.2246930 -0.0103093 0.0037817 3.8214 0.001061 ** #> 3 (98) 0.0193576 -0.0103093 0.0029386 0.5473 1.000000 #> 4 (98) 0.0042255 -0.0103093 0.0024974 0.2908 1.000000 #> 5 (98) 0.0875548 -0.0103093 0.0022875 2.0462 0.325909 #> 6 (98) 0.0758362 -0.0103093 0.0021583 1.8543 0.509609 #> 7 (98) -0.0752243 -0.0103093 0.0022282 -1.3752 1.000000 #> 8 (98) -0.0261063 -0.0103093 0.0025211 -0.3146 1.000000 #> --- #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 plot(Ispc) Cspc <- sp.correlogram(ncCC89_nb, tr.SIDS74, order=8, method=\"C\", zero.policy=TRUE) #> Warning: lag 1 neighbour object has 3 sub-graphs #> Warning: lag 2 neighbour object has 3 sub-graphs #> Warning: lag 3 neighbour object has 3 sub-graphs #> Warning: lag 4 neighbour object has 3 sub-graphs #> Warning: lag 5 neighbour object has 3 sub-graphs #> Warning: lag 6 neighbour object has 3 sub-graphs #> Warning: lag 7 neighbour object has 3 sub-graphs #> Warning: lag 8 neighbour object has 3 sub-graphs print(Cspc) #> Spatial correlogram for tr.SIDS74 #> method: Geary's C #> estimate expectation variance standard deviate Pr(I) two sided #> 1 (98) 0.7172624 1.0000000 0.0059986 -3.6506 0.0002617 *** #> 2 (98) 0.6817819 1.0000000 0.0046785 -4.6523 3.282e-06 *** #> 3 (98) 0.9470179 1.0000000 0.0044311 -0.7959 0.4260762 #> 4 (98) 1.0016202 1.0000000 0.0041985 0.0250 0.9800516 #> 5 (98) 0.8977501 1.0000000 0.0038054 -1.6575 0.0974119 . #> 6 (98) 0.9173310 1.0000000 0.0036428 -1.3697 0.1707819 #> 7 (98) 1.0527148 1.0000000 0.0037227 0.8640 0.3875979 #> 8 (98) 1.0067939 1.0000000 0.0036482 0.1125 0.9104415 #> --- #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 print(Cspc, \"bonferroni\") #> Spatial correlogram for tr.SIDS74 #> method: Geary's C #> estimate expectation variance standard deviate Pr(I) two sided #> 1 (98) 0.7172624 1.0000000 0.0059986 -3.6506 0.002093 ** #> 2 (98) 0.6817819 1.0000000 0.0046785 -4.6523 2.626e-05 *** #> 3 (98) 0.9470179 1.0000000 0.0044311 -0.7959 1.000000 #> 4 (98) 1.0016202 1.0000000 0.0041985 0.0250 1.000000 #> 5 (98) 0.8977501 1.0000000 0.0038054 -1.6575 0.779295 #> 6 (98) 0.9173310 1.0000000 0.0036428 -1.3697 1.000000 #> 7 (98) 1.0527148 1.0000000 0.0037227 0.8640 1.000000 #> 8 (98) 1.0067939 1.0000000 0.0036482 0.1125 1.000000 #> --- #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 plot(Cspc) drop.no.neighs <- !(1:length(ncCC89_nb) %in% which(card(ncCC89_nb) == 0)) sub.ncCC89.nb <- subset(ncCC89_nb, drop.no.neighs) plot(sp.correlogram(sub.ncCC89.nb, subset(tr.SIDS74, drop.no.neighs), order=8, method=\"corr\"))"},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"permutation test spatial general cross product statistic Moran (\\(C_{ij} = z_i z_j\\)), Geary (\\(C_{ij} = (z_i - z_j)^2\\)), Sokal (\\(C_{ij} = |z_i - z_j|\\)) criteria, \\(z_i = (x_i - \\bar{x}) / \\sigma_{x}\\). plot.mc.sim helper function plot outcomes permutation test.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"","code":"sp.mantel.mc(var, listw, nsim, type = \"moran\", zero.policy = attr(listw, \"zero.policy\"), alternative = \"greater\", spChk=NULL, return_boot=FALSE) # S3 method for class 'mc.sim' plot(x, xlim, xlab, main, sub, ..., ptype=\"density\")"},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"var numeric vector length neighbours list listw listw listw object created example nb2listw nsim number permutations type \"moran\", \"geary\" \"sokal\" criteria similarity zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"two.sided\", \"less\". spChk data vector names checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() return_boot return object class boot equivalent permutation bootstrap rather object class htest x object plotted xlim range x axis xlab title x axis main overall title plot sub sub title plot ptype either \"density\" \"hist\" ... arguments passed ","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"list class htest mc.sim containing following components: statistic value observed Geary's C. parameter rank observed Geary's C. alternative character string describing alternative hypothesis. method character string giving method used. data.name character string giving name(s) data, number simulations. p.value pseudo p-value test. res nsim simulated values statistic, final value observed statistic estimate mean variance simulated distribution.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 22-24, Haining, R. 1990 Spatial data analysis social environmental sciences, Cambridge: Cambridge University Press, p. 230–1. function checked general matrix code posted r-help list Ben Bolker 1 May 2001; another mantel() function vegan package.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/sp.mantel.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Mantel-Hubert spatial general cross product statistic — sp.mantel.mc","text":"","code":"data(oldcol) sim1 <- sp.mantel.mc(COL.OLD$CRIME, nb2listw(COL.nb), nsim=99, type=\"geary\", alternative=\"two.sided\") sim1 #> #> \tMantel permutation test for geary measure #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.nb) #> number of simulations + 1: 100 #> #> statistic = 51.927, observed rank = 1, p-value = 0.02 #> alternative hypothesis: two.sided #> sample estimates: #> mean of permutations sd of permutations #> 98.852997 8.934135 #> plot(sim1) sp.mantel.mc(COL.OLD$CRIME, nb2listw(COL.nb), nsim=99, type=\"sokal\", alternative=\"two.sided\") #> #> \tMantel permutation test for sokal measure #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.nb) #> number of simulations + 1: 100 #> #> statistic = 36.695, observed rank = 1, p-value = 0.02 #> alternative hypothesis: two.sided #> sample estimates: #> mean of permutations sd of permutations #> 56.418584 3.227064 #> sp.mantel.mc(COL.OLD$CRIME, nb2listw(COL.nb), nsim=99, type=\"moran\") #> #> \tMantel permutation test for moran measure #> #> data: COL.OLD$CRIME #> weights: nb2listw(COL.nb) #> number of simulations + 1: 100 #> #> statistic = 24.526, observed rank = 100, p-value = 0.01 #> alternative hypothesis: greater #> sample estimates: #> mean of permutations sd of permutations #> -0.3401381 4.5579226 #>"},{"path":"https://r-spatial.github.io/spdep/reference/spatialdelta.html","id":null,"dir":"Reference","previous_headings":"","what":"Weighted Multivariate Spatial Autocorrelation Measures — spatialdelta","title":"Weighted Multivariate Spatial Autocorrelation Measures — spatialdelta","text":"kernel-based weighted multivariate spatial autocorrelation measure delta proposed Bavaud (2024) implemented, together support functions create spatial weights matrices symmetric binary adjacency matrices; summary display methods provided.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spatialdelta.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Weighted Multivariate Spatial Autocorrelation Measures — spatialdelta","text":"","code":"spatialdelta(dissimilarity_matrix, adjusted_spatial_weights, regional_weights=NULL, alternative = \"greater\") # S3 method for class 'spatialdelta' summary(object, ...) # S3 method for class 'summary.spatialdelta' print(x, digits=getOption(\"digits\"), ...) linearised_diffusive_weights(adjacency_matrix, regional_weights, t_choice = 2) metropolis_hastings_weights(adjacency_matrix, regional_weights) iterative_proportional_fitting_weights(adjacency_matrix, regional_weights, g=0.001, iter=1000, tol=1e-10, tol.margins=1e-10, print=FALSE) graph_distance_weights(adjacency_matrix, regional_weights, c=NULL) # S3 method for class 'adjusted_spatial_weights' as.matrix(x, ...) plot_spatialcoords(x, ...) # Default S3 method plot_spatialcoords(x, ...) # S3 method for class 'spatialdelta' plot_spatialcoords(x, cols = c(1L, 2L), mult = c(1, 1), power = 1L, fmult = NULL, names = attr(x, \"rnames\"), bg = 1, pos = 3, cex = 0.6, largest = NULL, ...) plot_moran(x, y, ...) # Default S3 method plot_moran(x, y, ...) # S3 method for class 'spatialdelta' plot_moran(x, y, fmult = NULL, names = attr(x, \"rnames\"), bg = 1, pos = 3, cex = 0.6, largest = NULL, ...) plot_spatialscree(x, ...) # Default S3 method plot_spatialscree(x, ...) # S3 method for class 'spatialdelta' plot_spatialscree(x, lwd=2, ...) factorial_coordinates(x) # Default S3 method factorial_coordinates(x) # S3 method for class 'spatialdelta' factorial_coordinates(x) plot_factorialcoords(x, ...) # Default S3 method plot_factorialcoords(x, ...) # S3 method for class 'spatialdelta' plot_factorialcoords(x, cols = c(1L, 2L), mult = c(1, 1), fmult = NULL, names = attr(x, \"rnames\"), bg = 1, pos = 3, cex = 0.6, largest = NULL, ...) plot_factorialscree(x, ...) # Default S3 method plot_factorialscree(x, ...) # S3 method for class 'spatialdelta' plot_factorialscree(x, ...) localdelta(x, ...) # Default S3 method localdelta(x, ...) # S3 method for class 'spatialdelta' localdelta(x, names = attr(x, \"rnames\"), ...) cornish_fisher(x, ...) # Default S3 method cornish_fisher(x, ...) # S3 method for class 'spatialdelta' cornish_fisher(x, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/spatialdelta.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Weighted Multivariate Spatial Autocorrelation Measures — spatialdelta","text":"dissimilarity_matrix dissimilarity_matrix square matrix dissimilarities (possibly multivariate) observations adjusted_spatial_weights adjusted_spatial_weights square matrix spatial weights returned construction functions linearised_diffusive_weights, metropolis_hastings_weights, iterative_proportional_fitting_weights, graph_distance_weights similar; named construction functions pass regional_weights spatialdelta, matrices constructed ways, argument required regional_weights default NULL, regional_weights weights reflecting contribution observation (possibly multivariate) data set, may uniform, none can zero, must sum unity; adjusted_spatial_weights \"adjusted_spatial_weights\" object created linearised_diffusive_weights, metropolis_hastings_weights, iterative_proportional_fitting_weights graph_distance_weights, regional_weights passed attribute alternative character string specifying alternative hypothesis, must one \"greater\" (default), \"less\" \"two.sided\" object, x object, x objects returned spatialdelta class \"spatialdelta\", class \"adjusted_spatial_weights\" digits default getOption(\"digits\"), non-null value specifying minimum number significant digits printed values adjacency_matrix adjacency_matrix symmetric binary adjacency matrix t_choice default 2, inverse largest eigenvalue adjusted Laplacian adjacency matrix (t2, Bavaud 2024, page 583), otherwise 1 (t1, page 579) g default 0.001, (Bavaud 2024, page 579, 589), small quantity lift binary adjacency matrix zero iter, tol, tol.margins, print arguments passed Ipfp c default NULL, coefficient greater zero less equal -1/min(B) B matrix scalar products associated distance matrix; given, -1/min(B) used y numeric vector create Moran plot cols integer vector length 2, default c(1L, 2L), giving two columns regional factorial coordinates plot mult numeric vector length 2, default c(1, 1), scale reverse axes signs given different eigenproblem implementations power integer vector length 1, default 1; higher, use powered kernel fmult default NULL automatic scaling circle symbols expressing observation weights f plot (0.02*diff(range(X)))/diff(range(regional_weights)) X first vector coordinates; may set manually numeric value names default attr(x, \"rnames\"), coordinates annotated strings passed \"region.id\" attribute \"nb\" object used create adjusted_spatial_weights matrix \"adjacency_matrix\" object row column names bg, pos, cex, lwd arguments passed graphics functions methods largest default NULL, may integer > 0 <= region count, permitting names plotted largest circle symbols ... arguments passed functions methods","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spatialdelta.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Weighted Multivariate Spatial Autocorrelation Measures — spatialdelta","text":"general, user choose one functions constructing spatial weights symmetric binary, similar symmetric - example row-standardised - adjacency matrix. cornish_fisher method updates standard deviate p-value pair skewness excess kurtosis estimates within required domain.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spatialdelta.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Weighted Multivariate Spatial Autocorrelation Measures — spatialdelta","text":"spatialdelta returns object classes \"spatialdelta\" \"htest\". print method treats \"htest\" object. methods use additional attributes: Kx Multivariate kernel matrix eq. 16 Kw Spatial weights kernel matrix eq. 21 regional_weights Input observation weights adjusted_spatial_weights Input spatial adjusted_spatial_weightseights B symmetric matrix scalar products eq. 15 VI Spatial component delta variance Vx Multivariate component delta variance Vd0 Variance delta calculated another way eq. 38 alphamu Spatial component delta skewness alphalambda Multivariate component delta skewness gammamu Spatial component delta excess kurtosis gammalambda Multivariate component delta excess kurtosis rnames Region names passed row/column names adjusted_spatial_weights, \"region.id\" attribute \"nb\" object used create adjusted_spatial_weights matrix \"adjacency_matrix\" object linearised_diffusive_weights, metropolis_hastings_weights, iterative_proportional_fitting_weights graph_distance_weights return square spatial weights matrices (latter two return matrices created metropolis_hastings_weights igraph mipfp available); factorial_coordinates returns square factorial matrix; localdelta returns vector local deltas eq. 30.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spatialdelta.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Weighted Multivariate Spatial Autocorrelation Measures — spatialdelta","text":"Bavaud, F. (2024), Measuring Testing Multivariate Spatial Autocorrelation Weighted Setting: Kernel Approach. Geographical Analysis, 56: 573-599. doi:10.1111/gean.12390","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spatialdelta.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Weighted Multivariate Spatial Autocorrelation Measures — spatialdelta","text":"Roger Bivand, Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spatialdelta.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Weighted Multivariate Spatial Autocorrelation Measures — spatialdelta","text":"input adjacency matrix symmetric, sub-graphs islands - possible step across graph edges observation .","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/spatialdelta.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Weighted Multivariate Spatial Autocorrelation Measures — spatialdelta","text":"","code":"toy_f <- c(0.4, 0.1, 0.3, 0.2) toy_xa <- c(4, 9, 1, 1) toy_nba <- structure(list(c(2L, 3L, 4L), c(1L), c(1L, 4L), c(1L, 3L)), class=\"nb\", region.id=as.character(1:4)) toy_gla <- list(c(0.25, 0.5, 0.25), c(1), c(2/3, 1/3), c(0.5, 0.5)) toy_wa <- nb2mat(toy_nba, glist=toy_gla, style=\"W\") spatialdelta(dissimilarity_matrix=as.matrix(dist(toy_xa))^2, adjusted_spatial_weights=toy_wa, regional_weights=toy_f, alternative=\"two.sided\") #> #> \tBavaud delta normal approximation #> #> data: as.matrix(dist(toy_xa))^2 #> weights: toy_wa #> Standard deviate = 1.9799, p-value = 0.04771 #> alternative hypothesis: two.sided #> sample estimates: #> delta Expectation Variance Skewness Excess Kurtosis #> 0.13333333 -0.33333333 0.05555556 0.16162441 Inf #> toy_xb <- toy_xa toy_glb <- list(c(0.5, 0.125, 0.25, 0.125), c(0.5, 0.5), c(1/3, 0.5, 1/6), c(0.25, 0.25, 0.5)) toy_nbb <- include.self(toy_nba) toy_wb <- nb2mat(toy_nbb, glist=toy_glb, style=\"W\") spatialdelta(dissimilarity_matrix=as.matrix(dist(toy_xb))^2, adjusted_spatial_weights=toy_wb, regional_weights=toy_f, alternative=\"two.sided\") #> #> \tBavaud delta normal approximation #> #> data: as.matrix(dist(toy_xb))^2 #> weights: toy_wb #> Standard deviate = 1.9799, p-value = 0.04771 #> alternative hypothesis: two.sided #> sample estimates: #> delta Expectation Variance Skewness Excess Kurtosis #> 0.56666667 0.33333333 0.01388889 0.16162441 Inf #> toy_xc <- c(3, 3, 1, 1) toy_nbc <- structure(list(c(3L, 4L), c(3L, 4L), c(1L, 2L), c(1L, 2L)), class=\"nb\", region.id=as.character(1:4)) toy_glc <- list(c(0.6, 0.4), c(0.6, 0.4), c(0.8, 0.2), c(0.8, 0.2)) toy_wc <- nb2mat(toy_nbc, glist=toy_glc, style=\"W\") spatialdelta(dissimilarity_matrix=as.matrix(dist(toy_xc))^2, adjusted_spatial_weights=toy_wc, regional_weights=toy_f, alternative=\"two.sided\") #> #> \tBavaud delta normal approximation #> #> data: as.matrix(dist(toy_xc))^2 #> weights: toy_wc #> Standard deviate = -2.2361, p-value = 0.02535 #> alternative hypothesis: two.sided #> sample estimates: #> delta Expectation Variance Skewness Excess Kurtosis #> -1.00000000 -0.33333333 0.08888889 -0.63887656 Inf #> # \\donttest{ if (require(Guerry, quietly=TRUE)) { data(gfrance85) gfrance85 <- st_as_sf(gfrance85) moral <- scale(st_drop_geometry(gfrance85)[, 7:12]) Dmoral <- as.matrix(dist(moral))^2 fG <- gfrance85$Pop1831/sum(gfrance85$Pop1831) gnb <- poly2nb(gfrance85, row.names=gfrance85$Department) frG <- nb2mat(gnb, style=\"B\") ldwG <- linearised_diffusive_weights(adjacency_matrix=frG, regional_weights=fG) mhwG <- metropolis_hastings_weights(adjacency_matrix=frG, regional_weights=fG) ifwG <- iterative_proportional_fitting_weights(adjacency_matrix=frG, regional_weights=fG) gdwG <- graph_distance_weights(adjacency_matrix=frG, regional_weights=fG) (moral_ldw <- spatialdelta(dissimilarity_matrix=Dmoral, adjusted_spatial_weights=ldwG)) (cornish_fisher(moral_ldw)) moral_mhw <- spatialdelta(dissimilarity_matrix=Dmoral, adjusted_spatial_weights=mhwG) moral_ifw <- spatialdelta(dissimilarity_matrix=Dmoral, adjusted_spatial_weights=ifwG) moral_gdw <- spatialdelta(dissimilarity_matrix=Dmoral, adjusted_spatial_weights=gdwG) opar <- par(mfrow=c(2, 2)) plot_spatialcoords(moral_ldw, cols=c(2,1), mult=c(-1, -1), main=\"Linearised Diffusive\", asp=1) plot_spatialcoords(moral_mhw, cols=c(2,1), mult=c(1, 1), main=\"Metropolis-Hastings\", asp=1) plot_spatialcoords(moral_ifw, cols=c(2,1), mult=c(1, 1), main=\"Iterative fitting\", asp=1) plot_spatialcoords(moral_gdw, cols=c(2,1), mult=c(1, 1), main=\"Graph distance\", asp=1) par(opar) opar <- par(mfrow=c(2, 2)) plot_spatialscree(moral_ldw, main=\"linearised diffusive\") plot_spatialscree(moral_mhw, main=\"Metropolis-Hastings\") plot_spatialscree(moral_ifw, main=\"iterative fitting\") plot_spatialscree(moral_gdw, main=\"graph distance\") par(opar) Crime_pers <- scale(gfrance85$Crime_pers) funif <- rep(1/length(Crime_pers), length(Crime_pers)) lw <- nb2listw(gnb, style=\"W\") Crime_pers_delta <- spatialdelta(dissimilarity_matrix=as.matrix(dist(Crime_pers))^2, adjusted_spatial_weights=listw2mat(lw), regional_weights=funif) Crime_pers_delta$estimate[\"delta\"] locdelta <- localdelta(Crime_pers_delta) moran.test(Crime_pers, lw, randomisation=FALSE)$estimate[\"Moran I statistic\"] locmoran <- localmoran(c(Crime_pers), lw)[,1] all.equal(locmoran, locdelta) all.equal(unname(moral_ldw$estimate[\"delta\"]), # Eq. 30 p. 588 sum(fG * localdelta(moral_ldw))) all.equal(unname(moral_mhw$estimate[\"delta\"]), # Eq. 30 p. 588 sum(fG * localdelta(moral_mhw))) all.equal(unname(moral_ifw$estimate[\"delta\"]), # Eq. 30 p. 588 sum(fG * localdelta(moral_ifw))) all.equal(unname(moral_gdw$estimate[\"delta\"]), # Eq. 30 p. 588 sum(fG * localdelta(moral_gdw))) } # }"},{"path":"https://r-spatial.github.io/spdep/reference/spdep-defunct.html","id":null,"dir":"Reference","previous_headings":"","what":"Defunct Functions in Package spdep — spdep-defunct","title":"Defunct Functions in Package spdep — spdep-defunct","text":"functions defunct release 1.2-1. functions moved spatialreg package.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spdep-defunct.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Defunct Functions in Package spdep — spdep-defunct","text":"","code":"aple.plot() localAple() aple.mc() aple() lextrB() lextrW() lextrS() griffith_sone() subgraph_eigenw() mom_calc() mom_calc_int2() stsls() # S3 method for class 'stsls' impacts() GMerrorsar() # S3 method for class 'gmsar' summary() gstsls() # S3 method for class 'gmsar' impacts() # S3 method for class 'gmsar' Hausman.test() lagmess() ME() SpatialFiltering() LR.sarlm() # S3 method for class 'sarlm' logLik() LR1.sarlm() Wald1.sarlm() # S3 method for class 'sarlm' Hausman.test() as.spam.listw() as_dgRMatrix_listw() as_dsTMatrix_listw() as_dsCMatrix_I() as_dsCMatrix_IrW() Jacobian_W() powerWeights() # S3 method for class 'lagImpact' plot() # S3 method for class 'lagImpact' print() # S3 method for class 'lagImpact' summary() # S3 method for class 'lagImpact' HPDinterval() intImpacts() can.be.simmed() eigenw() similar.listw() do_ldet() jacobianSetup() cheb_setup() mcdet_setup() eigen_setup() eigen_pre_setup() spam_setup() spam_update_setup() Matrix_setup() Matrix_J_setup() LU_setup() LU_prepermutate_setup() moments_setup() SE_classic_setup() SE_whichMin_setup() SE_interp_setup() MCMCsamp() # S3 method for class 'spautolm' MCMCsamp() # S3 method for class 'sarlm' MCMCsamp() spautolm() # S3 method for class 'spautolm' summary() spBreg_sac() # S3 method for class 'MCMC_sar_g' impacts() # S3 method for class 'MCMC_sem_g' impacts() # S3 method for class 'MCMC_sac_g' impacts() spBreg_err() spBreg_lag() # S3 method for class 'SLX' predict() lmSLX() # S3 method for class 'SLX' impacts() create_WX() # S3 method for class 'sarlm' anova() bptest.sarlm() errorsarlm() # S3 method for class 'sarlm' impacts() lagsarlm() # S3 method for class 'sarlm' predict() # S3 method for class 'sarlm.pred' print() # S3 method for class 'sarlm.pred' as.data.frame() # S3 method for class 'sarlm' residuals() # S3 method for class 'sarlm' deviance() # S3 method for class 'sarlm' coef() # S3 method for class 'sarlm' vcov() # S3 method for class 'sarlm' fitted() sacsarlm() # S3 method for class 'sarlm' summary() # S3 method for class 'sarlm' print() # S3 method for class 'summary.sarlm' print() trW()"},{"path":"https://r-spatial.github.io/spdep/reference/spdep-defunct.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Defunct Functions in Package spdep — spdep-defunct","text":"Model-fitting functions functions supporting model fitting moved spatialreg package.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/spdep.html","id":null,"dir":"Reference","previous_headings":"","what":"Return package version number — spdep","title":"Return package version number — spdep","text":"function retreives package version build information","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spdep.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Return package version number — spdep","text":"","code":"spdep(build = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/spdep.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Return package version number — spdep","text":"build TRUE, also returns build information","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spdep.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Return package version number — spdep","text":"character vector one two elements","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spdep.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Return package version number — spdep","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":null,"dir":"Reference","previous_headings":"","what":"Provides constants for spatial weights matrices — spweights.constants","title":"Provides constants for spatial weights matrices — spweights.constants","text":"function calculates constants needed tests spatial autocorrelation general weights matrices represented listw objects. Note: spdep 0.3-32, values S1 S2 returned correctly underlying symmetric asymmetric neighbour lists, 0.3-32, S1 S2 wrong listw objects based asymmetric neighbour lists, k-nearest neighbours (thanks Luc Anselin finding bug).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Provides constants for spatial weights matrices — spweights.constants","text":"","code":"spweights.constants(listw, zero.policy=attr(listw, \"zero.policy\"), adjust.n=TRUE) Szero(listw)"},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Provides constants for spatial weights matrices — spweights.constants","text":"listw listw object example nb2listw zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; TRUE ignore zones without neighbours, FALSE fail encountered adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations adjusted","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Provides constants for spatial weights matrices — spweights.constants","text":"n number zones n1 n - 1 n2 n - 2 n3 n - 3 nn n * n S0 global sum weights S1 S1 sum weights S2 S2 sum weights","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Provides constants for spatial weights matrices — spweights.constants","text":"Haining, R. 1990 Spatial data analysis social environmental sciences, Cambridge University Press, p. 233; Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 19, 21.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Provides constants for spatial weights matrices — spweights.constants","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/spweights.constants.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Provides constants for spatial weights matrices — spweights.constants","text":"","code":"data(oldcol) B <- spweights.constants(nb2listw(COL.nb, style=\"B\")) W <- spweights.constants(nb2listw(COL.nb, style=\"W\")) C <- spweights.constants(nb2listw(COL.nb, style=\"C\")) S <- spweights.constants(nb2listw(COL.nb, style=\"S\")) U <- spweights.constants(nb2listw(COL.nb, style=\"U\")) print(data.frame(rbind(unlist(B), unlist(W), unlist(C), unlist(S), unlist(U)), row.names=c(\"B\", \"W\", \"C\", \"S\", \"U\"))) #> n n1 n2 n3 nn S0 S1 S2 #> B 49 48 47 46 2401 232 464.00000000 5.136000e+03 #> W 49 48 47 46 2401 49 23.29434146 2.048729e+02 #> C 49 48 47 46 2401 49 20.69827586 2.291085e+02 #> S 49 48 47 46 2401 49 21.25561347 2.134568e+02 #> U 49 48 47 46 2401 1 0.00862069 9.542212e-02"},{"path":"https://r-spatial.github.io/spdep/reference/ssw.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute the sum of dissimilarity — ssw","title":"Compute the sum of dissimilarity — ssw","text":"function computes sum dissimilarity observation mean (scalar vector) observations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/ssw.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute the sum of dissimilarity — ssw","text":"","code":"ssw(data, id, method = c(\"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\", \"minkowski\", \"mahalanobis\"), p = 2, cov, inverted = FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/ssw.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute the sum of dissimilarity — ssw","text":"data matrix observations nodes. id Node index compute cost method Character function declare distance method. method character, method must \"mahalanobis\" \"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\" \"minkowisk\". method one \"euclidean\", \"maximum\", \"manhattan\", \"canberra\", \"binary\" \"minkowisk\", see dist details, function used compute distance. method=\"mahalanobis\", mahalanobis distance computed neighbour areas. method function, function used compute distance. p power Minkowski distance. cov covariance matrix used compute mahalanobis distance. inverted logical. 'TRUE', 'cov' supposed contain inverse covariance matrix.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/ssw.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute the sum of dissimilarity — ssw","text":"numeric, sum dissimilarity observations id data mean (scalar vector) observations.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/ssw.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute the sum of dissimilarity — ssw","text":"Elias T. Krainski Renato M. Assuncao","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/ssw.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute the sum of dissimilarity — ssw","text":"","code":"data(USArrests) n <- nrow(USArrests) ssw(USArrests, 1:n) #> [1] 3701.394 ssw(USArrests, 1:(n/2)) #> [1] 1910.214 ssw(USArrests, (n/2+1):n) #> [1] 1625.882 ssw(USArrests, 1:(n/2)) + ssw(USArrests, (n/2+1):n) #> [1] 3536.096"},{"path":"https://r-spatial.github.io/spdep/reference/subset.listw.html","id":null,"dir":"Reference","previous_headings":"","what":"Subset a spatial weights list — subset.listw","title":"Subset a spatial weights list — subset.listw","text":"function subsets spatial weights list, retaining objects subset argument vector TRUE. present subset non-general weights lists (created nb2listw glist=NULL).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/subset.listw.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Subset a spatial weights list — subset.listw","text":"","code":"# S3 method for class 'listw' subset(x, subset, zero.policy = attr(x, \"zero.policy\"), ...)"},{"path":"https://r-spatial.github.io/spdep/reference/subset.listw.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Subset a spatial weights list — subset.listw","text":"x object class listw subset logical expression zero.policy default attr(x, \"zero.policy\") set x created, attribute set, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors - passed nb2listw ... generic function pass-","code":""},{"path":"https://r-spatial.github.io/spdep/reference/subset.listw.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Subset a spatial weights list — subset.listw","text":"function returns object class listw component style input object, component neighbours list integer vectors containing neighbour region number ids (compacted run 1:number regions subset), component weights weights computed neighbours using style. -neighbour observations created subsetting zero.policy input weights object FALSE, set TRUE warning issued.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/subset.listw.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Subset a spatial weights list — subset.listw","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/subset.listw.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Subset a spatial weights list — subset.listw","text":"","code":"col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) to.be.dropped <- c(31, 34, 36, 39, 42, 46) pre <- nb2listw(col.gal.nb) print(pre) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> #> Weights style: W #> Weights constants summary: #> n nn S0 S1 S2 #> W 49 2401 49 23.48489 204.6687 post <- subset(pre, !(1:length(col.gal.nb) %in% to.be.dropped)) print(post) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 43 #> Number of nonzero links: 212 #> Percentage nonzero weights: 11.46566 #> Average number of links: 4.930233 #> #> Weights style: W #> Weights constants summary: #> n nn S0 S1 S2 #> W 43 1849 43 19.26584 178.4604 columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) nb <- poly2nb(columbus) lw <- nb2listw(nb, style=\"W\") attr(lw, \"zero.policy\") #> [1] FALSE (lwa <- subset(lw, 1:nrow(columbus) != c(21))) #> Warning: subsetting caused increase in subgraph count #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 48 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.982639 #> Average number of links: 4.791667 #> 2 disjoint connected subgraphs #> #> Weights style: W #> Weights constants summary: #> n nn S0 S1 S2 #> W 48 2304 48 22.46811 199.4398 attr(lwa, \"zero.policy\") #> [1] FALSE (lwb <- subset(lw, !(1:nrow(columbus) %in% c(21, 36, 39)))) #> Warning: subsetting caused increase in subgraph count #> Warning: subsetting created no-neighbour observations, zero.policy set TRUE #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 46 #> Number of nonzero links: 216 #> Percentage nonzero weights: 10.20794 #> Average number of links: 4.695652 #> 1 region with no links: #> 46 #> 3 disjoint connected subgraphs #> #> Weights style: W #> Weights constants summary: #> n nn S0 S1 S2 #> W 45 2025 45 22.857 187.4843 attr(lwb, \"zero.policy\") #> [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/reference/subset.nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Subset a neighbours list — subset.nb","title":"Subset a neighbours list — subset.nb","text":"function subsets neighbors list, retaining objects subset argument vector TRUE.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/subset.nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Subset a neighbours list — subset.nb","text":"","code":"# S3 method for class 'nb' subset(x, subset, ...)"},{"path":"https://r-spatial.github.io/spdep/reference/subset.nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Subset a neighbours list — subset.nb","text":"x object class nb subset logical expression ... generic function pass-","code":""},{"path":"https://r-spatial.github.io/spdep/reference/subset.nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Subset a neighbours list — subset.nb","text":"function returns object class nb list integer vectors containing neighbour region number ids (compacted run 1:number regions subset).","code":""},{"path":"https://r-spatial.github.io/spdep/reference/subset.nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Subset a neighbours list — subset.nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/subset.nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Subset a neighbours list — subset.nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries plot(col.gal.nb, coords) to.be.dropped <- c(31, 34, 36, 39, 42, 46) text(coords[to.be.dropped,1], coords[to.be.dropped,2], labels=to.be.dropped, pos=2, offset=0.3) sub.col.gal.nb <- subset(col.gal.nb, !(1:length(col.gal.nb) %in% to.be.dropped)) plot(sub.col.gal.nb, coords[-to.be.dropped,], col=\"red\", add=TRUE) which(!(attr(col.gal.nb, \"region.id\") %in% attr(sub.col.gal.nb, \"region.id\"))) #> [1] 31 34 36 39 42 46"},{"path":"https://r-spatial.github.io/spdep/reference/summary.nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Print and summary function for neighbours and weights lists — summary.nb","title":"Print and summary function for neighbours and weights lists — summary.nb","text":"function prints summary measures links neighbours list. matrix coordinates given well, summary descriptive measures link lengths also printed. Print summary functions also available \"listw\" weights list objects, also reporting constants (S0, S1, S2) used inference global spatial autocorrelation statistics Moran's , Geary's C, join-count tests Getis-Ord G.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/summary.nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Print and summary function for neighbours and weights lists — summary.nb","text":"","code":"# S3 method for class 'nb' summary(object, coords=NULL, longlat = NULL, scale = 1, ...) # S3 method for class 'nb' print(x, ...) # S3 method for class 'listw' summary(object, coords, longlat, zero.policy = attr(object, \"zero.policy\"), scale = 1, adjust.n=TRUE, ...) # S3 method for class 'listw' print(x, zero.policy = attr(x, \"zero.policy\"), ...)"},{"path":"https://r-spatial.github.io/spdep/reference/summary.nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Print and summary function for neighbours and weights lists — summary.nb","text":"object object class nb coords matrix region point coordinates SpatialPoints object sfc points object longlat TRUE point coordinates longitude-latitude decimal degrees, case distances measured kilometers; coords SpatialPoints object, value taken object ... additional arguments affecting output produced x object class nb zero.policy default attr(listw, \"zero.policy\") set listw created, attribute set, use global option value; FALSE stop error empty neighbour sets scale passed stem() control plot length adjust.n default TRUE, FALSE number observations adjusted -neighbour observations, TRUE, number observations spweights.constants adjusted","code":""},{"path":"https://r-spatial.github.io/spdep/reference/summary.nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Print and summary function for neighbours and weights lists — summary.nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/summary.nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Print and summary function for neighbours and weights lists — summary.nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE) col.gal.nb #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 summary(col.gal.nb, coords) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> Link number distribution: #> #> 2 3 4 5 6 7 8 9 10 #> 7 7 13 4 9 6 1 1 1 #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links col.listw <- nb2listw(col.gal.nb, style=\"W\") col.listw #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> #> Weights style: W #> Weights constants summary: #> n nn S0 S1 S2 #> W 49 2401 49 23.48489 204.6687 summary(col.listw) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> Link number distribution: #> #> 2 3 4 5 6 7 8 9 10 #> 7 7 13 4 9 6 1 1 1 #> 7 least connected regions: #> 1 6 31 39 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links #> #> Weights style: W #> Weights constants summary: #> n nn S0 S1 S2 #> W 49 2401 49 23.48489 204.6687 col_geoms <- st_geometry(columbus) col_geoms[21] <- st_buffer(col_geoms[21], dist=-0.05) st_geometry(columbus) <- col_geoms nb <- poly2nb(columbus) #> Warning: some observations have no neighbours; #> if this seems unexpected, try increasing the snap argument. #> Warning: neighbour object has 3 sub-graphs; #> if this sub-graph count seems unexpected, try increasing the snap argument. summary(nb) #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> 1 region with no links: #> 21 #> 3 disjoint connected subgraphs #> Link number distribution: #> #> 0 2 3 4 5 6 7 8 9 10 #> 1 5 9 12 4 10 2 4 1 1 #> 5 least connected regions: #> 1 6 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links try(nb2listw(nb, style=\"W\")) #> Error in nb2listw(nb, style = \"W\") : #> Empty neighbour sets found (zero.policy: FALSE) summary(nb2listw(nb, style=\"W\", zero.policy=TRUE)) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> 1 region with no links: #> 21 #> 3 disjoint connected subgraphs #> Link number distribution: #> #> 0 2 3 4 5 6 7 8 9 10 #> 1 5 9 12 4 10 2 4 1 1 #> 5 least connected regions: #> 1 6 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links #> #> Weights style: W #> Weights constants summary: #> n nn S0 S1 S2 #> W 48 2304 48 22.46811 199.4398 summary(nb2listw(nb, style=\"W\", zero.policy=TRUE), adjust.n=FALSE) #> Characteristics of weights list object: #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 230 #> Percentage nonzero weights: 9.579342 #> Average number of links: 4.693878 #> 1 region with no links: #> 21 #> 3 disjoint connected subgraphs #> Link number distribution: #> #> 0 2 3 4 5 6 7 8 9 10 #> 1 5 9 12 4 10 2 4 1 1 #> 5 least connected regions: #> 1 6 42 46 47 with 2 links #> 1 most connected region: #> 20 with 10 links #> #> Weights style: W #> Weights constants summary: #> n nn S0 S1 S2 #> W 49 2401 48 22.46811 199.4398"},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":null,"dir":"Reference","previous_headings":"","what":"Test a neighbours list for symmetry — is.symmetric.nb","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"Checks neighbours list symmetry/transitivity (neighbour j, j neighbour ). holds distance contiguity based neighbours, k-nearest neighbours. helper function sym.attr.nb() calls .symmetric.nb() set sym attribute needed, make.sym.nb makes non-symmetric list symmetric adding neighbors. .symmetric.glist checks list general weights corresponding neighbours symmetry symmetric neighbours.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"","code":"is.symmetric.nb(nb, verbose = NULL, force = FALSE) sym.attr.nb(nb) make.sym.nb(nb) old.make.sym.nb(nb) is.symmetric.glist(nb, glist)"},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"nb object class nb list integer vectors containing neighbour region number ids. verbose default NULL, use global option value; TRUE prints non-matching pairs force respect neighbours list sym attribute test anyway glist list general weights corresponding neighbours","code":""},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"TRUE symmetric, FALSE ; .symmetric.glist returns value attribute, \"d\", indicating failed symmetry largest failing value.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"new version make.sym.nb Bjarke Christensen now included. older version renamed old.make.sym.nb, comparison constitutes nice demonstration vectorising speedup using sapply lapply rather loops. -neighbour observations present, old.make.sym.nb used.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/testnb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Test a neighbours list for symmetry — is.symmetric.nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) coords <- st_coordinates(st_centroid(columbus)) #> Warning: st_centroid assumes attributes are constant over geometries ind <- row.names(as(columbus, \"Spatial\")) print(is.symmetric.nb(col.gal.nb, verbose=TRUE, force=TRUE)) #> [1] TRUE k4 <- knn2nb(knearneigh(coords, k=4), row.names=ind) k4 <- sym.attr.nb(k4) print(is.symmetric.nb(k4)) #> [1] FALSE k4.sym <- make.sym.nb(k4) print(is.symmetric.nb(k4.sym)) #> [1] TRUE"},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"function creates object class nb (defined library spdep) containing connexion diagram. edges sites based tolerance angle maximum distance. angle directional; direction always bottow top screen.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"","code":"tolerance.nb(coords, unit.angle = \"degrees\", max.dist, tolerance, rot.angle, plot.sites=FALSE)"},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"coords matrix data frame containing X Y coordinates study sites. unit.angle Character. measurement units angles defined: either \"degrees\" (default) \"radians\". max.dist Numeric. maximum distance edge linking two sites together. tolerance Numeric. tolerance angle site can influence another site. angle measured vertically bottom top pictures rotation points. rot.angle Numeric, optional. angle set coordinates rotated creating connexion diagram. set coordinates rotated counterclockwise. Negative values produce clockwise rotation. plot.sites Logical (TRUE, FALSE) determining site plotted graphic window. graph allows one make sure points rotated correct direction.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"Even though function creates connexion diagram based tolerance angle going bottom top screen, resulting object symmetric, meaning site influences another vice versa. final object represent directional connexion network.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"function returns object class nb list integer vectors corresponding neighbour region numbers.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"warning","dir":"Reference","previous_headings":"","what":"Warning","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"function design handle large number rows coords. use function set coordinates 1500 entries memory intensive.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"F. Guillaume Blanchet","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/tolerance.nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Function to construct edges based on a tolerance angle and a maximum distance — tolerance.nb","text":"","code":"set.seed(1) ex.data<-cbind(runif(50),rexp(50)) ### Construct object of class nb with a tolerance angle of 30 degrees ### and a maximum distance of 2 m. nb.ex<-tolerance.nb(ex.data, unit.angle = \"degrees\", max.dist=1, tolerance = 30) #> Warning: neighbour object has 3 sub-graphs ### Construct object of class nb with a tolerance angle of 30 degrees ### and a maximum distance of 2 m. The coordinates are rotated at an angle ### of 45 degrees counterclockwise. nb.ex2<-tolerance.nb(ex.data, unit.angle = \"degrees\", max.dist=1, tolerance = 30, rot.angle = 45) #> Warning: neighbour object has 4 sub-graphs ### Construct object of class nb with a tolerance angle of pi/8 radians ### and a maximum distance of 1.5 m. The coordinates are rotated at ### an angle of pi/4 radians clockwise. nb.ex3<-tolerance.nb(ex.data, unit.angle = \"radians\", max.dist=1.5, tolerance = pi/8, rot.angle = -pi*2/3) #> Warning: neighbour object has 5 sub-graphs par(mfrow=c(1,3)) plot(nb.ex,ex.data,asp=1) plot(nb.ex2,ex.data,asp=1) plot(nb.ex3,ex.data,asp=1)"},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":null,"dir":"Reference","previous_headings":"","what":"Neighbours list from tri object — tri2nb","title":"Neighbours list from tri object — tri2nb","text":"function uses deldir package convert matrix two-dimensional coordinates neighbours list class nb list integer vectors containing neighbour region number ids.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Neighbours list from tri object — tri2nb","text":"","code":"tri2nb(coords, row.names = NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Neighbours list from tri object — tri2nb","text":"coords matrix, data.frame tibble point coordinates two columns, SpatialPoints object sfc points object row.names character vector region ids added neighbours list attribute region.id, default seq(1, nrow(x))","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Neighbours list from tri object — tri2nb","text":"coordinates duplicated, function used. coordinates grid, need ordered first three collinear, first triangle can constructed. can achieved randomising order coordinates (possibly several times), re-ordering order data match new order neighbour list - fix used, remember re-order row.names argument well coordinates! Please also note triangulation grid points give arbitrary diagonal neighbours, may sensible outcome, dnearneigh() may serve better tri2nb() used.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Neighbours list from tri object — tri2nb","text":"function returns object class nb list integer vectors containing neighbour region number ids.","code":""},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Neighbours list from tri object — tri2nb","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/tri2nb.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Neighbours list from tri object — tri2nb","text":"","code":"columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) coords <- st_centroid(st_geometry(columbus), of_largest_polygon=TRUE) ind <- row.names(columbus) suppressPackageStartupMessages(require(deldir)) col.tri.nb <- tri2nb(coords, row.names=ind) plot(st_geometry(columbus), border=\"grey\") plot(col.tri.nb, coords, add=TRUE) title(main=\"Raw triangulation links\", cex.main=0.6) x <- seq(0,1,0.1) y <- seq(0,2,0.2) xy <- expand.grid(x, y) try(xy.nb <- tri2nb(xy)) seed <- 1234 xid <- sample(1:nrow(xy)) xy.nb <- tri2nb(xy[xid,]) plot(xy.nb, xy[xid,]) # example of reading points with readr::read_csv() yielding a tibble load(system.file(\"etc/misc/coords.rda\", package=\"spdep\")) class(coords) #> [1] \"spec_tbl_df\" \"tbl_df\" \"tbl\" \"data.frame\" nb <- tri2nb(coords) plot(nb, coords)"},{"path":"https://r-spatial.github.io/spdep/reference/write.nb.gal.html","id":null,"dir":"Reference","previous_headings":"","what":"Write a neighbours list as a GAL lattice file — write.nb.gal","title":"Write a neighbours list as a GAL lattice file — write.nb.gal","text":"Write neighbours list GAL lattice file, may also use newer GeoDa header format","code":""},{"path":"https://r-spatial.github.io/spdep/reference/write.nb.gal.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Write a neighbours list as a GAL lattice file — write.nb.gal","text":"","code":"write.nb.gal(nb, file, oldstyle=TRUE, shpfile=NULL, ind=NULL)"},{"path":"https://r-spatial.github.io/spdep/reference/write.nb.gal.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Write a neighbours list as a GAL lattice file — write.nb.gal","text":"nb object class nb list integer vectors containing neighbour region number ids. file name file GAL lattice data oldstyle TRUE, first line file contains number spatial units, FALSE, uses newer GeoDa style shpfile Shapefile name taken GAL file dataset ind region id indicator variable name","code":""},{"path":"https://r-spatial.github.io/spdep/reference/write.nb.gal.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Write a neighbours list as a GAL lattice file — write.nb.gal","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spdep/reference/write.nb.gal.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Write a neighbours list as a GAL lattice file — write.nb.gal","text":"","code":"col.gal.nb <- read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) GALfile <- tempfile(\"GAL\") write.nb.gal(col.gal.nb, GALfile) col.queen <- read.gal(GALfile) summary(diffnb(col.queen, col.gal.nb)) #> Warning: neighbour object has 49 sub-graphs #> Neighbour list object: #> Number of regions: 49 #> Number of nonzero links: 0 #> Percentage nonzero weights: 0 #> Average number of links: 0 #> 49 regions with no links: #> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, #> 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, #> 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 #> 49 disjoint connected subgraphs #> Link number distribution: #> #> 0 #> 49"},{"path":[]},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-1-3-13-2025-06-10","dir":"Changelog","previous_headings":"","what":"Version 1-3-13 (2025-06-10)","title":"Version 1-3-13 (2025-06-10)","text":"Adds Bavaud’s multivariate spatialdelta support functions methods Add note changes output tests error autocorrelation contrast codings set non-default values","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-11-2025-04-24","dir":"Changelog","previous_headings":"","what":"Version 1.3-11 (2025-04-24)","title":"Version 1.3-11 (2025-04-24)","text":"CRAN release: 2025-04-24 introduce warnings factors (categorical variables) Durbin models (SD.RStests) remove |> vignette avoid R >= 4.1 dependency https://stat.ethz.ch/pipermail/r-devel/2025-January/083768.html update reference Koley (2024) man/SD.RStests.Rd add warnings Durbin terms including categorical variables SD.RStests","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-10-2025-01-20","dir":"Changelog","previous_headings":"","what":"Version 1.3-10 (2025-01-20)","title":"Version 1.3-10 (2025-01-20)","text":"CRAN release: 2025-01-20 R_NO_REMAP problem R < 4.4.1 fixed replacing COPY_TO_USER_STRING Rf_mkChar, include/Rdefines.h revision 86416 set COPY_TO_USER_STRING mkChar defined Rf_mkChar R_NO_REMAP defined, #176, thanks Edzer Pebesma disambiguate skater examples satisfy pkgdown, used rgeoda::skater; patches examples satisfy pkgdown use inherits skater","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-9-2025-01-16","dir":"Changelog","previous_headings":"","what":"Version 1.3-9 (2025-01-16)","title":"Version 1.3-9 (2025-01-16)","text":"CRAN release: 2025-01-16 revisit diffnb set operations like union.nb setdiff.nb following #175; diffnb largely rewritten longer generate deformed output; set operations modified match base functions actions convert error Rf_error, length Rf_length etc. accommodate R_NO_REMAP, see https://github.com/r-spatial/spdep/commit/b61f6b17be09383c94b45e912f9213735aa62212 R 4.5 re-instate rgeoda references","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-8-2024-12-02","dir":"Changelog","previous_headings":"","what":"Version 1.3-8 (2024-12-02)","title":"Version 1.3-8 (2024-12-02)","text":"CRAN release: 2024-12-02 Remove remaining spData ESRI shapefile use","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-7-2024-11-25","dir":"Changelog","previous_headings":"","what":"Version 1.3-7 (2024-11-25)","title":"Version 1.3-7 (2024-11-25)","text":"CRAN release: 2024-11-25 (temporarily) remove rgeoda references successfully re-submitted CRAN add write.swmdbf #171 complement #163 modify defaults licd_multi","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-6-2024-09-13","dir":"Changelog","previous_headings":"","what":"Version 1.3-6 (2024-09-13)","title":"Version 1.3-6 (2024-09-13)","text":"CRAN release: 2024-09-13 adding vignette describing recent changes poly2nb #162, subgraph -neighbour (island) handling adding prototype LICD ESDA function licd_multi hotspot method add read.swmdbf2listw #163 reading DBF files exported ArcGIS representing SWM objects; note problems observation IDs known, see help file #162 add option -neighbour checking poly2nb - default report whether -neighbour observations present #162 change default snap= argument poly2nb 10mm Condition forthcoming tmap 4 #160 handle n.comp.nb delay print.nb elsewhere total number neighbours large","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-5-2024-06-10","dir":"Changelog","previous_headings":"","what":"Version 1.3-5 (2024-06-10)","title":"Version 1.3-5 (2024-06-10)","text":"CRAN release: 2024-06-10 #157 migrate ESRI Shapefile GPKG files; convert bhicv.shp GPKG #155 Throw error hotspot despatched object without \"quadr\" attribute #154 turn s2 vignette","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-4-2024-05-31","dir":"Changelog","previous_headings":"","what":"Version 1.3-4 (2024-05-31)","title":"Version 1.3-4 (2024-05-31)","text":"CRAN release: 2024-05-31 add scale argument geary.test, geary.mc geary #151, appropriate tests Introduce error knearneigh k less largest count identical points; encountered, increase k remove spurious warning knearneigh longlat geometries fix https://github.com/edzer/sdsr/issues/121, wrong assignment old test names lmRStests fix #144 plot.nb nb2lines","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-3-2024-02-07","dir":"Changelog","previous_headings":"","what":"Version 1.3-3 (2024-02-07)","title":"Version 1.3-3 (2024-02-07)","text":"CRAN release: 2024-02-07 change lm.LMtests lm.RStests re-name Lagrange multiplier Rao’s score; add GNM_ prefix test names input object inherits SlX created spatialreg::lmSLX (Koley, forthcoming) add SD.RStests implementation Rao’s score tests spatial Durbin models (Koley Bera, 2024) SDEM models (Koley, forthcoming) #143 row.names pass-poly2nb corrected, harmonised row.names pass-also nbdists dnearneigh #139 add na.action argument geary.test, geary.mc globalG.test add style sn2listw use tri2nb","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-13-1-2023-11-23","dir":"Changelog","previous_headings":"","what":"Version 1.3-1 (2023-11-23)","title":"Version 1.3-1 (2023-11-23)","text":"CRAN release: 2023-11-23 functions creating nb objects now warn object sub-graph count > 1 get.SubgraphOption TRUE (default FALSE): complement.nb, diffnb, dnearneigh, droplinks, edit.nb, graph2nb, knn2nb, nb2blocknb, nblag, nblag_cumul, poly2nb, read.gal, read.gwt2nb, setdiff.nb, tolerance.nb, tri2nb, union.nb summary.nb, print.nb, summary.listw print.listw now report subgraph count n.comp.nb one subset.nb now reports subgraph count neighbour object increases subsetting adding zero.policy attribute functions creating listw objects: nb2listw, sn2listw, mat2listw, nb2listwdist. Default zero.policy= argument updated use attr(., \"zero.policy\") summary.listw, print.listw, moran, moran.test, moran.mc, moran.plot, geary.mc, geary, geary.test, globalG.test, joincount.test, joincount.mc, joincount.multi, localC, localC_perm, localmoran, localmoran_perm, localG, localG_perm, lee, lee.test, lee.mc, lm.morantest, lm.LMtests, sp.mantel.mc, listw2star, lag.listw, lm.morantest, lm.LMtests, subset.listw, EBImoran.mc, LOSH, LOSH.mc, LOSH.cs, lm.morantest.exactand lm.morantest.sad confusing error message moran.plot() -neighbour cases, zero.policy=FALSE replace rgrass7 rgrass vignette fix #133 (edit.nb affected attaching sp)","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-8-2023-02-28","dir":"Changelog","previous_headings":"","what":"Version 1.2-8 (2023-02-28)","title":"Version 1.2-8 (2023-02-28)","text":"CRAN release: 2023-02-28 mat2listw() warning style= argument given, M\" given https://github.com/r-spatial/spatialreg/issues/24, https://github.com/r-spatial/spatialreg/issues/23. remaining users run_perm() - localC(), localmoran_bv() local_joincount_uni() get no_repeat_in_row= arguments. Address 2) #124; localG_perm() localmoran_perm() get no_repeat_in_row= arguments use conditional permutation without replacement sample vectors; default implementation uses sampling replacement, acceptable across simulation draws, arguably less acceptable within draws. Feedback valued. Address 1) #124; localG_perm() localG() now return analytical standard deviates. standard deviates simulated distributions now returned attr(., \"internals\")[,\"StdDev.Gi\"] localG_perm(), p-values, etc. move sp Depends Imports, reduce visual impression sp objects required spdep; sf objects now preferred, sp objects can used , although users may need attach sp expliciitly. fix #121 #123; correcting returned values localG_perm() estimating G-star measure (fix self x values weights) address #120, moving documentation listw2U() ?lm.morantest ?nb2listw addressing #119 interpretation moran_bv() results adding #116, René Westerholt fix #113, low R version grDevices::hcl.colors() addressing #111 Josiah Parry PRs René Westerholt, ending #109, local GS measure","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-7-2022-10-01","dir":"Changelog","previous_headings":"","what":"Version 1.2-7 (2022-10-01)","title":"Version 1.2-7 (2022-10-01)","text":"CRAN release: 2022-10-01 #103 refactoring local joincount test Josiah Parry add hotspot methods localmoran (analytical, permutation, Saddlepoint exact), localC (univariate multivariate) localG (analytical permutation) #95 add \"two.sided\" lee.mc(), sp.mantel.mc(), EBImoran.mc(), joincount.mc(), geary.mc() #92, #93, #94, #96, #97 contributions prototype bivariate Moran, local bivariate Moran local joincount bivariate joincount tests Josiah Parry #91 tolerance.nb() update F. Guillaume Blanchet updating coercion Matrix 1.4-2 fix ncpus issue dontrun examples remove suggested packages rgdal, rgeos, maptools","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-5-2022-08-11","dir":"Changelog","previous_headings":"","what":"Version 1.2-5 (2022-08-11)","title":"Version 1.2-5 (2022-08-11)","text":"CRAN release: 2022-08-11 permit use data.frame tibble matrix functions creating neighbour objects 2D points (preferred use object inheriting `\"SpatialPoints\" \"sfc\") fix #87 wrong logic infinite weights nb2listwdist() https://github.com/r-spatial/s2/pull/174 speeds dnearneigh() geographical coordinates without using s2::s2_closest_edges(). Adapting vignettes absence rgdal maptools","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-4-2022-04-18","dir":"Changelog","previous_headings":"","what":"Version 1.2-4 (2022-04-18)","title":"Version 1.2-4 (2022-04-18)","text":"CRAN release: 2022-04-18 added remove.self(), thanks Josiah Parry #83. unescape underscores help pages.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-3-2022-03-29","dir":"Changelog","previous_headings":"","what":"Version 1.2-3 (2022-03-29)","title":"Version 1.2-3 (2022-03-29)","text":"CRAN release: 2022-03-29 replace deprecated S-compatibility macros DOUBLE_ #81 improved dnearneigh() help page. #79 remove \"htest\" class LOSH.mc() output object. Added GA SI article citations.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-2-2022-01-28","dir":"Changelog","previous_headings":"","what":"Version 1.2-2 (2022-01-28)","title":"Version 1.2-2 (2022-01-28)","text":"CRAN release: 2022-01-28 Replace rainbow() hcl.colors(..., \"Set 2\") plot.skater(). Add link R-sig-geo thread EBlocal() NaN estimates many counts zero help page. Revise add documentation object returned localC_perm() #68 #72 #73 #74 #75 #76 localmoran.sad(), localmoran.exact() localmoran.exact.alt() now use multiple compute nodes needed; Omega used, multiple cores may need memory #77 s2 > 1.0.7, use indexed distances dnearneigh() https://github.com/r-spatial/s2/pull/162.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-12-1-2022-01-05","dir":"Changelog","previous_headings":"","what":"Version 1.2-1 (2022-01-05)","title":"Version 1.2-1 (2022-01-05)","text":"CRAN release: 2022-01-04 Switching deprecated functions moved spatialreg defunct.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-13-2021-12-14","dir":"Changelog","previous_headings":"","what":"Version 1.1-13 (2021-12-14)","title":"Version 1.1-13 (2021-12-14)","text":"CRAN release: 2021-12-14 Recent changes poly2nb() reduced recently (1.1-8) removed use snap= finding candidate neighbours; many thanks Matilda Brown clear well-documented issue #65 Add local Geary’s C #66 thanks Josiah Parry, discussion work #68 localmoran_perm() returns look-folded rank p-values","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-12-2021-11-09","dir":"Changelog","previous_headings":"","what":"Version 1.1-12 (2021-11-09)","title":"Version 1.1-12 (2021-11-09)","text":"CRAN release: 2021-11-09 poly2nb(), reverted removal legacy interpreted overlapping envelope code sp objects coerced sf without rgeos. Add Fortran character handling USE_FC_LEN_T WRE §6.6.1. Checks OK forthcoming deldir 1.0-0. Fixes #62 clarifying dnearneigh() help page","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-11-2021-09-07","dir":"Changelog","previous_headings":"","what":"Version 1.1-11 (2021-09-07)","title":"Version 1.1-11 (2021-09-07)","text":"CRAN release: 2021-09-07 knearneigh() nbdists(); added prototype adaptation s2 unprojected coordinates, used sf_use_s2() TRUE became default sf 1.0.0 https://github.com/r-spatial/s2/issues/125. activated default. dnearneigh() can choose prototype s2 approach sf_use_s2() TRUE use_s2=TRUE unprojected coordinates; https://github.com/r-spatial/s2/issues/125 seems distance thresholds present use brute-force rather spatial indexing. Use activated default. poly2nb() now uses sf::st_intersects() find candidate neighbours unless findInBounds= NULL. spatial indexing, fast scales well large data sets. sf_use_s2() TRUE, sf::st_intersects() passes geometries s2::s2_intersects_matrix(), also uses spatial indexing fast, scaling well large data sets. localmoran() localmoran_perm() return cluster quadrants attribute three splits, zeros, means medians variable interest spatial lag. localmoran_perm() returns skewness kurtosis permutation samples.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-8-2021-05-23","dir":"Changelog","previous_headings":"","what":"Version 1.1-8 (2021-05-23)","title":"Version 1.1-8 (2021-05-23)","text":"CRAN release: 2021-05-23 #55 related #20 cycling order setting grids provoked re-design interface cell2nb(), passing \"GridTopology\" \"SpatialGrid\" objects unnamed first x= argument. Coerce \"RasterLayer\" similar raster, terra stars objects sp class objects first need . working renewing arguments cell2nb(), useful add tinytest support, now present function may extended functions creating \"nb\" objects. #58 contributed Jeff Sauer Levi Wolf (https://doi.org/10.31219/osf.io/ugkhp) providing conditional standard deviates local Moran’s Error assignment matrix detected CRAN check SIDS vignette, section median polish","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-7-2021-04-03","dir":"Changelog","previous_headings":"","what":"Version 1.1-7 (2021-04-03)","title":"Version 1.1-7 (2021-04-03)","text":"CRAN release: 2021-04-03 Changes continuous integration vignettes. Error poly2nb(, queen=FALSE) sf grids (double counting closed polygon start/end points), https://github.com/r-spatial/spdep/issues/50, thanks Christopher Kenny. Adding local Moran local G conditional permutation: localmoran_perm() localG_perm(). Adding nb2listwdist() contributed René Westerholt. Adding use sf GEOS find polygon contiguity candidates poly2nb() geometry count >= 500 - uses intersections polygon envelopes. #38, #53 removing RANN, adding dbscan suggestions fast dnearneigh() knearneigh() via use_kd_tree= argument fast planar neighbour set finding 2D 3D. Affects soi.graph() , used RANN. #54 avoid partial matching glist= handling. Disambiguating spdep spatialreg model output object class names prior making spdep model fitting functions defunct.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-5-2020-06-29","dir":"Changelog","previous_headings":"","what":"Version 1.1-5 (2020-06-29)","title":"Version 1.1-5 (2020-06-29)","text":"CRAN release: 2020-06-29 Replacing broken geoda URLs, moving knitr rmarkdown, work-around missing weights files spData.","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-3-2019-09-18","dir":"Changelog","previous_headings":"","what":"Version 1.1-3 (2019-09-18)","title":"Version 1.1-3 (2019-09-18)","text":"CRAN release: 2019-09-18 small maintenance update accommodate forthcoming change spData (dataset used example spdep spData changing name; name involved putting “x”, “y” “xyz” global environment lazy loading dataset).","code":""},{"path":"https://r-spatial.github.io/spdep/news/index.html","id":"version-11-2-2019-04-05","dir":"Changelog","previous_headings":"","what":"Version 1.1-2 (2019-04-05)","title":"Version 1.1-2 (2019-04-05)","text":"CRAN release: 2019-04-05 Follow-version spdep functions methods transferred spatialreg package marked deprecated, still exported spdep. 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Description of variables in the Geary data set.