Elderly Motion Analytics for Fall Prevention

This project analyzes how vertical acceleration, measured through wearable motion sensors, influences the probability of lying down among older adults. Using binomial logistic regression, I aim to model this relationship to inform the development of fall detection and elderly monitoring systems. The project uses Python libraries such as pandas, seaborn, statsmodels, and scikit-learn for data preprocessing, visualization, modeling, and performance evaluation.

Project Overview

The Elderly Motion Analytics for Fall Prevention project aims to:

• Model LyingDown Behavior: Predict the likelihood of an individual lying down based on vertical acceleration data
• Evaluate Predictive Power: Interpret coefficients and assess model accuracy using ROC-AUC, F1 Score, and other metrics
• Check Assumptions: Assess the linearity of the logit and consider implications of assumption violations
• Support Fall Detection Research: Provide practical insights that can assist in real-time motion monitoring and early detection systems

Dataset Structure

The dataset contains motion sensor readings collected from elderly individuals. The main features used in this analysis include:

• Acc (vertical): Continuous variable representing vertical acceleration from the sensor
• LyingDown: Binary outcome variable indicating whether the individual is lying down (1) or not (0)

Additional derived columns were created for diagnostic and visualization purposes.

Data Processing and Analysis Steps

• Data Cleaning:

  • Filter relevant observations and drop missing values
  • Convert data types and validate binary encoding for the target variable

• Exploratory Data Analysis (EDA):

  • Visualize the overall distribution of vertical acceleration
  • Plot class-specific histograms to assess overlap between LyingDown classes

• Modeling Approach:

  • Fit a binomial logistic regression using statsmodels
  • Interpret coefficients and calculate odds ratios
  • Assess model assumptions including linearity of the logit
  • Evaluate model performance using accuracy, precision, recall, F1 score, and ROC-AUC

• Linearity of Logit:

  • A plot of binned Acc (vertical) values against log-odds revealed a non-linear, U-shaped trend, violating the linearity of the logit assumption.
  • This suggests the predictor is not perfectly captured by a simple linear term.
  • To better model this, I could consider polynomial transformations, splines, or interaction terms.
  • However, given the moderate level of non-linearity, and since my primary goal is prediction, I’m comfortable proceeding without adjustment for now—especially if performance metrics (e.g., accuracy, ROC-AUC, F1) remain strong. I’ll keep this in mind for future refinements if necessary.

Key Insights

Predictor Strength

• The histogram by class shows two distinct peaks for Acc (vertical), suggesting it is a meaningful predictor of body position
• While some overlap exists between classes in the middle range, the separation is clear enough to aid classification

Coefficient Interpretation

• The model shows a statistically significant negative coefficient for Acc (vertical), indicating that higher values are associated with lower odds of lying down
• Odds ratio interpretation: For each unit increase in vertical acceleration, the odds of lying down decrease

Model Evaluation

• Accuracy, F1 score, and ROC-AUC indicate that the model performs well in distinguishing between classes
• Despite mild assumption violations, the model shows strong predictive ability

Project Highlights

• Applied logistic regression to a real-world binary classification task
• Performed EDA and visual diagnostics to support modeling decisions
• Evaluated model assumptions and discussed limitations openly
• Interpreted results in terms of practical implications for fall detection and elderly care
• Used ROC-AUC and classification metrics to validate model performance

Future Work

• Refine Model Formulation: Apply non-linear transformations or splines to better model the relationship
• Add More Predictors: Incorporate additional motion metrics or contextual features (e.g., time of day, activity type)
• Develop Real-Time Monitoring Tools: Translate the model into deployable systems for wearable or smart home devices
• Explore Alternative Models: Compare logistic regression with tree-based or ensemble classifiers
• Evaluate on Broader Data: Test on larger, more diverse samples of elderly individuals for generalizability

This project highlights how a well-structured statistical approach, even with assumption trade-offs, can yield interpretable and actionable insights in health-related motion analytics.