Multinomial Logistic Modeling, Epidemiological Feature Selection, and Interpretable Machine Learning: An R-Based Analysis of Physical Activity and Depression Stratification

This project executed an epidemiological data analysis and categorical regression modeling pipeline in R to evaluate the relationship between physical activity, socioeconomic covariates, and depression severity levels across a large-scale population dataset ($N \approx 10,000$).The analytical workflow involved collapsing a 4-category depression scale into a consolidated 3-tier outcome variable ("None", "Some", "Many") by merging sparse upper categories ("Majority" and "Almost all"). Addressing a high-dimensional feature space (~75 candidate covariates), predictor selection was guided by clinical literature and domain plausibility—focusing on physical activity indicators, sleep patterns, and socioeconomic determinants—rather than simple bivariate correlations.Using a baseline-category logit framework with "None" as the reference group, a Multinomial Logistic Regression model was fitted to estimate log-odds and exponentiated odds ratios ($OR$) with corresponding 95% confidence intervals. Non-significant predictors were iteratively pruned to yield a parsimonious, highly interpretable model. Finally, the multinomial model's classification performance and goodness-of-fit were benchmarked against a tree-based machine learning baseline (Random Forest) to evaluate the trade-off between predictive accuracy and clinical interpretability.