Variable Selection in Generalized Linear Models

Abstract

Abstract This chapter provides a comprehensive overview of variable selection techniques within the framework of generalized linear models (GLMs), focusing on their application in clinical epidemiology using real-world data from the All of Us Research Program. Both frequentist and Bayesian approaches are explored in depth, including stepwise regression, likelihood-based inference, information criteria, and advanced Bayesian strategies such as Leave-One-Out Cross-Validation (LOO-CV), Bayesian Model Averaging (BMA), and Projection Predictive Variable Selection. This chapter contrasts these methodologies in terms of their theoretical underpinnings, computational strategies, and implications for model interpretability and predictive performance. The empirical analysis reveals consistent predictors of infection risk, such as intubation, endocrine disorders, and transplant history, across multiple modeling strategies, supporting the validity of results and reinforcing the value of principled variable selection in healthcare analytics.