EFFICIENT MODEL SELECTION FOR HIGH-DIMENSIONAL AND HIERARCHICAL DATA USING BAYESIAN HIERARCHICAL GENERALIZED LINEAR MODELS WITH LASSO REGULARIZATION

Abstract

High-dimensional and hierarchical data structures are increasingly prevalent in real-world applications, posing significant challenges to traditional statistical modeling. This study addresses these challenges by developing a novel Bayesian Hierarchical Generalized Linear Model (BHGLM) that incorporates Lasso regularization for variable selection and improved interpretability. The proposed model extends existing hierarchical Bayesian frameworks to binary outcomes using Bernoulli likelihood and Laplace priors, enabling automatic sparsity in the fixed effects. Comparative simulation diagnostics, bias and coverage analysis, and model selection criteria including AIC, BIC, MDL, ICOMP, WAIC, and LOO demonstrate that the proposed model achieves superior estimation accuracy, parsimony, and predictive performance while maintaining robust MCMC convergence. Although the computational cost is higher relative to traditional BHGLMs, the benefits in regularization and model selection make the proposed approach highly suitable for complex, high-dimensional, hierarchical data environments found in healthcare, genomics, education, and social sciences.