Bayesian model selection for generalized linear mixed models.

Area of Science:

• Statistics
• Computational Statistics

Background:

• Generalized linear mixed models (GLMMs) are essential for analyzing complex data structures like longitudinal, genomic, and spatial data.
• Model selection for GLMMs is challenging due to the intractability of integrating out random effects.

Purpose of the Study:

• To develop a robust Bayesian model selection approach for GLMMs.
• To address the analytical intractability of random effects integration using pseudo-likelihood approximation.
• To provide a flexible framework for comparing covariance structures in various statistical applications.

Main Methods:

• A Bayesian model selection framework for GLMMs utilizing a pseudo-likelihood approximation for the integrated likelihood.
• Implementation of fractional Bayes factors to derive posterior model probabilities, accommodating improper priors on fixed effects.
• Consideration of various covariance structures for random effects, including spatial and overdispersion components.

Main Results:

• Simulation studies demonstrated superior performance of the proposed method compared to existing Bayesian criteria (DIC, WAIC) for Poisson GLMMs.
• The approach effectively handles spatial random effects and overdispersion in simulated data.
• Case studies involving longitudinal and spatial models confirmed the approach's practical utility and flexibility.

Conclusions:

• The proposed Bayesian model selection approach offers a reliable and flexible alternative for GLMM analysis.
• The fractional Bayes factor method provides accurate posterior model probabilities, enhancing model comparison.
• The R package GLMMselect facilitates the application of this advanced statistical methodology.