Title: Objective Bayesian model selection for generalized linear mixed models
Authors: Shuangshuang Xu - Virginia Tech (United States) [presenting]
Marco Ferreira - Virginia Tech (United States)
Erica Porter - Virginia Tech Department of Statistics (United States)
Christopher Franck - Virginia Tech (United States)
Abstract: An objective Bayesian model selection approach is proposed for generalized linear mixed models. Since random effects cannot be integrated out of GLMMs analytically, we approximate the integrated likelihood function using a pseudo-likelihood approach. We study performance assuming an approximate reference prior for the parameters of the model. In addition to the approximate reference prior, we also consider the half-Cauchy prior for the square root of variance components of the random effects. Since the approximate reference prior is improper, we develop a fractional Bayes factor approach with a minimum training fraction. We then perform model selection based on the resulting posterior probabilities of the several competing models. Simulation studies with Poisson generalized linear mixed models with spatial random effects and overdispersion random effects show that our approach performs favorably when compared to widely used competing Bayesian methods, including DIC and WAIC. We illustrate the usefulness and flexibility of our approach with three case studies, including a Poisson longitudinal model, a Poisson spatial model, and a logistic mixed model.