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Abstract:
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We propose an objective Bayesian model selection approach for generalized linear mixed models. To deal with the issue of integration of random effects, we approximate the likelihood function using a pseudo-likelihood approach. In addition, we assume approximate reference priors for the parameters of the model. In addition to the approximate reference prior, we also propose a novel non-local prior for the variance components of random effects. To deal with the impropriety of the prior, 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. We illustrate the usefulness and flexibility of our approach with three case studies on a Poisson longitudinal model, a Poisson spatial model, and a logistic mixed model.
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