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Abstract We propose a Bayesian model selection approach for generalized linear mixed models (GLMMs). We consider covariance structures for the random effects that are widely used in areas such as longitudinal studies, genome-wide association studies, and spatial statistics. Since the random effects cannot be integrated out of GLMMs analytically, we approximate the integrated likelihood function using a pseudo-likelihood approach. Our Bayesian approach assumes a flat prior for the fixed effects and includes both approximate reference prior and half-Cauchy prior choices for the variances of random effects. Since the flat prior on the fixed effects is improper, we develop a fractional Bayes factor approach to obtain posterior probabilities of the several competing models. Simulation studies with Poisson GLMMs with spatial random effects and overdispersion random effects show that our approach performs favorably when compared to widely used competing Bayesian methods including deviance information criterion and Watanabe–Akaike information criterion. 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. Our proposed approach is implemented in the R package GLMMselect that is available on CRAN.
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Bayes Factors for Mixed Models: a Discussion
Abstract van Doorn et al. (2021) outlined various questions that arise when conducting Bayesian model comparison for mixed effects models. Seven response articles offered their own perspective on the preferred setup for mixed model comparison, on the most appropriate specification of prior distributions, and on the desirability of default recommendations. This article presents a round-table discussion that aims to clarify outstanding issues, explore common ground, and outline practical considerations for any researcher wishing to conduct a Bayesian mixed effects model comparison.
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- Award ID(s):
- 2145308
- PAR ID:
- 10397380
- Author(s) / Creator(s):
- ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Computational Brain & Behavior
- Volume:
- 6
- Issue:
- 1
- ISSN:
- 2522-0861
- Page Range / eLocation ID:
- p. 140-158
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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