Default Bayesian model determination methods for generalised linear mixed models

Authors:
Antony M. Overstall;Jonathan J. Forster
Affiliations:
Southampton Statistical Sciences Research Institute (S3RI), University of Southampton, Highfield, Southampton, SO17 1BJ, UK;School of Mathematics, University of Southampton, Highfield, Southampton, SO17 1BJ, UK
Venue:
Computational Statistics & Data Analysis
Year:
2010

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Abstract

A default strategy for fully Bayesian model determination for generalised linear mixed models (GLMMs) is considered which addresses the two key issues of default prior specification and computation. In particular, the concept of unit-information priors is extended to the parameters of a GLMM. A combination of Markov chain Monte Carlo (MCMC) and Laplace approximations is used to compute approximations to the posterior model probabilities to find a subset of models with high posterior model probability. Bridge sampling is then used on the models in this subset to approximate the posterior model probabilities more accurately. The strategy is applied to four examples.