Overstall, Anthony M. and Forster, Jonathan J.
Default Bayesian model determination methods for generalised linear mixed models , Southampton, UK Southampton Statistical Sciences Research Institute 25pp.
(S3RI Methodology Working Papers, (doi:10.1016/j.csda.2010.03.008) , M09/01).
In this paper, we consider a default strategy for fully Bayesian model determination for GLMMs. We address the two key issues of default prior specification and computation. In particular, we extend a concept of unit information to the priors for the parameters of a GLMM. We rely on a combination of MCMC and Laplace approximations to compute approximations to the posterior model probabilities and then further approximate these posterior model probabilities using bridge sampling. We apply our strategy to two examples.
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