Prior elicitation for model selection and estimation in generalized linear mixed models

Generalized linear models serve as a useful class of regression models for discrete and continuous data. In applications such as longitudinal studies, observations are typically correlated. The correlation structure in the data is induced by introducing a random effect, leading to the generalized linear mixed model (GLMM). In this paper, we propose a class of informative prior distributions for the class of GLMMs and investigate their theoretical as well as computational properties. Specifically, we investigate conditions for propriety of the proposed priors for the class of GLMMs and show that they are proper under some very general conditions. In addition, we examine recent computational methods such as hierarchical centering and semi-hierarchical centering for performing Gibbs sampling for this class of models. One of the main applications of the proposed priors is variable subset selection. Novel computational tools are developed for sampling from the posterior distributions and computing the prior and posterior model probabilities. We demonstrate our methodology with two real longitudinal datasets. (C) 2002 Elsevier Science B.V. All rights reserved.