Posterior consistency of random effects models for binary data

In longitudinal studies or clustered designs, observations for each subject or cluster are dependent and exhibit intra-correlation. To account for this dependency, we consider Bayesian analysis for conditionally specified models, so-called generalized linear mixed model. In nonlinear mixed models, the maximum likelihood estimator of the regression coefficients is typically a function of the distribution of random effects, and so the misspecified choice of the distribution of random effects can cause bias in the estimator. To avoid the problem of the misspecification of the distribution of random effects, one can resort in nonparametric approaches. We give sufficient conditions for posterior consistency of the distribution of random effects as well as regression coefficients.