An Approximate Posterior Simulation for GLMM with Large Samples

Generalized linear mixed models are commonly used when modeling counts or dichotomous observations on subjects within clusters such as patients in hospitals. When the sample sizes at the cluster levels are large, Bayesian inference about parameters of generalized linear mixed models using Markov Chain Monte Carlo sampling can be computationally slow. Standard large sample approximations can provide reasonable approximation for inference about cluster-level parameters which are near the “middle” but not necessarily for those parameters away from the middle. We provide an approach to simulating from the posterior distribution that gives better approximation when the sample sizes at the cluster levels are large and a multivariate normal prior or the default flat prior is used.