Semiparametric Bayesian Analysis for Longitudinal Mixed Effects Models with Non-Normal AR(1) Errors

This paper studies Bayesian inference on longitudinal mixed effects models with non-normal AR(1) errors. We model the nonparametric zero-mean noise in the autoregression residual with a Dirichlet process (DP) mixture model. Applying the empirical likelihood tool, an adjusted sampler based on the Pólya urn representation of DP is proposed to incorporate information of the moment constraints of the mixing distribution. A Gibbs sampling algorithm based on the adjusted sampler is proposed to approximate the posterior distributions under DP priors. The proposed method can easily be extended to address other moment constraints owing to the wide application background of the empirical likelihood. Simulation studies are used to evaluate the performance of the proposed method. Our method is illustrated via the analysis of a longitudinal dataset from a psychiatric study.