Bayesian analysis of hierarchical linear mixed modeling using the multivariate t distribution

This article presents a fully Bayesian approach to modeling incomplete longitudinal data using the t linear mixed model with AR(p) dependence. Markov chain Monte Carlo (MCMC) techniques are implemented for computing posterior distributions of parameters. To facilitate the computation, two types of auxiliary indicator matrices are incorporated into the model. Meanwhile, the constraints on the parameter space arising from the stationarity conditions for the autoregressive parameters are handled by a reparametrization scheme. Bayesian predictive inferences for the future vector are also investigated. An application is illustrated through a real example from a multiple sclerosis clinical trial.