Bayesian Inference in Multivariate t Linear Mixed Models Using the IBF-Gibbs Sampler

• Activity Number: 620
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 8:30 AM to 10:20 AM
• Sponsor: International Chinese Statistical Association
• Author(s): Wan-Lun Wang*+ and Tsai-Hung Fan
• Companies: Feng Chia University and National Central University
• Keywords: AR(p) ; Conjugate priors ; Hierarchical models ; Inverse Bayes formulae ; MCMC ; Multivariate longitudinal data

Abstract

The multivariate linear mixed model (MLMM) has become the most widely used tool for analyzing multi-outcome longitudinal data. Although it offers great flexibility for modeling the between- and within-subject correlation among multi-outcome repeated measures, the underlying normality assumption is vulnerable to potential atypical observations. We present a fully Bayesian approach to the multivariate t linear mixed model (MtLMM), which is a robust extension of MLMM with the random effects and errors jointly distributed as a multivariate t distribution. Due to the introduction of too many latent variables in the model, the conventional MCMC method may converge painfully slowly and thus fails to provide valid inference. To alleviate this problem, a computationally efficient inverse Bayes formula (IBF) sampler coupled with the Gibbs scheme, called the IBF-Gibbs sampler, is developed and shown to be effective in drawing samples from the target distributions. The issues related to model determination and Bayesian predictive inference for random effects are also investigated. The proposed methodology is illustrated with a real example from an AIDS data.