A Bayesian semiparametric model framework is proposed to analyze multivariate longitudinal data. The new framework leads to simple explicit posterior distributions of model parameters. It results in easy implementation of the MCMC algorithm for estimation of model parameters and demonstrates fast convergence. The proposed model framework associated with the MCMC algorithm is validated by four covariance structures and a real-life dataset. A simple Monte Carlo study of the model under four covariance structures and an analysis of the real dataset show that the new model framework and its associated Bayesian posterior inferential method through the MCMC algorithm perform fairly well in the sense of easy implementation, fast convergence, and smaller root mean square errors compared with the same model without the specified autoregression structure.
