• conditional predictive ordinate;
  • longitudinal data;
  • mixture of Polya trees;
  • penalized spline


We extend the standard multivariate mixed model by incorporating a smooth time effect and relaxing distributional assumptions. We propose a semiparametric Bayesian approach to multivariate longitudinal data using a mixture of Polya trees prior distribution. Usually, the distribution of random effects in a longitudinal data model is assumed to be Gaussian. However, the normality assumption may be suspect, particularly if the estimated longitudinal trajectory parameters exhibit multi-modality and skewness. In this paper we propose a mixture of Polya trees prior density to address the limitations of the parametric random effects distribution. We illustrate the methodology by analysing data from a recent HIV-AIDS study.