Department of Quantitative Methods & Information Systems, Indian Institute of Management, Bangalore, Bangalore 560076, India. e-mail: firstname.lastname@example.org
A SEMIPARAMETRIC BAYESIAN APPROACH TO MULTIVARIATE LONGITUDINAL DATA
Article first published online: 14 SEP 2010
© 2010 Australian Statistical Publishing Association Inc.
Australian & New Zealand Journal of Statistics
Volume 52, Issue 3, pages 275–288, September 2010
How to Cite
Ghosh, P. and Hanson, T. (2010), A SEMIPARAMETRIC BAYESIAN APPROACH TO MULTIVARIATE LONGITUDINAL DATA. Australian & New Zealand Journal of Statistics, 52: 275–288. doi: 10.1111/j.1467-842X.2010.00581.x
- Issue published online: 29 SEP 2010
- Article first published online: 14 SEP 2010
- 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.