Bayesian hierarchical models for multi-level repeated ordinal data using WinBUGS

Multi-level repeated ordinal data arise if ordinal outcomes are measured repeatedly in subclusters of a cluster or on subunits of an experimental unit. If both the regression coefficients and the correlation parameters are of interest, the Bayesian hierarchical models have proved to be a powerful tool for analysis with computation being performed by Markov Chain Monte Carlo (MCMC) methods. The hierarchical models extend the random effects models by including a (usually flat) prior on the regression coefficients and parameters in the distribution of the random effects. Because the MCMC can be implemented by the widely available BUGS or WinBUGS software packages, the computation burden of MCMC has been alleviated. However, thoughtfulness is essential in order to use this software effectively to analyze such data with complex structures. For example, we may have to reparameterize the model and standardize the covariates to accelerate the convergence of the MCMC, and then carefully monitor the convergence of the Markov chain. This article aims at resolving these issues in the application of the WinBUGS through the analysis of a real multi-level ordinal data. In addition, we extend the hierarchical model to include a wider class of distributions for the random effects. We propose to use the deviance information criterion (DIC) for model selection. We show that the WinBUGS software can readily implement such extensions and the DIC criterion.