Modelling and estimating heterogeneous variances in threshold models for ordinal discrete data via Winbugs/Openbugs

Analysis of discrete repeated outcomes is an important issue in biomedical studies. The aim of this paper is to propose a flexible and parsimonious model to account for heterogeneous variances for discrete outcomes. The proposed method is based on the use of a linear mixed model on the log of the standard deviation parameters. It is also shown how parameter estimation in this model can be performed with an exact procedure based on a Gibbs sampling algorithm implemented with the Winbugs/Openbugs software. A model comparison study is presented to illustrate the efficiency of this procedure using a well known example from the clinical trial literature. It was found that the proposed methodology considerably improved the predictive ability of the model while remaining very parsimonious. In particular, it was found that adding a random subject effect in the variance model significantly improved the posterior predictive p-value criterion of the model.