A Dirichlet process mixture model for the analysis of correlated binary responses

The multivariate probit model is a popular choice for modelling correlated binary responses. It assumes an underlying multivariate normal distribution dichotomized to yield a binary response vector. Other choices for the latent distribution have been suggested, but basically all models assume homogeneity in the correlation structure across the subjects. When interest lies in the association structure, relaxing this homogeneity assumption could be useful. The latent multivariate normal model is replaced by a location and association mixture model defined by a Dirichlet process. Attention is paid to the parameterization of the covariance matrix in order to make the Bayesian computations convenient. The approach is illustrated on a simulated data set and applied to oral health data from the Signal Tandmobiel^® study to examine the hypothesis that caries is mainly a spatially local disease.