Multivariate logit copula model with an application to dental data.

Applications of copulas for multivariate continuous data abound but there are only a few that treat multivariate binary data. In the present paper, we model multivariate binary data based on copulas using mixtures of max-infinitely divisible copulas, introduced by Joe and Hu (J. Multivar. Anal. 1996; 57(2): 240-265). When applying copulas to binary data the marginal distributions also contribute to the dependence measures. We propose the use of covariate information in the copula parameters to obtain a direct effect of a covariate on dependence. To deal with model uncertainty due to selecting among several candidate models, we use a model averaging technique. We apply the model to data from the Signal-Tandmobiel dental study and, in particular, to four binary responses that refer to caries experience in the mandibular and maxillary left and right molars. We aim to model Kendall's tau associations between them, and examine how covariate information affects these associations. We found that there are systematically larger associations between the two mandibular and the two maxillary molars. Using covariates to model these associations more closely, we found that the systematic fluoride and age of the children affect the associations. Note that such relationships could not have been revealed by methods that focus on the marginal models. Copyright 2008 John Wiley & Sons, Ltd.