Properties of prior and posterior distributions for multivariate categorical response data models

In this article, we model multivariate categorical (binary and ordinal) res ponse data using a very rich class of scale mixture of multivariate normal (SMMVN) link functions to accommodate heavy tailed distributions. We consid er both noninformative as well as informative prior distributions for SMMVN -link models. The notation of informative prior elicitation is based on ava ilable similar historical studies. The main objectives of this article are (i) to derive theoretical properties of noninformative and informative prio rs as well as the resulting posteriors and (ii) to develop an efficient Mar kov chain Monte Carlo algorithm to sample from the resulting posterior dist ribution. A real data example from prostate cancer studies is used to illus trate the proposed methodologies. (C) 1999 Academic Press AMS 1991 subject classifications: primary 62A15; secondary 62H05, 62E15.