ABSTRACT
In this chapter we consider an exact small sample Bayesian analysis of the models proposed by Prentice (1988) and also by Ochi and Prentice (1984). Our models can be classified into two groups. The first group of models generalize the binary logistic model to multivariate data by considering a particular parameterized representation for the correlations using the notion of random effects on the logistic regression structure or in terms of pairwise odds ratios. The other group of models are obtained by introducing a link function using an inverse cumulative distribution function ( cdf). Multivariate pro bit (MVP) and multivariate t-link (MVT) models are obtained in this scenario. The MVP model was first introduced by Ashford and Sowden (1970) and studied further by Amemiya (1985). Recently, by introducing latent variables Chib and Greenberg (1998) analyzed the MVP model in a Bayesian framework.
