is equivalent to probit, logit, and related models. However, the formulation that assumes latent variable Zi is allowing Gibbs sampling scheme (eg., Chib and Albert 1993) and Johnson and Albert (1999)). Successive sampling from full conditionals, (i) [β|Z, Y ] and (ii) [Z|β, Y ]. Assume that F is normal distribution and that the above model is probit. Then the distribution for β given Z is simp...

In many social science researches and econometric applications data that arise through measurement of discrete outcomes or discrete choice among a set of alternatives are in the form of ordinal or ordered categorical data. Such examples, among others, are selfreport responses in household surveys, modeling labor force participate, or decision of which product to choose or which candidate to ele...

Current opinion regarding the selection of link function in binary response models is that the probit and logit links give essentially similar results. This seems to be true for univariate binary response models; however, for multivariate binary response models such advice is misleading. We address a gap in the literature by empirically examining the relationship between link function selection...

Multivariate ordinal data arise in many areas of applications. This paper proposes new efficient methodology for Bayesian inference for multivariate probit models using Markov chain Monte Carlo techniques. The key idea for our approach is the novel use of parameter expansion to sample correlation matrices. We also propose methodology for model selection. Our approach is demonstrated through sev...

The multivariate probit model (MVP) is a popular classic model for studying binary responses of multiple entities. Nevertheless, the computational challenge of learning the MVP model, given that its likelihood involves integrating over a multidimensional constrained space of latent variables, significantly limits its application in practice. We propose a flexible deep generalization of the clas...

Categorical outcome (or discrete outcome or qualitative response) regression models are models for a discrete dependent variable recording in which of two or more categories an outcome of interest lies. For binary data (two categories) probit and logit models or semiparametric methods are used. For multinomial data (more than two categories) that are unordered, common models are multinomial and...

This paper provides a practical simulation-based Bayesian and non-Bayesian analysis of correlated binary data using the multivariate probit model. The posterior distribution is simulated by Markov chain Monte Carlo methods and maximum likelihood estimates are obtained by a Monte Carlo version of the EM algorithm. A practical approach for the computation of Bayes factors from the simulation outp...