Bayesian Analysis of Ordinal Outcomes Through Latent Variable Approach

Modeling and predicting of ordinal outcomes have become essential study to many statisticians due to the numerous forms of data encountered in real life, which has such format. Many authors have proposed variant methods in modeling these type of data either in classical approaches (McCullagh, 1980a) or from the Bayesian perspective (Albert and Chib, 1993) (Cowles et al., 1996). A commonly adopted way of modeling ordinal data is via an underlying continuous latent variable. That is to say that the observed ordinal outcomes have a correspondence with the latent variable through some set of cutoff points. Thus, it can be established that the probability of an ordinal outcome is equivalent to a continuous latent variable falling into an interval on the real line. Sometimes, there exist some difficulties in the estimation of these cutoff categories. (Albert and Chib, 1993) proposed an ordinal probit model in a Bayesian framework, in-cooperating a vague prior on the cutoff point parameters. However, in this work, we try to establish a correspondence between the cutoff categories through the Dirichlet distribution via a reasonable transformation. The Gibbs sampling approach is used to estimate these parameters from their posterior distribution. We then compare our result after prediction to the well known Polytomous Ordinal Logistic Regression. It tends out that, our method yields more parsimonious results as compared to the POLR model