The Analysis of Bayesian Probit Regression of Binary and Polychotomous Response Data

The goal of this study is to introduce a statistical method regarding the analysis of specific latent data for regression analysis of the discrete data and to build a relation between a probit regression model (related to the discrete response) and normal linear regression model (related to the latent data of continuous response). This method provides precise inferences on binary and multinomial models which particularly in the case of small samples, has preference to maximum likelihood methods. The probit regression model for binary outcomes can be easily and precisely explained using different normal distributions for latent data modeling. Applying this approach and using Gibbs sampler method needs simulation of standard distributions such as multivariate normal distribution. Therefore, it can be easily implemented by many softwares and it provides a general method for analyzing binary (or polychotomous) response regression models.