A computational method for ordinal probit regression base on polar metropolis

Abstract

The problem of estimating the cutpoints of an ordinal probit model in a Bayesian setting is a problem of constrained cumulative normal distribution. The Gibbs sampler method, applied to this problem, demonstrated a slow convergence rate due to the conical geometry of the support of the distribution. This research presents a new MCMC method based on the Metropolis algorithm operating on the polar coordinate of the problem. The efficiency of both algorithms is measured based on the number of iterations necessary until all cutpoints converge. The algorithm is applied to a credit rating data set to demonstrate its efficiency.