The purpose of this study is to compare the maximum likelihood (ML) and Bayesian estimation methods for polychoric correlation (PCC) under diverse conditions using a Monte Carlo simulation. Two new Bayesian estimates, maximum a posteriori (MAP) and expected a posteriori (EAP), are compared to ML, the classic solution, to estimate PCC. Different types of prior distributions are used to investigate the sensitivity of a prior distribution onto the Bayesian PCC estimation. In this simulation study, it appears that the MAP would be the estimator of choice for the PCC. The performance of the MAP is not only better than the ML but also appears to overcome the limitations of the EAP (i.e., the shrinkage effect). (Contains 4 tables and 6 figures.)