Bayesian estimation of the polychoric correlation coefficient

The problem of estimating a polychoric correlation coefficient from a latent bivariate normal distribution is considered from a Bayesian viewpoint. Using the Gibbs sampling algorithm, one can simulate the joint posterior distribution of the correlation coefficient and row and column thresholds and estimate any marginal posterior density of interest. This algorithm is generalized to handle bivariate lognormal and bivariate tlatent distributions. The methods are illustrated for two examples.