Estimation of polychoric correlation with elliptical latent variables

Abstract
The problem of estimating the parameters in a polychoric correlation model is considered with the latent variables be distributed according to a bivariate elliptical distribution. Situations that based on bivariate t distribution and bivariate contaminated normal distribution normal distribution are studied in detail. Algorithms for computing the maximum likelihood estimates, the minimum chi–square estimates and the modified minimum chi–square estimates are implemented. Based on the results developd, simulation studies are conducted for investigating the robustness of the normality assumption.