Bivariate Distributions Underlying Responses to Ordinal Variables

The association between two ordinal variables can be expressed with a polychoric correlation coefficient. This coefficient is conventionally based on the assumption that responses to are generated by underlying continuous latent bivariate normal distribution. When normality violated, estimated may biased. In such case, we consider other distributions. this paper, aimed provide an illustration of fitting various distributions empirical data and examining how estimates vary under different distributional assumptions. Results suggested skew-normal rarely hold in datasets. contrast, mixtures were often not rejected.