Simulating correlated ordinal data via the multivariate Student’s t distribution

We propose a statistical model for correlated ordinal data based on the discretization of the multivariate Student’s t distribution. We examine how the correlation matrix R and the degrees-of-freedom parameter ν of the latent continuous distribution, together with the choice of marginal distributions for the ordinal variables, affect the resulting correlation structure. The analysis focuses on discrete uniform margins and margins with decreasing probabilities, with varying number of categories.