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.