A method for multivariate ordinal data generation given marginal distributions and correlations

Abstract

A method is described for simulating multivariate ordinal variates with specified marginal distributions and correlation structure. The method relies on simulating correlated binary variates as an intermediate step. After collapsing the ordinal levels to the binary ones, it is straightforward to obtain binary means. Corresponding binary correlations are computed via simulation in a way to ensure that re-conversion to the ordinal scale delivers the original distributional properties. Employing binary data generation is shown to be an effective method for simulating ordinal variates for a broad range of given marginals and pairwise associations.