Assessing copula models for mixed continuous-ordinal variables

Vine pair-copula constructions exist for a mix of continuous and ordinal variables. In some steps, this can involve estimating a bivariate copula for a pair of mixed continuous-ordinal variables. To assess the adequacy of copula fits for such a pair, diagnostic and visualization methods based on normal score plots and conditional Q–Q plots are proposed. The former uses a latent continuous variable for the ordinal variable. The methods are applied to data generated from some existing probability models for a mixed continuous-ordinal variable pair, and for such models, Kullback-Leibler divergence is used to assess whether simple parametric copula families can provide adequate fits. The effectiveness of the proposed visualization and diagnostic methods is illustrated on a dataset.