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 utilizes a latent continuous variable for the ordinal variable. Using the Kullback-Leibler divergence, existing probability models for mixed continuous-ordinal variable pair are assessed for the adequacy of fit with simple parametric copula families. The effectiveness of the proposed visualization and diagnostic methods is illustrated on simulated and real datasets.