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.

翻译：针对连续变量与序数变量的混合情形，存在藤对连接函数构造方法。在某些步骤中，需要估计混合连续-序数变量对的双变量连接函数。为评估该类变量对的连接函数拟合优度，本文提出基于正态得分图与条件QQ图的诊断及可视化方法。前者通过为序数变量引入潜在连续变量实现。利用Kullback-Leibler散度，对混合连续-序数变量对的现有概率模型进行简单参数化连接函数族的拟合优度评估。通过模拟数据集与实际数据集验证了所提可视化及诊断方法的有效性。