Visualization of Dependence in Multidimensional Contingency Tables with an Ordinal Dependent Variable via Copula Regression

Visualization is an essential component of the exploratory data analysis (EDA) in discovering and understanding dependence structure of the data for formal statistical modeling and inference. In this paper, we propose a graphical approach designed to explore and visualize the regression dependence structure in a multi-way contingency table with an ordinal dependent variable and a set of independent categorical (ordinal or nominal) variables. The proposed method is based on copula regressions developed for ordinal variables which enable prediction of the category of the ordinal dependent variable for any given combination of categories of independent variables in a model-free manner. We then employ resampling techniques to facilitate visualizing the uncertainty involved in the prediction and significance of the discovered regression associations. Since estimation of copula regression and its prediction do not require any parametric assumption on the dependence structure between an ordinal dependent variable and a set of independent categorical variables, one can use the proposed method as a non-model-based visualization tool for the EDA of multidimensional contingency tables with an ordinal dependent variable.