On exploratory analytic method for multi-way contingency tables with an ordinal response variable and categorical explanatory variables

Abstract

In this paper, we propose a new model-free exploratory method for descriptive modeling that identifies and measures the regression dependence between an ordinal response variable and categorical (ordinal or nominal) explanatory variables in a multi-way contingency table. The proposed methodology consists of three parts, checkerboard copula score, checkerboard copula regression, and checkerboard copula association measure. The checkerboard copula score is a new type of score for ordinal variables that preserves the natural ordering of the categorical scale and it will be exploited for developing the methods measuring the association between the variables of interest. The checkerboard copula regression identifies the regression dependence between an ordinal response variable and categorical explanatory variables. It enables delineating the identified dependence in an exploratory manner. The checkerboard copula association measure quantifies the strength of the dependence identified by the checkerboard copula regression. We investigate the properties of checkerboard copula scores, checkerboard copula regression, its association measure, and their estimators. Finally, the performance of the proposed method is illustrated with simulation and real data.