Subcopula-based measure of asymmetric association for contingency tables

For the analysis of a two-way contingency table, a new asymmetric association measure is developed. The proposed method uses the subcopula-based regression between the discrete variables to measure the asymmetric predictive powers of the variables of interest. Unlike the existing measures of asymmetric association, the subcopula-based measure is insensitive to the number of categories in a variable, and thus, the magnitude of the proposed measure can be interpreted as the degree of asymmetric association in the contingency table. The theoretical properties of the proposed subcopula-based asymmetric association measure are investigated. We illustrate the performance and advantages of the proposed measure using simulation studies and real data examples.