Testing conditional independence and homogeneity in large sparse three‐way tables using conditional distance covariance

Abstract

AbstractConditional independence test for three‐way contingency tables is a classic problem in multivariate statistics. Traditional methods including Cochran–Mantel–Haenszel test and conditional mutual information test are powerful under sufficient sample size; however, in sparse settings, these methods may fail to detect the association due to the violation of normality assumption. In this paper, we propose to use a recently developed measure, namely, conditional distance covariance, to test conditional independence in large sparse R×C×K tables. We derive the explicit formula of conditional distance covariance between three categorical variables, and we suggest a maximum‐type statistic for hypothesis testing. In addition, we introduce a new statistic based on distance covariance to test homogeneity in three‐way tables. We conduct an extensive simulation study to illustrate the superiority of our method to the existing ones.