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

Abstract

Conditional 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.

Unraveling Potential Confounding Variables in the Association Between Maternal Malaria and Child Stunting in Papua: A Case-Control Study with Mantel-Haenszel Analysis

“…We also conducted analyses of the Test of Conditional Independence and the Test of Homogeneity of the Odds Ratio (Breslow-Day). The Test of Conditional Independence aims to assess whether there is a significant relationship between two categorical variables (malaria during pregnancy and the occurrence of stunting) after controlling or adjusting for stratification by categorical confounding variables (p < 0.05) (Adetunji, Jemilohun, & Adaraniwon, 2015;Zhang & Tinker, 2019). The Test of Homogeneity of the Odds Ratio (Breslow-Day) is used to evaluate whether the estimated association between malaria during pregnancy and the occurrence of stunting is the same in all strata or subgroups identified in the Mantel-Haenszel analysis (homogeneity p > 0.05) (Adetunji et al, 2015;Zhang & Tinker, 2019).…”

A Class of Association Measures for Categorical Variables Based on Weighted Minkowski Distance

“…A similar permutation procedure can be applied to evaluate the statistical significance. One can also define the distance between and to test the mutual independence of Furthermore, the framework can be extended to conditional independence test in three-way tables [ 14 ], by defining distance between conditional joint probabilities and the product of conditional marginal probabilities …”