On the exploration of regression dependence structures in multidimensional contingency tables with ordinal response variables

Abstract

In this paper, we propose a new data-driven method to explore complex regression dependence structures in a multi-dimensional contingency table with an ordinal response variable and categorical (ordinal or nominal) explanatory variables. The proposed method is based on a sequential decomposition of the overall regression dependence for the data quantified by the checkerboard copula regression association measure (Wei and Kim, 2021) in an informative and interpretable fashion. It can measure the marginal and conditional contributions of any subset of all available explanatory variables to the overall regression association in a hierarchical manner taking into account the order of the explanatory variables. Thus, the proposed method enables a holistic description of various aspects of regression association in a multivariate contingency table, including marginal and conditional associations between an ordinal response variable and a subset of explanatory variables of interest. We investigate theoretical properties of the proposed decomposition method, and we further illustrate its performance through simulation and two real data examples, one from a randomized controlled trial and the other from a longitudinal epidemiological study.