Exploration of Dependence Structures in Longitudinal Categorical Data with Ordinal Responses

An important principal step prior to formal statistical inference for longitudinal categorical data is to explore the data at hand and uncover potential information on dependence in repeatedly measured outcomes, which may be valuable for building statistical models for explanation and prediction. This paper proposes an explorative approach to facilitate the understanding of dependence structures in longitudinal categorical data with ordinal outcome variables and categorical (nominal or ordinal) covariates. The proposed approach utilizes a model-free association measure (Wei Z and Kim D, J Multivariate Anal 186:104793, 2021), the Scaled Checkerboard Copula Regression Association Measure (SCCRAM), developed for multivariate contingency tables with an ordinal response variable and a set of categorical predictors. In order to properly apply the SCCRAM for investigating the dependence structure among repeatedly measured ordinal outcome variables and their relationship with categorical covariates, the proposed approach consists of a set of SCCRAM-based strategies that take into account time dependence, data format, potential of asymmetric dependence, and model-free inference. The utility of the proposed method is demonstrated using two longitudinal categorical datasets, one for trend data obtained from independent samples over time and the other for panel data collected from the same sample over time.