A Directional Measure of Marginal Inhomogeneity for Square Contingency Tables using Discrete-time hazard

Abstract: In the analysis of square contingency tables with ordered categories, it is essential to assess deviations from marginal homogeneity (MH) when marginal equivalency between row and column variables does not hold. Some measures for evaluating the degree of departure from the MH model have been proposed. This study proposes a new directional measure using the discrete-time hazard, assuming that categories represent discrete time points. The proposed measure is capable of capturing both the magnitude and direction of deviation from the MH model. It is defined on a continuous scale from $-1$ to $1$, which allows for intuitive interpretation of the nature of marginal change. An estimator of the proposed measure and an asymptotic confidence interval are derived using the delta method. The theoretical properties of the measure are also discussed. The proposed measure provides a flexible tool for characterizing marginal inhomogeneity in square contingency tables under ordinal settings.