A Measure of Departure from Marginal Homogeneity using Continuation Odds for Square Contingency Tables with Ordered Categories

Abstract For the analysis of square contingency tables with ordinal classifications, the marginal homogeneity (MH) model is the one of important models. Some measures for analyzing the degree of departure from the MH model have been proposed. This study proposes a new measure using the continuation odds. Continuation odds may be considered as discrete time hazard. The proposed measure is expressed in the form of Cressie-Read’s power-divergence (including the Kullback-Leibler divergence) or Patil and Taillie’s diversity index (including Shannon entropy). This study derives a plug-in estimator of the proposed measure and an approximate confidence interval for the proposed measure. Through numerical examples, we evaluate the performances of them. Additionally. the usefulness of the proposed measure is demonstrated by applying it to real data that the row and column variables are the discrete survival time variables.