Abstract
AbstractFor 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.
Funder
Tokyo University of Science
Publisher
Springer Science and Business Media LLC
Reference14 articles.
1. Stuart, A.: A test for homogeneity of the marginal distributions in a two-way classification. Biometrika 42(3/4), 412–416 (1955)
2. McCullagh, P.: A logistic model for paired comparisons with ordered categorical data. Biometrika 64(3), 449–453 (1977)
3. Kurakami, H., Tahata, K., Tomizawa, S.: Extension of the marginal cumulative logistic model and decompositions of marginal homogeneity for multi-way tables. Journal of Statistics: Advances in Theory and Applications 3(2), 135–152 (2010)
4. Kurakami, H., Tahata, K., Tomizawa, S.: Generalized marginal cumulative logistic model for multi-way contingency tables. SUT Journal of Mathematics 49(1), 19–32 (2013)
5. Iki, K., Tahata, K., Tomizawa, S.: Measure of departure from marginal homogeneity using marginal odds for multi-way tables with ordered categories. Journal of Applied Statistics 39(2), 279–295 (2012)