Journal of Mathematics and Statistics

Decompositions for Ordinal Quasi-Symmetry Model in Square Contingency Tables with Ordered Categories

Kouji Yamamoto, Satoru Shinoda and Sadao Tomizawa

DOI : 10.3844/jmssp.2011.314.318

Journal of Mathematics and Statistics

Volume 7, Issue 4

Pages 314-318

Abstract

Problem statement: For square contingency tables with ordered categories, this study considers four kinds of extensions of the marginal homogeneity model and gives decompositions for the ordinal quasi-symmetry model. The decompositions are extensions of some existing decompositions. Approach: This study gives a decomposition theorem that the ordinal quasi-symmetry model holds if and only if the quasi-symmetry model and the proposed weighted marginal homogeneity model hold. An example is given. Results: For the data of cross-classification of father's and his son's occupational status in Denmark, the decomposition of the ordinal quasi-symmetry model is applied and the detailed analysis is given. Conclusion: When the ordinal quasi-symmetry model fits the data poorly, this decomposition is useful for seeing which of decomposed two models influences stronger.

Copyright

© 2011 Kouji Yamamoto, Satoru Shinoda and Sadao Tomizawa. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.