Research Article Open Access

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

Kouji Yamamoto, Satoru Shinoda and Sadao Tomizawa

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.

Journal of Mathematics and Statistics
Volume 7 No. 4, 2011, 314-318

DOI: https://doi.org/10.3844/jmssp.2011.314.318

Submitted On: 5 October 2011 Published On: 28 October 2011

How to Cite: Yamamoto, K., Shinoda, S. & Tomizawa, S. (2011). Decompositions for Ordinal Quasi-Symmetry Model in Square Contingency Tables with Ordered Categories. Journal of Mathematics and Statistics, 7(4), 314-318. https://doi.org/10.3844/jmssp.2011.314.318

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Keywords

  • Linear diagonals-parameter symmetry
  • score
  • quasi-symmetry
  • weighted marginal homogeneity