@article {10.3844/jmssp.2011.314.318,
article_type = {journal},
title = {Decompositions for Ordinal Quasi-Symmetry Model in Square Contingency Tables with Ordered Categories},
author = {Yamamoto, Kouji and Shinoda, Satoru and Tomizawa, Sadao},
volume = {7},
year = {2011},
month = {Oct},
pages = {314-318},
doi = {10.3844/jmssp.2011.314.318},
url = {https://thescipub.com/abstract/jmssp.2011.314.318},
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.},
journal = {Journal of Mathematics and Statistics},
publisher = {Science Publications}
}