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

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.