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Orthogonal decomposition of symmetry model using the ordinal quasi-symmetry model based on \(f\)-divergence for square contingency tables. (English) Zbl 1328.62362

Summary: For square contingency tables, H. Caussinus [Ann. Fac. Sci. Univ. Toulouse, IV. Sér. 29, 77–183 (1966; Zbl 0168.39904)] considered the quasi-symmetry (QS) model. M. Kateri and A. Agresti [Stat. Probab. Lett. 77, No. 6, 598–603 (2007; Zbl 1116.62067)] considered the ordinal quasi-symmetry (OQS[\(f\)]) model based on \(f\)-divergence. The present paper gives a decomposition of the symmetry (\(S\)) model into the OQS[\(f\)] and marginal mean equality models. It also shows that the test statistic for goodness-of-fit of the \(S\) model is asymptotically equivalent to the sum of those for the decomposed models.

MSC:

62H17 Contingency tables
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