## 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

### Citations:

Zbl 0168.39904; Zbl 1116.62067
Full Text:

### References:

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