Orthogonal decomposition of symmetry model using the ordinal quasi-symmetry model based onf-divergence for square contingency tables

For square contingency tables, Caussinus (1965) considered the quasi-symmetry (QS) model. Kateri and Agresti (2007) 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.