  In this paper, we propose a model that indicates the asymmetry structure for
cell probabilities in multivariate contingency tables with the same ordered
categories. The proposed model is the closest to the symmetry model in terms of
the $f$-divergence under certain conditions and incorporates various asymmetry
models as special cases, including existing models. We elucidate the
relationship between the proposed model and conventional models from several
aspects of divergence in $f$-divergence. Furthermore, we provide theorems
showing that the symmetry model can be decomposed into two or more models, each
imposing less restrictive parameter constraints than the symmetry condition. We
also discuss the properties of goodness-of-fit statistics, particularly
focusing on the likelihood ratio test statistics and Wald test statistics.
Finally, we summarize the proposed model and discuss some problems and future
work.
