Many statisticians have considered various symmetry and asym-
metry models to analyze square contingency tables with ordinal categories. We
propose a generalized model, which indicates the asymmetric structure for cell
probabilities. This model is the closest to the symmetry model in terms of
the f-divergence under certain conditions. Then we decompose the symmetry
model using the proposed model, and partition the likelihood-ratio chi-square
test statistics for the symmetry model. The decomposition is useful to deduce
the reason for a poor t of the symmetry model.departmental bulletin pape
