Asymmetry model based on f-divergence and orthogonal decomposition of symmetry for square contingency tables with ordinal categories

Abstract

Many statisticians have considered various symmetry and asymmetry 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 fit of the symmetry model.