Extended asymmetry model based on logit transformation and decomposition of symmetry for square contingency tables with ordered categories

The issues of symmetry (or asymmetry) arises naturally for the analysis of square contingency tables. Many existing asymmetry models do not have the constraints on the main diagonal cells. Thus, the observations on the main diagonal cells do not contribute to the likelihood ratio chi-squared test statistics. Herein we propose a model that indicates the asymmetry for the log odds.It can utilize the information in the main diagonal cells. Also, the symmetry model is separated into some models including the proposed model.