An index for measuring departure from an anti-sum-symmetry model for square contingency tables with ordered categories

Abstract In the analysis of square contingency tables, which are two-way contingency tables in which the row and column variables consist of the same classification, statistical models regarding the symmetry of row and column variables are often used rather than the independence. This study proposes an index for measuring the degree of departure from the anti-sum-symmetry model. The proposed index is constructed using the Kullback–Leibler divergence. The anti-sum-symmetry model is useful to evaluate whether symmetric and asymmetric structures exist with respect to the anti-diagonal of the table. We derive the plug-in estimator and large-sample confidence interval for the proposed index. The usefulness of the proposed index is demonstrated by applying it to real data.