Generalized Sum-Asymmetry Model and Orthogonality of Test Statistic for Square Contingency Tables

For analyzing contingency tables, we are usually interested in whether or not the independence model holds. On the other hand, for the analysis of square contingency tables, we are usually interested in whether or not the model having the structure of symmetry or asymmetry with respect to the main diagonals cells holds. This study proposes a generalized sum-asymmetry model including the exponential and relative exponential sum-symmetry models. This generalized model indicates that the cumulative probability that the sum of classes for row and column variables is s within the upper right cell of the table, is exponentially higher than the cumulative probability that the sum of classes for row and column variables is s within the lower left cell. Additionally, this study gives a separation of the sum-symmetry model using the proposed model, and reveals that the new separation satisfies the asymptotic equivalence for the test statistic. The utilities of the proposed methods are demonstrated through the real data analysis.