On Quasi-Symmetry Based on Ridit for Analysis of Square Contingency Tables

For square contingency tables with the same row and column ordinal classifications, we propose a model of quasi-symmetry using the row and column marginal ridits scores. Using the proposed model, the model of equality of marginal mean ridits and the model of equality of marginal variance ridits, we give a theorem such that the symmetry model holds if and only if all these models hold. Moreover, we show that the likelihood ratio statistic for testing goodness-of-fit of the symmetry model is asymptotically equivalent to the sum of those for the decomposed models. The proposed model is illustrated with an application to occupational status data.