Ridit Score Type Quasi-Symmetry and Decomposition of Symmetry for Square Contingency Tables with Ordered Categories

Abstract

For square contingency tables with the same row and column ordinal classifications, this paper proposes the quasi-symmetry model based on the marginal ridits. The model indicates that the log-odds that an observation will fall in the (i; j) cell instead of in the (j; i) cell, i < j, is proportional to the difference between the average ridit score of row and column marginal distributions for category j and that for category i. This paper also gives a theorem such that the symmetry model holds if and only if both the proposed model and the marginal mean equality model hold. Examples are given.