A class of parametric models for the analysis of square contingency tables with ordered categories

Abstract

SUMMARY A parametric model is developed for the analysis of square contingency tables with ordered categories. Order among the categories is a built-in feature of the new model and this means that it is unnecessary to assign arbitrary 'scores' to the row and column variables. Special cases of the proposed model include conditional symmetry and symmetry. The relationship with marginal homogeneity is also described. The model for quasisymmetry is considered and is shown to be invariant under general permutation transformations of the indices, which makes it suitable for analysing data on a nominal scale. On the other hand, the new model, called p symmetry, is invariant only under the special reverse permutation transformation. This restricted invariance property makes the latter model more suitable for analysing data on an ordinal scale.