Asymmetry Models for Contingency Tables

Abstract

For the quasi-symmetry (QS) model, applicable to square contingency tables with commensurable classification variables, it is proved that under certain conditions, it is the closest model to symmetry in terms of the Kullback-Leibler distance. Replacing the Kullback-Leibler distance by f -divergence we introduce a generalized quasi-symmetry model, the QS[ f ], and develop interpretational aspects for its parameters. QS is a special case of QS[ f ], whereas the most characteristic of the newly introduced QS-type models is the Pearsonian QS model. We compute maximum likelihood estimates of the parameters of the Pearsonian QS model and compare it, through examples and simulation studies, to the classical QS model in terms of goodness of fit and of the powers of the tests for marginal homogeneity conditional on the QS and Pearsonian QS models.