MARGINAL HOMOGENEITY AND DISTANCE SUBSYMMETRY MODELS IN SQUARE CONTINGENCY TABLES WITH ORDERED CATEGORIES

Abstract

In this study, we have employed the GSK and the non-standard log-linear model
approaches to fit the class of distance sub-symmetry models to square contingency
tables having ordered categories. SAS PROCs CATMOD and GENMOD were
employed to implement our models. A macro generates the factor variables to
implement models in the latter approach. Except for the DCS-k where no maxi-
mum likelihood closed form exists, all other models are easily implemented with
the non standard log-linear model approach. The GSK on the other hand readily
fits all the models considered in this study. These models are applied to the 5×5
British generational data as well as the 4× 4 unaided distance vision data. Both
data have received considerable attention and analyses in the literature. Results
obtained where applicable agree with those published in previous literature on
the subject. The approaches suggest here eliminate any programming that might
be required in order to apply these class of models to square contingency tables.