Alternative interaction structures in square contingency tables having ordered classificatory variables

Goodman (1972) proposed several models for the analysis of the general I x I square tables with particular emphasis on social mobility data. We demonstrate in this paper, that most of his models can be reproduced by combinations of both new models proposed here and the various well known models that have received considerable attention in the literature. Our presentation here is both concise and simple to comprehend. The various models considered in this study are fitted to ten data sets that include the much analyzed 5×5 Danish and British Social mobility data sets. Results suggest that in some cases more parsimonious models than those considered earlier by various authors are possible for the explanations of the variations in the data analyzed in this study.