SPECIFICATIONS OF MODELS FOR CROSS-CLASSIFIED COUNTS - COMPARISONS OFTHE LOG-LINEAR MODELS AND MARGINAL MODELS PERSPECTIVES

Log-linear models are useful for analyzing cross-classifications of co unts arising in sociology, but it has been argued that in some cases, an alternative approach for formulating models-one based on simultaneo usly modeling univariate marginal logits and marginal associations-can lead to models that are more directly relevant for addressing the kin ds of questions arising in those cases. In this article, the authors e xplore some of the similarities and differences between the log-linear models approach to modeling categorical data and a marginal modeling approach. It has been noted in past literature that the model of stati stical independence is conveniently represented within both approaches to specifying models for cross-classifications of counts. The authors examine further the extent to which the two families of models overla p, as well as some important differences. The authors do not present a complete characterization of the conditions describing the intersecti on of the two families of models but cover many of the models for biva riate contingency tables and for three-way contingency tables that are routinely used in sociological research.