Modeling conditional and marginal association in contingency tables

— Standard tools for the analysis of the (average) conditional association structure of the distribution on a multiway contingency table are log-linear models. A different association concept is that of marginal association and this paper demonstrates how marginal log-linear parameters can be used to measure this aspect of association. The paper gives a non-technical discussion of these two aspects of association by discussing their complementary nature and also describes how conditional association is naturally incorporated in the framework provided by marginal log-linear parameters. The properties and interpretation of these parameters are discussed, including the variation independence of hierarchically related marginal log-linear parameters, and the modeling implications of these results are indicated. (∗) Reçu le 18 septembre 2001, accepté le 18 septembre 2002 (1) Department of Methodology, Faculty of Social and Behavioral Sciences, Tilburg University, 5000 LE Tilburg, The Netherlands. E-mail:[email protected] (2) Department of Statistics, School of Sociology and Social Policy, Eötvös Loránd University, Hungary. E-mail: [email protected]