Modelling 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 long-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 complimentary 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 heirarchically related marginal log-linear parameters, and the modelling implications of these results are indicated.