Iterative Scaling for Irregular Patterns of Association

Some patterns of association that naturally appear in, for example, market basket analysis, text recognition, multistage capture-recapture procedures, and others seem irregular if considered from the point of view of conventional log-linear models. Such patterns of association cannot be described using partitions in a contingency table, and thus are lacking the so-called overall effect. The lack of the overall effect is an intrinsic property of a model, and cannot be fixed by a re-parameterization. Models without the overall effect are illustrated using a model of independence between two morphological structures in the Hungarian language. Traditional iterative scaling procedures, used for computing the expected cell counts in contingency tables, do not work for such a model. The algorithm described in this presentation can be used for models with or without the overall effect.