University of Washington - Department of Statistics
Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of special structures, marginal independence hypotheses cannot be accommodated by these traditional models. For example, it is not possible to formulate a model for four variables (A,B,X,Y) such that A is independent of B, and X is independent of Y (and no other restrictions are imposed). Focusing on binary variables I will present a new model class that provides a framework for addressing this problem. The approach is graphical and based on bi-directed graphs, which are in the tradition of path diagrams. In many respects the resulting models and associated fitting algorithms are dual to graphical log-linear models.