Marginalization and Collapsibility in Graphical Interaction Models

Abstract

The behaviour of a graphical interaction model under marginalization is discussed. A graphical interaction model is called collapsible onto a set of variables if the class of marginal distributions is the same as that implied by the related subgraph. The necessary and sufficient condition for collapsibility is found and it is shown that collapsibility is equivalent to a range of other important statistical properties of the model.