An extension of the results of Asmussen and Edwards on collapsibility in contingency tables
David Madigan, Krzysztof Mosurski · Biometrika · 1990
Asmussen & Edwards (1983) defined necessary and sufficient conditions for collapsibility of a hierarchical log linear model for a multidimensional contingency table. We have shown that for decomposable log linear models these conditions can be combined with various graph-theoretic algorithms to provide useful classes of sub-tables which are collapsible onto. In particular, the SAHR algorithm finds the minimal set onto which the model can be collapsed and which contains a sub-table of interest. In the context of expert systems, by reducing a probabilistic influence network onto only the relevant nodes, the algorithms reduce the required computation and simplify interpretation