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Biometrika 1990 77(2):315-319; doi:10.1093/biomet/77.2.315
© 1990 by Biometrika Trust
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An extension of the results of Asmussen and Edwards on collapsibility in contingency tables

DAVID MADIGAN and KRZYSZTOF MOSURSKI

Department of Statistics, Trinity College Dublin, Republic of Ireland

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

Key Words: Collapsibility • Decomposable model • Expert system • Graphical model • Log linear model


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