An extension of the results of Asmussen and Edwards on collapsibility in contingency tables. (English) Zbl 0731.62113

Madigan, David; Mosurski, Krzysztof

Biometrika 77, No. 2, 315-319 (1990).

Summary: S. Asmussen and D. Edwards [ibid. 70, 567-578 (1983; Zbl 0549.62041)] 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.

MSC:

62H17

Contingency tables

Keywords:

collapsibility; decomposable log linear models; graph-theoretic algorithms; SAHR algorithm; expert systems

Citations:

Zbl 0549.62041