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Biometrika 1985 72(2):339-351; doi:10.1093/biomet/72.2.339
© 1985 by Biometrika Trust
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A fast procedure for model search in multidimensional contingency tables

DAVID EDWARDS and HAVRÁNEK TOMÁ{caron}

Regional Computing Centre at the University of Copenhagen 2100 Copenhagen, Denmark
Centre of Biomathematics, Institute of Physiology, Czechoslovak Academy of Sciences, Prague, Czechoslovakia

A procedure to select the simplest acceptable models for a multidimensional contingency table is proposed. It is based on two rules: first, that if a model is accepted, then all models that include it are considered to be accepted, and secondly, that if a model is rejected, then all its submodels are considered to be rejected. Two versions are described, one for the class of graphical models, and the other for the class of hierarchical log linear models. Application of both versions to a six-dimensional table is illustrated. The procedure can be regarded as an alternative to fitting all possible models, made computationally feasible by application of the two rules. It is a generalization of the procedure proposed by Havranek (1984), but is in many cases considerably faster.

Key Words: Coherence • Contingency table • Distributive lattice • Graphical model • Log linear model • Model selection


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