A fast model selection procedure for large families of models

Abstract An efficient procedure for model selection from large families of models is described. It is closely related to the all possible models approach but is considerably faster. It is based on two principles: first, if a model is accepted, then all models that include it are considered to be accepted; second, if a model is rejected, then all of its submodels are considered to be rejected. Application of the procedure to variable selection in multiple regression is illustrated. General algorithms are described that enable the procedure to be applied to any family of models that forms a lattice. As an example, a problem in multiple comparisons is considered.

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