Model Selection in Logistic Regression Using p-Values and Greedy Search

We study new logistic model selection criteria based on pvalues. The rules are proved to be consistent provided suitable assumptions on design matrix and scaling constants are satisfied and the search is performed over the family of all submodels. As a byproduct, consistency of Bayesian Information Criterion (BIC) for logistic regression models proved by Qian and Field in [11] is obtained under milder assumptions. Moreover, we investigate practical performance of the introduced criteria in conjunction with greedy search methods such as initial ordering, forward and backward search and genetic algorithm which restrict the range of family of models over which an optimal value of the respective criterion is sought. Scaled minimal p-value criterion with initial ordering turns out to be a promising alternative to BIC.