Modified versions of the Bayesian Information Criterion for sparse Generalized Linear Models |
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Authors: | Ma?gorzata ?ak-Szatkowska Ma?gorzata Bogdan |
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Affiliation: | a Institute of Mathematics and Computer Science, Wroc?aw University of Technology, Polandb Statistical Bioinformatics Center, Department of Statistics, Purdue University, USAc Department of Mathematics and Computer Science, Jan Dlugosz University, Poland |
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Abstract: | The classical model selection criteria, such as the Bayesian Information Criterion (BIC) or Akaike information criterion (AIC), have a strong tendency to overestimate the number of regressors when the search is performed over a large number of potential explanatory variables. To handle the problem of the overestimation, several modifications of the BIC have been proposed. These versions rely on supplementing the original BIC with some prior distributions on the class of possible models. Three such modifications are presented and compared in the context of sparse Generalized Linear Models (GLMs). The related choices of priors are discussed and the conditions for the asymptotic equivalence of these criteria are provided. The performance of the modified versions of the BIC is illustrated with an extensive simulation study and a real data analysis. Also, simplified versions of the modified BIC, based on least squares regression, are investigated. |
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Keywords: | Model selection Generalized Linear Models Bayesian Information Criterion Sparse linear models |
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