Annals of the Institute of Statistical Mathematics

, 62:117

Model selection bias and Freedman’s paradox

Authors

    • Colorado Division of Wildlife
  • Kenneth P. Burnham
    • U.S. Geological Survey, Colorado Cooperative Fish and Wildlife Research UnitColorado State University
  • David R. Anderson
    • U.S. Geological Survey, Colorado Cooperative Fish and Wildlife Research UnitColorado State University
Article

DOI: 10.1007/s10463-009-0234-4

Cite this article as:
Lukacs, P.M., Burnham, K.P. & Anderson, D.R. Ann Inst Stat Math (2010) 62: 117. doi:10.1007/s10463-009-0234-4

Abstract

In situations where limited knowledge of a system exists and the ratio of data points to variables is small, variable selection methods can often be misleading. Freedman (Am Stat 37:152–155, 1983) demonstrated how common it is to select completely unrelated variables as highly “significant” when the number of data points is similar in magnitude to the number of variables. A new type of model averaging estimator based on model selection with Akaike’s AIC is used with linear regression to investigate the problems of likely inclusion of spurious effects and model selection bias, the bias introduced while using the data to select a single seemingly “best” model from a (often large) set of models employing many predictor variables. The new model averaging estimator helps reduce these problems and provides confidence interval coverage at the nominal level while traditional stepwise selection has poor inferential properties.

Keywords

Akaike’s information criterionConfidence interval coverageFreedman’s paradoxModel averagingModel selection biasModel selection uncertaintyMultimodel inferenceStepwise selection

Copyright information

© The Institute of Statistical Mathematics, Tokyo 2009