Model selection for incomplete and design-based samples.
The Akaike information criterion, AIC, is one of the most frequently used methods to select one or a few good, optimal regression models from a set of candidate models. In case the sample is incomplete, the naive use of this criterion on the so-called complete cases can lead to the selection of poor or inappropriate models. A similar problem occurs when a sample based on a design with unequal selection probabilities, is treated as a simple random sample. In this paper, we consider a modification of AIC, based on reweighing the sample in analogy with the weighted Horvitz-Thompson estimates. It is shown that this weighted AIC-criterion provides better model choices for both incomplete and design-based samples. The use of the weighted AIC-criterion is illustrated on data from the Belgian Health Interview Survey, which motivated this research. Simulations show its performance in a variety of settings.
Hens
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Center for Statistics, Universiteit Hasselt, Campus Diepenbeek, Agoralaan-Gebouw D, B-3590 Diepenbeek, Belgium. niel.hens@ahasselt.be
Aerts
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M
Molenberghs
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G
D000328:Adult; D001530:Belgium / Q000453:epidemiology; D003198:Computer Simulation; D003661:Decision Support Techniques; D005260:Female; D006801:Humans; D016013:Likelihood Functions; D008403:Mass Screening; D008875:Middle Aged; D012044:Regression Analysis; D012107:Research Design; D002583:Uterine Cervical Neoplasms / Q000453:epidemiology / Q000517:prevention & control; D014626:Vaginal Smears