Model selection for regression analyses with missing data

Abstract

The Akaiki Information Criterion, AIC, is one of the leading selection methods for regression models. In case of partially missing covariates with missingness probability depending on the response, regression estimates based on the so-called complete cases are known to be biased. In this contribution it is shown that model selection using AIC-values based on the complete cases can lead to the choice of wrong or less optimal models. In analogy with the weighted Horvitz-Thompson estimator, we propose a weighted version of AIC. It is shown that this weighted AIC criterion improves model choices.