AIC and BIC for modeling with complex survey data

Model-selection criteria such as AIC and BIC are widely used in applied statistics. In recent years, there has been a huge increase in modeling data from large complex surveys, and a resulting demand for versions of AIC and BIC that are valid under complex sampling. In this paper, we show how both criteria can be modified to handle complex samples. We illustrate with two examples, the first using data from NHANES and the second using data from a case–control study.