"Akaike Information Criterion for Selecting Variables in a Nested Error Regression Model"

The Akaike Information Criterion (AIC) is developed for selecting the variables of a nested error regression model where an unobservable random effect is present. Using the idea of decomposing the marginal distribution into two parts of 'within' and 'between' analysis of variance, we derive the AIC when the number of groups is large. The unconditional AIC, the conditional AIC and the proposed AIC are compared using simulation. Based on the rates of selecting the true model, the proposed AIC performs better.