On the Behavior of Marginal and Conditional Akaike Information Criteria in Linear Mixed Models

• Activity Number: 424
• Type: Contributed
• Date/Time: Wednesday, August 5, 2009 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Sonja Greven*+ and Thomas Kneib
• Companies: Johns Hopkins University and Ludwig-Maximilains-Universitaet Muenchen
• Keywords: Kullback-Leibler information ; model selection ; penalized splines ; random effect ; variance component

Abstract

The Akaike information criterion (AIC) is often used in linear mixed models to decide on the inclusion of a random effect. An important special case is the choice between a linear and a nonparametric regression model using mixed model penalized splines. Two versions of the AIC have been proposed, using either the marginal or the conditional likelihood. We show that the marginal AIC is not asymptotically unbiased for the Kullback-Leibler distance and favors models without random effects. For the conditional AIC, it is computationally costly but essential to correct for estimation uncertainty in the effective degrees of freedom. The often used uncorrected AIC always chooses inclusion of the random effect whenever its variance is estimated to be positive, no matter how small the estimate. We illustrate all results in simulation studies and in an analysis of childhood malnutrition in Zambia.