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Biometrika 2005 92(2):351-370; doi:10.1093/biomet/92.2.351
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© 2005 Biometrika Trust

Conditional Akaike information for mixed-effects models

Florin Vaida1 and Suzette Blanchard2

1 Division of Biostatistics, Department of Family and Preventive Medicine, University of California at San Diego School of Medicine, La Jolla, California 92093, U.S.A. vaida{at}ucsd.edu, 2 Frontier Science and Technology Research Foundation Inc., Boston, Massachusetts 02215, U.S.A. suzette{at}sdac.harvard.edu

This paper focuses on the Akaike information criterion, AIC, for linear mixed-effects models in the analysis of clustered data. We make the distinction between questions regarding the population and questions regarding the particular clusters in the data. We show that the AIC in current use is not appropriate for the focus on clusters, and we propose instead the conditional Akaike information and its corresponding criterion, the conditional AIC, cAIC. The penalty term in cAIC is related to the effective degrees of freedom {rho} for a linear mixed model proposed by Hodges & Sargent (2001); {rho} reflects an intermediate level of complexity between a fixed-effects model with no cluster effect and a corresponding model with fixed cluster effects. The cAIC is defined for both maximum likelihood and residual maximum likelihood estimation. A pharmacokinetics data application is used to illuminate the distinction between the two inference settings, and to illustrate the use of the conditional AIC in model selection.

Key Words: Akaike information; AIC; Effective degrees of freedom; Linear mixed model

Received November 2002. Revised September 2004.


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