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Modfiied Conditional AIC in Linear Mixed Models


  • Yuki Kawakubo

    (Graduate School of Economics, University of Tokyo)

  • Tatsuya Kubokawa

    (Faculty of Economics, University of Tokyo)


   In linear mixed models, the conditional Akaike Information Criterion (cAIC) is a procedure for variable selection in light of the prediction of specific clusters or random effects. This is useful in problems involving prediction of random effects such as small area estimation, and much attention has been received since suggested by Vaida and Blanchard (2005). A weak point of cAIC is that it is derived as an unbiased estimator of conditional Akaike information (cAI) in the overspecified case, namely in the case that candidate models include the true model. This results in larger biases in the underspecified case that the true model is not included in candidate models. In this paper, we derive the modified cAIC (McAIC) to cover both the underspecified and overspecified cases, and investigate properties of McAIC. It is numerically shown that McAIC has less biases and less prediction errors than cAIC.

Suggested Citation

  • Yuki Kawakubo & Tatsuya Kubokawa, 2013. "Modfiied Conditional AIC in Linear Mixed Models," CIRJE F-Series CIRJE-F-895, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2013cf895

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    References listed on IDEAS

    1. Srivastava, Muni S. & Kubokawa, Tatsuya, 2010. "Conditional information criteria for selecting variables in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 1970-1980, October.
    2. Kubokawa, Tatsuya & Nagashima, Bui, 2012. "Parametric bootstrap methods for bias correction in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 1-16.
    3. M. C. Donohue & R. Overholser & R. Xu & F. Vaida, 2011. "Conditional Akaike information under generalized linear and proportional hazards mixed models," Biometrika, Biometrika Trust, vol. 98(3), pages 685-700.
    4. Sonja Greven & Thomas Kneib, 2010. "On the behaviour of marginal and conditional AIC in linear mixed models," Biometrika, Biometrika Trust, vol. 97(4), pages 773-789.
    5. Kubokawa, Tatsuya, 2011. "Conditional and unconditional methods for selecting variables in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 641-660, March.
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