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On the behaviour of marginal and conditional AIC in linear mixed models

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  • Sonja Greven
  • Thomas Kneib
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    Abstract

    In linear mixed models, model selection frequently includes the selection of random effects. Two versions of the Akaike information criterion, aic , have been used, based either on the marginal or on the conditional distribution. We show that the marginal aic is not an asymptotically unbiased estimator of the Akaike information, and favours smaller models without random effects. For the conditional aic , we show that ignoring estimation uncertainty in the random effects covariance matrix, as is common practice, induces a bias that can lead to the selection of any random effect not predicted to be exactly zero. We derive an analytic representation of a corrected version of the conditional aic , which avoids the high computational cost and imprecision of available numerical approximations. An implementation in an R package (R Development Core Team, 2010) is provided. All theoretical results are illustrated in simulation studies, and their impact in practice is investigated in an analysis of childhood malnutrition in Zambia. Copyright 2010, Oxford University Press.

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    Bibliographic Info

    Article provided by Biometrika Trust in its journal Biometrika.

    Volume (Year): 97 (2010)
    Issue (Month): 4 ()
    Pages: 773-789

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    Handle: RePEc:oup:biomet:v:97:y:2010:i:4:p:773-789

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    Cited by:
    1. Yu, Dalei & Yau, Kelvin K.W., 2012. "Conditional Akaike information criterion for generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 629-644.
    2. 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.
    3. Sonja Greven & Ciprian Crainiceanu, 2013. "On likelihood ratio testing for penalized splines," AStA Advances in Statistical Analysis, Springer, vol. 97(4), pages 387-402, October.
    4. Braun, Julia & Sabanés Bové, Daniel & Held, Leonhard, 2014. "Choice of generalized linear mixed models using predictive crossvalidation," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 190-202.
    5. van den Hout, Ardo & Muniz-Terrera, Graciela & Matthews, Fiona E., 2013. "Change point models for cognitive tests using semi-parametric maximum likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 684-698.
    6. Yu, Dalei & Zhang, Xinyu & Yau, Kelvin K.W., 2013. "Information based model selection criteria for generalized linear mixed models with unknown variance component parameters," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 245-262.

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