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Conditional information criteria for selecting variables in linear mixed models

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  • Srivastava, Muni S.
  • Kubokawa, Tatsuya

Abstract

In this paper, we consider the problem of selecting the variables of the fixed effects in the linear mixed models where the random effects are present and the observation vectors have been obtained from many clusters. As the variable selection procedure, here we use the Akaike Information Criterion, AIC. In the context of the mixed linear models, two kinds of AIC have been proposed: marginal AIC and conditional AIC. In this paper, we derive three versions of conditional AIC depending upon different estimators of the regression coefficients and the random effects. Through the simulation studies, it is shown that the proposed conditional AIC's are superior to the marginal and conditional AIC's proposed in the literature in the sense of selecting the true model. Finally, the results are extended to the case when the random effects in all the clusters are of the same dimension but have a common unknown covariance matrix.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:9:p:1970-1980
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    References listed on IDEAS

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    1. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    2. Florin Vaida & Suzette Blanchard, 2005. "Conditional Akaike information for mixed-effects models," Biometrika, Biometrika Trust, vol. 92(2), pages 351-370, June.
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    Cited by:

    1. Yuki Kawakubo & Tatsuya Kubokawa & Muni S. Srivastava, 2015. "A Variant of AIC Using Bayesian Marginal Likelihood," CIRJE F-Series CIRJE-F-971, CIRJE, Faculty of Economics, University of Tokyo.
    2. Kawakubo, Yuki & Kubokawa, Tatsuya, 2014. "Modified conditional AIC in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 44-56.
    3. Yuki Kawakubo & Shonosuke Sugasawa & Tatsuya Kubokawa, 2014. "Conditional AIC under Covariate Shift with Application to Small Area Prediction," CIRJE F-Series CIRJE-F-944, CIRJE, Faculty of Economics, University of Tokyo.
    4. Simona Buscemi & Antonella Plaia, 2020. "Model selection in linear mixed-effect models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 529-575, December.
    5. 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.
    6. Masahiro Kojima & Tatsuya Kubokawa, 2013. "Bartlett Adjustments for Hypothesis Testing in Linear Models with General Error Covariance Matrices," CIRJE F-Series CIRJE-F-884, CIRJE, Faculty of Economics, University of Tokyo.
    7. 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.
    8. Yuki Kawakubo & Tatsuya Kubokawa & Muni S. Srivastava, 2018. "A Variant of AIC Based on the Bayesian Marginal Likelihood," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 60-84, May.

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