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New variable selection for linear mixed-effects models

Author

Listed:
  • Ping Wu

    (East China Normal University)

  • Xinchao Luo

    (East China Normal University)

  • Peirong Xu

    (Southeast University)

  • Lixing Zhu

    (Beijing Normal University
    Hong Kong Baptist University)

Abstract

In this paper, we consider how to select both the fixed effects and the random effects in linear mixed models. To make variable selection more efficient for such models in which there are high correlations between covariates associated with fixed and random effects, a novel approach is proposed, which orthogonalizes fixed and random effects such that the two sets of effects can be separately selected with less influence on one another. Also, unlike most of existing methods with parametric assumptions, the new method only needs fourth order moments of involved random variables. The oracle property is proved. the performance of our method is examined by a simulation study.

Suggested Citation

  • Ping Wu & Xinchao Luo & Peirong Xu & Lixing Zhu, 2017. "New variable selection for linear mixed-effects models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(3), pages 627-646, June.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:3:d:10.1007_s10463-016-0555-z
    DOI: 10.1007/s10463-016-0555-z
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Pu, Wenji & Niu, Xu-Feng, 2006. "Selecting mixed-effects models based on a generalized information criterion," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 733-758, March.
    3. Howard D. Bondell & Arun Krishna & Sujit K. Ghosh, 2010. "Joint Variable Selection for Fixed and Random Effects in Linear Mixed-Effects Models," Biometrics, The International Biometric Society, vol. 66(4), pages 1069-1077, December.
    4. Joseph G. Ibrahim & Hongtu Zhu & Ramon I. Garcia & Ruixin Guo, 2011. "Fixed and Random Effects Selection in Mixed Effects Models," Biometrics, The International Biometric Society, vol. 67(2), pages 495-503, June.
    5. Ping Wu & Li Xing Zhu, 2010. "An Orthogonality‐Based Estimation of Moments for Linear Mixed Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 253-263, June.
    6. Peng, Heng & Lu, Ying, 2012. "Model selection in linear mixed effect models," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 109-129.
    7. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
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