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Generalized degrees of freedom and adaptive model selection in linear mixed-effects models

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  • Zhang, Bo
  • Shen, Xiaotong
  • Mumford, Sunni L.

Abstract

Linear mixed-effects models involve fixed effects, random effects and covariance structures, which require model selection to simplify a model and to enhance its interpretability and predictability. In this article, we develop, in the context of linear mixed-effects models, the generalized degrees of freedom and an adaptive model selection procedure defined by a data-driven model complexity penalty. Numerically, the procedure performs well against its competitors not only in selecting fixed effects but in selecting random effects and covariance structure as well. Theoretically, asymptotic optimality of the proposed methodology is established over a class of information criteria. The proposed methodology is applied to the BioCycle Study, to determine predictors of hormone levels among premenopausal women and to assess variation in hormone levels both between and within women across the menstrual cycle.

Suggested Citation

  • Zhang, Bo & Shen, Xiaotong & Mumford, Sunni L., 2012. "Generalized degrees of freedom and adaptive model selection in linear mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 574-586.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:3:p:574-586
    DOI: 10.1016/j.csda.2011.09.001
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    References listed on IDEAS

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    1. Shen, Xiaotong & Huang, Hsin-Cheng, 2006. "Optimal Model Assessment, Selection, and Combination," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 554-568, June.
    2. Bradley Efron, 2004. "The Estimation of Prediction Error: Covariance Penalties and Cross-Validation," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 619-632, January.
    3. Robert Tibshirani & Keith Knight, 1999. "The Covariance Inflation Criterion for Adaptive Model Selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 529-546.
    4. Shen X. & Ye J., 2002. "Adaptive Model Selection," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 210-221, March.
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    1. María José Lombardía & Esther López‐Vizcaíno & Cristina Rueda, 2017. "Mixed generalized Akaike information criterion for small area models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1229-1252, October.
    2. Cristina Rueda & Miguel A. Fernández & Sandra Barragán & Kanti V. Mardia & Shyamal D. Peddada, 2016. "Circular piecewise regression with applications to cell‐cycle data," Biometrics, The International Biometric Society, vol. 72(4), pages 1266-1274, December.

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