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

Bo Zhang, Xiaotong Shen, Sunni L. Mumford

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)574-586
Number of pages13
JournalComputational Statistics and Data Analysis
Issue number3
StatePublished - Mar 1 2012

Bibliographical note

Funding Information:
The authors would like to sincerely thank Editor, Associate Editor and two anonymous referees for their insightful comments that have led to significant improvement of this paper. Bo Zhang and Sunni L. Mumford’s research was supported by the Intramural Research Program of the National Institutes of Health, Eunice Kennedy Shriver National Institute of Child Health and Human Development. Xiaotong Shen’s research was supported in part by NIH grant 1R01GM081535-01 , and NSF grants DMS-0604394 and DMS-0906616 . The authors also thank the Center for Information Technology, the National Institutes of Health, for providing access to the high performance computational capabilities of the Biowulf Linux cluster.


  • Adaptive penalty
  • Generalized degrees of freedom
  • Linear mixed-effects models
  • Loss estimation


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