IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i3p574-586.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311003197
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2011.09.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Philip Reiss & Lei Huang & Joseph Cavanaugh & Amy Roy, 2012. "Resampling-based information criteria for best-subset regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(6), pages 1161-1186, December.
    2. Giessing, Alexander & He, Xuming, 2019. "On the predictive risk in misspecified quantile regression," Journal of Econometrics, Elsevier, vol. 213(1), pages 235-260.
    3. Daudin, Jean-Jacques & Mary-Huard, Tristan, 2008. "Estimation of the conditional risk in classification: The swapping method," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3220-3232, February.
    4. Hirose, Kei & Tateishi, Shohei & Konishi, Sadanori, 2013. "Tuning parameter selection in sparse regression modeling," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 28-40.
    5. Yi, Feng & Zou, Hui, 2013. "SURE-tuned tapering estimation of large covariance matrices," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 339-351.
    6. Yongli Zhang & Xiaotong Shen, 2015. "Adaptive Modeling Procedure Selection by Data Perturbation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 541-551, October.
    7. Gao, Zhikun & Tang, Yanlin & Wang, Huixia Judy & Wu, Guangying K. & Lin, Jeff, 2020. "Automatic identification of curve shapes with applications to ultrasonic vocalization," Computational Statistics & Data Analysis, Elsevier, vol. 148(C).
    8. Borra, Simone & Di Ciaccio, Agostino, 2010. "Measuring the prediction error. A comparison of cross-validation, bootstrap and covariance penalty methods," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2976-2989, December.
    9. Jin‐Hua Chen & Chun‐Shu Chen & Meng‐Fan Huang & Hung‐Chih Lin, 2016. "Estimating the Probability of Rare Events Occurring Using a Local Model Averaging," Risk Analysis, John Wiley & Sons, vol. 36(10), pages 1855-1870, October.
    10. Theo Dijkstra, 2014. "Ridge regression and its degrees of freedom," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(6), pages 3185-3193, November.
    11. Sieds, 2012. "Complete Volume LXVI n.1 2012," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - The Italian Journal of Economic, Demographic and Statistical Studies, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 66(1), pages 1-296.
    12. 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.
    13. Hettihewa, Samanthala & Saha, Shrabani & Zhang, Hanxiong, 2018. "Does an aging population influence stock markets? Evidence from New Zealand," Economic Modelling, Elsevier, vol. 75(C), pages 142-158.
    14. Mendez, Guillermo & Lohr, Sharon, 2011. "Estimating residual variance in random forest regression," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2937-2950, November.
    15. Yanagihara, Hirokazu & Satoh, Kenichi, 2010. "An unbiased Cp criterion for multivariate ridge regression," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1226-1238, May.
    16. Meiri, Ronen & Zahavi, Jacob, 2006. "Using simulated annealing to optimize the feature selection problem in marketing applications," European Journal of Operational Research, Elsevier, vol. 171(3), pages 842-858, June.
    17. Zhang, Xinyu & Yu, Jihai, 2018. "Spatial weights matrix selection and model averaging for spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 203(1), pages 1-18.
    18. Chunming Zhang, 2008. "Prediction Error Estimation Under Bregman Divergence for Non‐Parametric Regression and Classification," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 496-523, September.
    19. James Younker, 2022. "Calculating Effective Degrees of Freedom for Forecast Combinations and Ensemble Models," Discussion Papers 2022-19, Bank of Canada.
    20. Wang, You-Gan & Hin, Lin-Yee, 2010. "Modeling strategies in longitudinal data analysis: Covariate, variance function and correlation structure selection," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3359-3370, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:56:y:2012:i:3:p:574-586. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.