IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v32y2023i3d10.1007_s10260-023-00685-2.html
   My bibliography  Save this article

Partial least square based approaches for high-dimensional linear mixed models

Author

Listed:
  • Caroline Bazzoli

    (Universitê Grenoble Alpes)

  • Sophie Lambert-Lacroix

    (Universitê Grenoble Alpes)

  • Marie-José Martinez

    (Universitê Grenoble Alpes)

Abstract

To deal with repeated data or longitudinal data, linear mixed effects models are commonly used. A classical parameter estimation method is the Expectation–Maximization (EM) algorithm. In this paper, we propose three new Partial Least Square (PLS) based approaches using the EM-algorithm to reduce the high-dimensional data to a lower one for fixed effects in linear mixed models. Unlike the Principal Component Regression approach, the PLS method allows to take into account the link between the outcome and the independent variables. We compare these approaches from a simulation study and a yeast cell-cycle gene expression data set. We demonstrate the performance of two of them and we recommend their use to conduct future analyses for high dimensional data in linear mixed effect models context.

Suggested Citation

  • Caroline Bazzoli & Sophie Lambert-Lacroix & Marie-José Martinez, 2023. "Partial least square based approaches for high-dimensional linear mixed models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 769-786, September.
    • Handle: RePEc:spr:stmapp:v:32:y:2023:i:3:d:10.1007_s10260-023-00685-2
    DOI: 10.1007/s10260-023-00685-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10260-023-00685-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10260-023-00685-2?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. Rohart, Florian & San Cristobal, Magali & Laurent, Béatrice, 2014. "Selection of fixed effects in high dimensional linear mixed models using a multicycle ECM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 209-222.
    2. Shayle Searle, 1995. "An overview of variance component estimation," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 42(1), pages 215-230, December.
    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. Eliot Melissa & Ferguson Jane & Reilly Muredach P. & Foulkes Andrea S., 2011. "Ridge Regression for Longitudinal Biomarker Data," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-11, September.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Ollier, Edouard & Samson, Adeline & Delavenne, Xavier & Viallon, Vivian, 2016. "A SAEM algorithm for fused lasso penalized NonLinear Mixed Effect Models: Application to group comparison in pharmacokinetics," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 207-221.
    3. Mammen, Enno & Wilke, Ralf A. & Zapp, Kristina Maria, 2022. "Estimation of group structures in panel models with individual fixed effects," ZEW Discussion Papers 22-023, ZEW - Leibniz Centre for European Economic Research.
    4. Abhik Ghosh & Magne Thoresen, 2018. "Non-concave penalization in linear mixed-effect models and regularized selection of fixed effects," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(2), pages 179-210, April.
    5. Jan Pablo Burgard & Joscha Krause & Ralf Münnich, 2019. "Penalized Small Area Models for the Combination of Unit- and Area-level Data," Research Papers in Economics 2019-05, University of Trier, Department of Economics.
    6. M. Revan Özkale & Funda Can, 2017. "An evaluation of ridge estimator in linear mixed models: an example from kidney failure data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(12), pages 2251-2269, September.
    7. 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.
    8. Kramlinger, Peter & Schneider, Ulrike & Krivobokova, Tatyana, 2023. "Uniformly valid inference based on the Lasso in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    9. 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.
    10. Huaihou Chen & Donglin Zeng & Yuanjia Wang, 2017. "Penalized nonlinear mixed effects model to identify biomarkers that predict disease progression," Biometrics, The International Biometric Society, vol. 73(4), pages 1343-1354, December.
    11. Mojtaba Ganjali & Taban Baghfalaki, 2018. "Application of Penalized Mixed Model in Identification of Genes in Yeast Cell-Cycle Gene Expression Data," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 6(2), pages 38-41, April.
    12. Daniel R. Kowal, 2023. "Subset selection for linear mixed models," Biometrics, The International Biometric Society, vol. 79(3), pages 1853-1867, September.
    13. Hou Jiayi & Archer Kellie J., 2015. "Regularization method for predicting an ordinal response using longitudinal high-dimensional genomic data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 14(1), pages 93-111, February.
    14. Luoying Yang & Tong Tong Wu, 2023. "Model‐based clustering of high‐dimensional longitudinal data via regularization," Biometrics, The International Biometric Society, vol. 79(2), pages 761-774, June.
    15. Shakhawat Hossain & Trevor Thomson & Ejaz Ahmed, 2018. "Shrinkage estimation in linear mixed models for longitudinal data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(5), pages 569-586, July.
    16. Mingan Yang & Min Wang & Guanghui Dong, 2020. "Bayesian variable selection for mixed effects model with shrinkage prior," Computational Statistics, Springer, vol. 35(1), pages 227-243, March.
    17. Peirong Xu & Lixing Zhu & Yi Li, 2014. "Ultrahigh dimensional time course feature selection," Biometrics, The International Biometric Society, vol. 70(2), pages 356-365, June.
    18. Wafa Alwakid & Sebastian Aparicio & David Urbano, 2020. "Cultural Antecedents of Green Entrepreneurship in Saudi Arabia: An Institutional Approach," Sustainability, MDPI, vol. 12(9), pages 1-20, May.
    19. Wei, Yuting & Wang, Qihua & Duan, Xiaogang & Qin, Jing, 2021. "Bias-corrected Kullback–Leibler distance criterion based model selection with covariables missing at random," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    20. Gerhard Tutz & Gunther Schauberger, 2015. "A Penalty Approach to Differential Item Functioning in Rasch Models," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 21-43, March.

    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:spr:stmapp:v:32:y:2023:i:3:d:10.1007_s10260-023-00685-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.