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Model selection in linear mixed effect models

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  • Peng, Heng
  • Lu, Ying

Abstract

Mixed effect models are fundamental tools for the analysis of longitudinal data, panel data and cross-sectional data. They are widely used by various fields of social sciences, medical and biological sciences. However, the complex nature of these models has made variable selection and parameter estimation a challenging problem. In this paper, we propose a simple iterative procedure that estimates and selects fixed and random effects for linear mixed models. In particular, we propose to utilize the partial consistency property of the random effect coefficients and select groups of random effects simultaneously via a data-oriented penalty function (the smoothly clipped absolute deviation penalty function). We show that the proposed method is a consistent variable selection procedure and possesses some oracle properties. Simulation studies and a real data analysis are also conducted to empirically examine the performance of this procedure.

Suggested Citation

  • Peng, Heng & Lu, Ying, 2012. "Model selection in linear mixed effect models," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 109-129.
    • Handle: RePEc:eee:jmvana:v:109:y:2012:i:c:p:109-129
    DOI: 10.1016/j.jmva.2012.02.005
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    Cited by:

    1. Francis K. C. Hui & Samuel Müller & A. H. Welsh, 2017. "Joint Selection in Mixed Models using Regularized PQL," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1323-1333, July.
    2. 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.
    3. Haidong Zhao & Lina Zhang & M. B. Kirkham & Stephen M. Welch & John W. Nielsen-Gammon & Guihua Bai & Jiebo Luo & Daniel A. Andresen & Charles W. Rice & Nenghan Wan & Romulo P. Lollato & Dianfeng Zheng, 2022. "U.S. winter wheat yield loss attributed to compound hot-dry-windy events," Nature Communications, Nature, vol. 13(1), pages 1-9, December.
    4. Hang Lai & Xin Gao, 2023. "Modified BIC Criterion for Model Selection in Linear Mixed Models," Mathematics, MDPI, vol. 11(9), pages 1-26, May.
    5. Pelinescu Elena & Simionescu Mihaela, 2019. "Higher Education Policies and Employability of University Graduates in the EU-28," Journal of Intercultural Management, Sciendo, vol. 11(3), pages 105-133, September.
    6. 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.
    7. 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.
    8. Jakob Peterlin & Nataša Kejžar & Rok Blagus, 2023. "Correct specification of design matrices in linear mixed effects models: tests with graphical representation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 184-210, March.
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    10. Sawadogo, Alidou & Dossou-Yovo, Elliott R. & Kouadio, Louis & Zwart, Sander J. & Traoré, Farid & Gündoğdu, Kemal S., 2023. "Assessing the biophysical factors affecting irrigation performance in rice cultivation using remote sensing derived information," Agricultural Water Management, Elsevier, vol. 278(C).
    11. Chih-Hao Chang & Hsin-Cheng Huang & Ching-Kang Ing, 2022. "Inference of random effects for linear mixed-effects models with a fixed number of clusters," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(6), pages 1143-1161, December.

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