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Shrinkage estimation in linear mixed models for longitudinal data

Author

Listed:
  • Shakhawat Hossain

    (University of Winnipeg)

  • Trevor Thomson

    (University of Winnipeg)

  • Ejaz Ahmed

    (Brock University)

Abstract

This paper is concerned with the selection and estimation of fixed effects in linear mixed models while the random effects are treated as nuisance parameters. We propose the non-penalty James–Stein shrinkage and pretest estimation methods based on linear mixed models for longitudinal data when some of the fixed effect parameters are under a linear restriction. We establish the asymptotic distributional biases and risks of the proposed estimators, and investigate their relative performance with respect to the unrestricted maximum likelihood estimator (UE). Furthermore, we investigate the penalty (LASSO and adaptive LASSO) estimation methods and compare their relative performance with the non-penalty pretest and shrinkage estimators. A simulation study for various combinations of the inactive covariates shows that the shrinkage estimators perform better than the penalty estimators in certain parts of the parameter space. This particularly happens when there are many inactive covariates in the model. It also shows that the pretest, shrinkage, and penalty estimators all outperform the UE. We further illustrate the proposed procedures via a real data example.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:81:y:2018:i:5:d:10.1007_s00184-018-0656-1
    DOI: 10.1007/s00184-018-0656-1
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
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    Cited by:

    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.

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