Constrained S-estimators for linear mixed effects models with covariance components

Authors

  • Inna Chervoneva,

    Corresponding author
    1. Division of Biostatistics, Department of Pharmacology and Experimental Therapeutics, Thomas Jefferson University, Philadelphia, PA 19107, U.S.A.
    • Division of Biostatistics, Department of Pharmacology and Experimental Therapeutics, Thomas Jefferson University, Philadelphia, PA 19107, U.S.A.
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  • Mark Vishnyakov

    1. Division of Biostatistics, Department of Pharmacology and Experimental Therapeutics, Thomas Jefferson University, Philadelphia, PA 19107, U.S.A.
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Abstract

Linear mixed effects (LME) models are increasingly used for analyses of biological and biomedical data. When the multivariate normal assumption is not adequate for an LME model, then a robust estimation approach is preferable to the maximum likelihood one. M-estimators were considered before for robust estimation of the LME models, and recently a constrained S-estimator was proposed. This S-estimator cannot be applied directly to LME models with correlated error terms and vector random effects with correlated dimensions. Therefore, a modification is proposed, which extends application of the constrained S-estimator to the LME models for multivariate responses with correlated dimensions and to longitudinal data. Also, a new computational algorithm is developed for computing constrained S-estimators. Performance of the S-estimators based on the original Tukey's biweight and translated biweight is evaluated in a small simulation study with repeated multivariate responses with correlated dimensions. The proposed methodology is applied to jointly analyze repeated measures on three cholesterol components, HDL, LDL, and triglycerides. Copyright © 2011 John Wiley & Sons, Ltd.

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