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Robust Estimation of General Linear Mixed Effects Models

In: Robust and Multivariate Statistical Methods

Author

Listed:
  • Manuel Koller

    (University of Bern, Institute of Social and Preventive Medicine
    ETH Zürich, Seminar für Statistik)

  • Werner A. Stahel

    (ETH Zürich, Seminar für Statistik)

Abstract

The classical REML estimator for fitting a general linear mixed effects model is modified by bounding the terms appearing in the scoring equations. This leads to a generally applicable robust M-type estimator that we call robust scoring equations estimator. It requires only minor assumptions on the covariance matrices (block diagonal for the random effects and diagonal, known up to scale for the residual errors) additional to those of the classical methods. The structure of the data is arbitrary as long as the model is estimable in the classical sense. The estimator can detect and contain the effect of outliers in moderately contaminated datasets. Contamination is detected and treated at all levels of variability of the model, e.g., at both the subject and the observation level for a one-way ANOVA model. The estimator’s properties are studied by simulation and two examples. One example implies crossed random effects, for which the known robust methods are not applicable.

Suggested Citation

  • Manuel Koller & Werner A. Stahel, 2023. "Robust Estimation of General Linear Mixed Effects Models," Springer Books, in: Mengxi Yi & Klaus Nordhausen (ed.), Robust and Multivariate Statistical Methods, pages 297-322, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-22687-8_14
    DOI: 10.1007/978-3-031-22687-8_14
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