Robust Estimation of General Linear Mixed Effects Models

Manuel Koller () and Werner A. Stahel ()
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Manuel Koller: University of Bern, Institute of Social and Preventive Medicine
Werner A. Stahel: ETH Zürich, Seminar für Statistik

A chapter in Robust and Multivariate Statistical Methods, 2023, pp 297-322 from Springer

Abstract: 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.

Keywords: Mixed model; Variance components; Hierarchical models; Crossed random effects; Robustness; Huberizing (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-22687-8_14

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DOI: 10.1007/978-3-031-22687-8_14

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