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Title: Robust, rank-based estimation of mixed effects models Authors:  Barbara Brune - TU Wien (Austria) [presenting]
Irene Ortner - TUV AUSTRIA Data Intelligence GmbH (Austria)
Peter Filzmoser - TU Wien (Austria)
Abstract: Existing robust methods for the estimation of mixed effects models based on M-estimation and related concepts are often computationally very expensive and rely on parameter tuning. Rank-based estimation methods offer an attractive alternative to classic M-estimation, as they are computationally cheap and robust. So far, the methodology published in this field only covers simple mixed effects models with random intercepts. We aim to close a gap in the literature regarding the estimation of more complex random effects structures, and develop an estimation framework for mixed effects models with random slopes. By modifying the norm used for estimation, the estimates can further be robustified against leverage points. The resulting residuals and weights can be used for diagnostic purposes, such as identifying unusual observations on both overall and group levels. The theoretical properties of the estimator are studied by means of simulation studies. The method is illustrated with an application to data from accelerated ageing experiments on photovoltaic modules.