A rank-based estimation method for mixed effects models in the presence of outlying data

We present an approach to the rank-based estimation of mixed effects models, extending existing methods to random effects structures beyond random intercepts. The estimates obtained from our procedure are insensitive to outlying observations including leverage points, (almost) tuning-parameter free and can be computed very efficiently. Furthermore, the resulting estimates allow for model diagnostics, especially with respect to the identification of outlying observations or groups in the data. The properties of the proposed estimators, in particular, their robustness to different outlier types, are studied by means of simulation studies. The methodology is illustrated with applications to the sleep study data set and to data from accelerated aging experiments on photovoltaic (PV) modules.