Abstract: Linear mixed effects (LME) models are important statistical tools for analysis of clustered and correlated data. High breakdown estimators are currently the robust methods of choice for multivariate linear regression, but extensions of such estimators have been developed only for completely balanced LME models. In this work, we propose a generalized S-estimator for a general unbalanced LME model. Our GS-estimator reduces to the classic high breakdown S-estimator when the LME model reduces to a multivariate normal location and scale model or multivariate regression model. The asymptotic properties are established, and we show that the estimator may be viewed as a redescending M-estimator. A small simulation study is conducted to compare performance of the GS-estimates, monotone M-estimates, and restricted maximum likelihood (REML) estimates under various contamination patterns. The proposed estimator is used for analysis of age-related changes in hemoglobin levels of sickle cell disease patients.

Key words and phrases: Breakdown, clustered data, longitudinal data, redescending M-estimators, robust estimation.