Constrained S-estimators for linear mixed effects models with covariance components.

Linear mixed effects (LME) models are increasingly used for analyses of biological and biomedical data. When the multivariate normal assumption is not adequate for an LME model, then a robust estimation approach is preferable to the maximum likelihood one. M-estimators were considered before for robust estimation of the LME models, and recently a constrained S-estimator was proposed. This S-estimator cannot be applied directly to LME models with correlated error terms and vector random effects with correlated dimensions. Therefore, a modification is proposed, which extends application of the constrained S-estimator to the LME models for multivariate responses with correlated dimensions and to longitudinal data. Also, a new computational algorithm is developed for computing constrained S-estimators. Performance of the S-estimators based on the original Tukey's biweight and translated biweight is evaluated in a small simulation study with repeated multivariate responses with correlated dimensions. The proposed methodology is applied to jointly analyze repeated measures on three cholesterol components, HDL, LDL, and triglycerides.