title: Constrained S-estimators for linear mixed effects models with covariance components.
abstract: 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.
authors.affiliation: Division of Biostatistics, Department of Pharmacology and Experimental Therapeutics, Thomas Jefferson University, Philadelphia, PA 19107, USA. i_chervoneva@mail.jci.tju.edu
authors.forename: Inna
authors.initials: I
authors.lastname: Chervoneva
authors.forename: Mark
authors.initials: M
authors.lastname: Vishnyakov
mesh_terms: D000465:Algorithms; D000927:Anticonvulsants / Q000494:pharmacology / Q000627:therapeutic use; D015982:Bias; D056808:Biostatistics / Q000379:methods*; D001769:Blood / Q000187:drug effects; D003198:Computer Simulation; D004827:Epilepsy / Q000097:blood / Q000188:drug therapy; D006801:Humans; D016013:Likelihood Functions; D016014:Linear Models; D008075:Lipoproteins, HDL / Q000097:blood; D008077:Lipoproteins, LDL / Q000097:blood; D015233:Models, Statistical; D015999:Multivariate Analysis; D014280:Triglycerides / Q000097:blood
chemical_list: D000927:Anticonvulsants; D008075:Lipoproteins, HDL; D008077:Lipoproteins, LDL; D014280:Triglycerides