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Constrained S‐estimators for linear mixed effects models with covariance components
Author(s) -
Chervoneva Inna,
Vishnyakov Mark
Publication year - 2011
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4169
Subject(s) - estimator , multivariate statistics , covariance , random effects model , statistics , computer science , linear model , mixed model , multivariate normal distribution , mathematics , econometrics , medicine , meta analysis
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. Copyright © 2011 John Wiley & Sons, Ltd.