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

Inna Chervoneva1, Mark Vishnyakov

  • 1Division of Biostatistics, Department of Pharmacology and Experimental Therapeutics, Thomas Jefferson University, Philadelphia, PA 19107, USA. i_chervoneva@mail.jci.tju.edu

Statistics in Medicine
|June 4, 2011
PubMed
Summary
This summary is machine-generated.

Robust estimation methods are crucial when multivariate normal assumptions fail in linear mixed effects (LME) models. A modified S-estimator extends robust analysis to complex LME models with correlated dimensions and longitudinal data.

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Area of Science:

  • Biostatistics
  • Longitudinal Data Analysis
  • Robust Statistics

Background:

  • Linear mixed effects (LME) models are widely used in biological and biomedical research.
  • Maximum likelihood estimation in LME models can be sensitive to violations of the multivariate normal assumption.
  • Existing robust methods like M-estimators and constrained S-estimators have limitations for complex LME models.

Purpose of the Study:

  • To extend the application of constrained S-estimators to LME models with correlated error terms and vector random effects.
  • To develop a new computational algorithm for computing constrained S-estimators.
  • To evaluate the performance of modified S-estimators for analyzing repeated multivariate responses with correlated dimensions.

Main Methods:

  • Modification of the constrained S-estimator to handle LME models with multivariate responses and correlated dimensions.
  • Development of a novel computational algorithm for the modified constrained S-estimator.
  • Simulation study comparing S-estimators (Tukey's biweight, translated biweight) with existing methods.
  • Application to a real-world dataset of repeated cholesterol measurements (HDL, LDL, triglycerides).

Main Results:

  • The modified constrained S-estimator successfully extends robust analysis to complex LME models.
  • The new computational algorithm efficiently computes the S-estimators.
  • Simulation results demonstrate the performance of the proposed S-estimators for multivariate longitudinal data.
  • The methodology provides a robust approach for jointly analyzing correlated cholesterol components.

Conclusions:

  • The proposed modified constrained S-estimator offers a robust alternative to maximum likelihood estimation for complex LME models.
  • This approach is particularly valuable for longitudinal and multivariate data where normality assumptions may not hold.
  • The methodology is effective for analyzing correlated repeated measures, as demonstrated with cholesterol data.