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Sparse Estimation Strategies in Linear Mixed Effect Models for High-Dimensional Data Application.

Eugene A Opoku1, Syed Ejaz Ahmed2, Farouk S Nathoo1

  • 1Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8P 5C2, Canada.

Entropy (Basel, Switzerland)
|October 23, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces new pretest and shrinkage estimation strategies for linear mixed models (LMM) to address multicollinearity in high-dimensional data. These methods improve parameter estimation for complex biomedical and business applications.

Keywords:
LASSO estimationasymptotic bias and riskhigh-dimensional datalinear mixed modelmulticollinearitypretest and shrinkage estimationridge estimation

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Multicollinearity is a common challenge in longitudinal data analysis using linear mixed models (LMM).
  • High-dimensional data, where parameter dimensions exceed observations, requires efficient estimation strategies.
  • Prior information on parameters can be incorporated via linear restrictions.

Purpose of the Study:

  • To develop and evaluate pretest and shrinkage estimation strategies for LMM with multicollinearity.
  • To address parameter estimation in high-dimensional settings using linear restrictions.
  • To compare proposed methods against existing ridge and LASSO-type estimators.

Main Methods:

  • Utilizing a ridge full model as the base estimator.
  • Proposing pretest and shrinkage estimation strategies.
  • Establishing asymptotic distributional bias and risks.
  • Conducting simulation studies and applying to Alzheimer's disease data.

Main Results:

  • The proposed pretest and shrinkage estimators demonstrate competitive performance.
  • Asymptotic distributional bias and risks are established for the novel estimators.
  • Numerical performance is compared against ridge and LASSO-type estimators.
  • The methodology is validated through simulations and a real-world application.

Conclusions:

  • The developed pretest and shrinkage strategies offer efficient solutions for multicollinearity in LMM.
  • These methods are particularly valuable for high-dimensional data analysis in various fields.
  • The study provides a robust framework for parameter estimation with prior information.