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VARIABLE SELECTION IN LINEAR MIXED EFFECTS MODELS.

Yingying Fan1, Runze Li2

  • 1Information and Operations Management, Department Marshall School of Business, University of Southern California, Los Angeles, CA 90089, USA.

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|May 23, 2014
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Summary
This summary is machine-generated.

This study introduces new methods for selecting and estimating effects in linear mixed models. These techniques improve accuracy for both fixed and random effects, even with large datasets.

Keywords:
Adaptive LassoSCADgroup variable selectionlinear mixed effects modelsoracle property

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Area of Science:

  • Statistics
  • Statistical Modeling

Background:

  • Linear mixed effects models are widely used in various scientific fields.
  • Accurate selection and estimation of fixed and random effects are crucial for model validity.
  • Challenges exist in estimating unknown covariance matrices for random effects.

Purpose of the Study:

  • To develop novel methods for selecting and estimating fixed and random effects in linear mixed models.
  • To address the challenge of unknown covariance matrices in random effects.
  • To ensure model selection consistency and accurate identification of true effects.

Main Methods:

  • Nonconcave penalized profile likelihood methods for fixed effects selection and estimation.
  • Utilizing a proxy matrix to approximate the unknown covariance matrix of random effects.
  • Developing a group variable selection strategy for simultaneous selection and estimation of random effects.

Main Results:

  • Proposed methods achieve model selection consistency for fixed effects, even with exponentially growing numbers of effects.
  • The procedure can identify all true random effects with asymptotic probability one.
  • Demonstrated effectiveness through Monte Carlo simulations and a real data example.

Conclusions:

  • The proposed penalized profile likelihood and group variable selection methods offer robust solutions for linear mixed models.
  • These methods provide reliable estimation and selection of both fixed and random effects.
  • The techniques are validated for their performance in finite samples and complex scenarios.