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The use of the EM algorithm for regularization problems in high-dimensional linear mixed-effects models.

Daniela Cr Oliveira1, Fernanda L Schumacher2, Victor H Lachos3

  • 1Department of Mathematics and Statistics, Federal University of Sao Joao del-Rei, Brazil.

Statistical Methods in Medical Research
|December 9, 2025
PubMed
Summary
This summary is machine-generated.

The new EMLMLasso algorithm enhances variable selection for linear mixed-effects models, especially in high-dimensional settings. It outperforms existing methods in simulated and real-world data, offering a robust and generalizable solution.

Keywords:
EM algorithmR package glmnethigh-dimensional datamixed-effects modelsregularized variable selection methods

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Area of Science:

  • Statistics
  • Computational Biology
  • Biostatistics

Background:

  • The expectation-maximization (EM) algorithm is widely used for maximum likelihood estimation.
  • Its application in high-dimensional regularization for linear mixed-effects models is limited.
  • Effective variable selection is crucial in these complex statistical models.

Purpose of the Study:

  • Introduce the EMLMLasso algorithm for variable selection in high-dimensional linear mixed-effects models.
  • Evaluate the performance of EMLMLasso against existing algorithms.
  • Demonstrate the algorithm's robustness and effectiveness, particularly when predictors exceed observations.

Main Methods:

  • Combine the expectation-maximization (EM) algorithm with the R package glmnet for Lasso regularization.
  • Implement automatic tuning parameter selection.
  • Compare EMLMLasso with glmmLasso and splmm using simulated and real-world data.

Main Results:

  • EMLMLasso demonstrated robust and effective variable selection capabilities.
  • The algorithm performed well even when the number of predictors (p) was greater than the number of observations (n).
  • EMLMLasso consistently outperformed glmmLasso and splmm in most evaluated scenarios.

Conclusions:

  • EMLMLasso offers a significant advancement for variable selection in high-dimensional linear mixed-effects models.
  • The method is general, simple to implement, and extensible to other penalties like ridge and elastic net.
  • EMLMLasso provides a superior alternative to existing methods for complex statistical modeling.