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

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.