Variable Selection in High-Dimensional Generalized Linear Mixed Models for Binary Data

doi:10.1007/s12561-025-09509-1

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Variable Selection in High-Dimensional Generalized Linear Mixed Models for Binary Data

2025-10-01

PRE

Jalmar M. F. Carrasco

Lizandra C. Fábio

Dipak Dey

Víctor H. Lachos *

DOI：10.1007/s12561-025-09509-1

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Abstract

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High-dimensional data are now routinely analyzed, typically with many more covariates than observations, and are often solved using computationally expensive Markov Chain Monte Carlo techniques or very complicated optimization algorithms. An alternative method for regularizing selected variables is the Lasso, which is widely applied to generalized linear models, where fast and efficient methods based on the gradient descent algorithm are available. In this paper, we propose an approach that combines the expectation-maximization algorithm and the popular Lasso for variable selection of fixed effects in Bernoulli generalized linear mixed effects models under probit and logit links. We perform extensive simulation studies to show the computational advantage of our method compared to alternative approach available in the literature for binary responses related to its power to identify significant predictors and asymptotically consistent estimators. The application shows the performance of the proposal procedure in handling predictors of different types and cumulative noise.

Keywords:

Correlated binary data

EM algorithm

Generalized linear mixed models

High-dimensional data

Truncated multivariate normal distribution

Glmnet