GLMMLasso: An Algorithm for High-Dimensional Generalized Linear Mixed Models Using L1-Penalization

TL;DR

This paper introduces GLMMLasso, an L1-penalized algorithm designed for high-dimensional generalized linear mixed models, enabling effective variable screening and correction through refitting, with implementation in an R package.

Contribution

The paper presents a novel L1-penalized algorithm specifically for high-dimensional GLMMs, including a variable screening method and a refitting step to improve accuracy.

Findings

Effective variable screening in high-dimensional GLMMs

Improved model fitting through refitting after screening

Algorithm demonstrated on simulated and real data

Abstract

We propose an L1-penalized algorithm for fitting high-dimensional generalized linear mixed models. Generalized linear mixed models (GLMMs) can be viewed as an extension of generalized linear models for clustered observations. This Lasso-type approach for GLMMs should be mainly used as variable screening method to reduce the number of variables below the sample size. We then suggest a refitting by maximum likelihood based on the selected variables only. This is an effective correction to overcome problems stemming from the variable screening procedure which are more severe with GLMMs. We illustrate the performance of our algorithm on simulated as well as on real data examples. Supplemental materials are available online and the algorithm is implemented in the R package glmmixedlasso.