GLMMLasso: An Algorithm for High-Dimensional Generalized Linear Mixed Models Using ℓ1-Penalization

• Published in: Journal of computational and graphical statistics Vol. 23; no. 2; pp. 460 - 477
• Main Authors: Schelldorfer, Jürg, Meier, Lukas, Bühlmann, Peter
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 01.06.2014; American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America; Taylor & Francis Ltd
• Subjects: Algorithms; Approximation; Coordinate gradient descent; Coordinate systems; Covariance; Dimensional analysis; Effectiveness studies; Estimation bias; Estimators; Generalized linear model; Generalized linear models; Laplace approximation; Large p Small n; Logistics; Mathematical problems; Maximum likelihood method; Multilevel models; Random-effects model; Sample size; Simulations; Threshing; Variable selection
• ISSN: 1061-8600; 1537-2715
• DOI: 10.1080/10618600.2013.773239

We propose an ℓ 1 -penalized algorithm for fitting high-dimensional generalized linear mixed models (GLMMs). GLMMs can be viewed as an extension of generalized linear models for clustered observations. Our 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 that are more severe with GLMMs than for generalized linear models. We illustrate the performance of our algorithm on simulated as well as on real data examples. Supplementary materials are available online and the algorithm is implemented in the R package glmmixedlasso .