Variable selection for generalized linear mixed models by L1-penalized estimation

Authors:
Andreas Groll;Gerhard Tutz
Affiliations:
Department of Mathematics, Ludwig-Maximilians-University Munich, Munich, Germany 80333;Institute for Statistics, Seminar for Applied Stochastics, Ludwig-Maximilians-University Munich, Munich, Germany 80799
Venue:
Statistics and Computing
Year:
2014

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Abstract

Generalized linear mixed models are a widely used tool for modeling longitudinal data. However, their use is typically restricted to few covariates, because the presence of many predictors yields unstable estimates. The presented approach to the fitting of generalized linear mixed models includes an L1-penalty term that enforces variable selection and shrinkage simultaneously. A gradient ascent algorithm is proposed that allows to maximize the penalized log-likelihood yielding models with reduced complexity. In contrast to common procedures it can be used in high-dimensional settings where a large number of potentially influential explanatory variables is available. The method is investigated in simulation studies and illustrated by use of real data sets.