Statistics and Computing

, Volume 24, Issue 2, pp 137-154

First online:

Variable selection for generalized linear mixed models by L 1-penalized estimation

  • Andreas GrollAffiliated withDepartment of Mathematics, Ludwig-Maximilians-University Munich Email author 
  • , Gerhard TutzAffiliated withInstitute for Statistics, Seminar for Applied Stochastics, Ludwig-Maximilians-University Munich

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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 L 1-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.


Generalized linear mixed model Lasso Gradient ascent Penalty Linear models Variable selection