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

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 L 1 -penalty term that enforces variable selection and shrinkage simultaneously. A gradient ascent algorithm is proposed that allows to maximize the penalized loglikelihood 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.

Variable selection in discrete survival models including heterogeneity

“…In the famous lasso the log-likelihood is replaced by a penalized log-likelihood that includes a penalty term of the form λ p i=1 |γ i |, see Tibshirani (1996), Park and Hastie (2007) and Zou (2006). As shown by Groll and Tutz (2014), for simple binary random effects models the inclusion of a lasso penalty can be used within the framework of penalized quasi-likelihood yielding selection procedures for random effects models. Groll and Tutz (2014) gave a detailed algorithm which is based on an approximate EM-method.…”

“…As shown by Groll and Tutz (2014), for simple binary random effects models the inclusion of a lasso penalty can be used within the framework of penalized quasi-likelihood yielding selection procedures for random effects models. Groll and Tutz (2014) gave a detailed algorithm which is based on an approximate EM-method.…”

“…In the following we use the glmmLasso algorithm (Groll and Tutz, 2014) for two different fitting approaches: in the first approach (denoted by glmmLasso dis ) we fit the model directly, using a small ridge penalty on the parameters γ 0t , t = 1, . .…”

“…We use forward subset selection in order to perform variable selection and compare the results with our glmmLasso algorithm, implemented in the corresponding R-package glmmLasso (Groll, 2011). We restrict consideration to forward procedures because forward/backward procedures imply huge computational costs.…”

Bayesian adaptive lasso with variational Bayes for variable selection in high-dimensional generalized linear mixed models

“…Classical methods for variable selection, such as the ones based on hypothesis testing or subset selection, are restricted to a few covariates. Notable works are two recent papers by Groll and Tutz (2012) and Schelldorfer et al (2013) which can do variable selection for GLMMs in high dimensions. Their approach first estimates the likelihood by approximating the integrals over the random effects using the Laplace method, then minimizes the sum of this estimated likelihood and a Lasso-type penalty which is the l 1 -norm of the fixed effect coefficients.…”