Regularization for Generalized Additive Mixed Models by Likelihood-Based Boosting

With the emergence of semi- and nonparametric regression the generalized linear mixed model has been expanded to account for additive predictors. In the present paper an approach to variable selection is proposed that works for generalized additive mixed models. In contrast to common procedures it can be used in high-dimensional settings where many covariates are available and the form of the influence is unknown. It is constructed as a componentwise boosting method and hence is able to perform variable selection. The complexity of the resulting estimator is determined by information criteria. The method is nvestigated in simulation studies for binary and Poisson responses and is illustrated by using real data sets