Regularization for Generalized Additive Mixed Models by Likelihood-based Boosting

Abstract

With the emergence of semi- and nonparametric regression the generalized linear mixed model has been extended to account for additive predictors. However, available fitting methods fail in high dimensional settings where many explanatory variables are present. We extend the concept of boosting to generalized additive mixed models and present an appropriate algorithm that uses two different approaches for the fitting procedure of the variance components of the random effects. The main tool developed is likelihood-based componentwise boosting that enforces variable selection in generalized additive mixed models. In contrast to common procedures they can be used in high-dimensional settings where many covariates are available and the form of the influence is unknown. The complexity of the resulting estimators is determined by information criteria. The performance of the methods is investigated in simulation studies for binary and Poisson responses with comparisons to alternative approaches and it is applied to clinical real world data. Simulations show that the proposed methods are considerably more stable and more accurate in estimating the regression function than the conventional approach, especially when a large number of predictors is available. The methods also produce reasonable results in applications to real data sets, which is illustrated by the Multicenter AIDS Cohort Study. The boosting algorithm allows to extract relevant predictors in generalized additive mixed models. It works in high-dimensional settings and is very stable.