Variable Selection for Generalized Linear Mixed Models by L1-Penalized Estimation

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 loglikelihood yielding models with reduced complexity. In contrast to common procedures it can be used in high-dimensional settings where a large number of otentially influential explanatory variables is available. The method is investigated in simulation studies and illustrated by use of real data sets

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

Binary and Ordinal Random Effects Models Including Variable Selection

A likelihood-based boosting approach for fitting binary and ordinal mixed models is presented. In contrast to common procedures it can be used in high-dimensional settings where a large number of potentially influential explanatory variables is available. Constructed as a componentwise boosting method it is able to perform variable selection with the complexity of the resulting estimator being determined by information criteria. The method is investigated in simulation studies both for cumulative and sequential models and is illustrated by using real data sets

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

Variable Selection for Generalized Linear Mixed Models by L1-Penalized Estimation

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 loglikelihood yielding models with reduced complexity. In contrast to common procedures it can be used in high-dimensional settings where a large number of otentially influential explanatory variables is available. The method is investigated in simulation studies and illustrated by use of real data sets

Measuring Concentration in Data with an Exogenous Order

Concentration measures order the statistical units under observation according to their market share. However, there are situations where an order according to an exogenous variable is more appropriate or even required. The present article introduces a generalized definition of market concentration and defines a corresponding concentration measure. It is shown that this generalized concept of market concentration satisfies the common axioms of (classical) concentration measures. In an application example, the proposed approach is compared with classical concentration measures; the data are transfer spendings of German Bundesliga soccer teams, the ``obvious'' exogenous order of the teams is the league ranking

A generalized additive model approach to time-to-event analysis

This tutorial article demonstrates how time-to-event data can be modelled in a very flexible way by taking advantage of advanced inference methods that have recently been developed for generalized additive mixed models. In particular, we describe the necessary pre-processing steps for transforming such data into a suitable format and show how a variety of effects, including a smooth nonlinear baseline hazard, and potentially nonlinear and nonlinearly time-varying effects, can be estimated and interpreted. We also present useful graphical tools for model evaluation and interpretation of the estimated effects. Throughout, we demonstrate this approach using various application examples. The article is accompanied by a new R-package called pammtools implementing all of the tools described here

Who’s the Favourite? – A Bivariate Poisson Model for the UEFA European Football Championship 2016

Many approaches that analyze and predict the results of soccer matches are based on two independent pairwise Poisson distributions. The dependence between the scores of two competing teams is simply displayed by the inclusion of the covariate information of both teams. One objective of this article is to analyze if this type of modeling is appropriate or if an additional explicit modeling of the dependence structure for the joint score of a soccer match needs to be taken into account. Therefore, a specific bivariate Poisson model for the two numbers of goals scored by national teams competing in UEFA European football championship matches is fitted to all matches from the three previous European championships, including covariate information of both competing teams. A boosting approach is then used to select the relevant covariates. Based on the estimates, the current tournament is simulated 1,000,000 times to obtain winning probabilities for all participating national teams