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

Andreas Groll (LMU)
Monday, December 2, 2013 - 2:00pm
Spandauer Strasse 1, Room 23

Generalized linear mixed models (GLMMs) 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. In the talk an approach to the fitting of generalized linear mixed models is presented, which includes an L1-penalty term that enforces variable selection and shrinkage simultaneously (Groll and Tutz, 2012). 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 in sequential explanatory variables is available. The method is investigated in simulation studies and illustrated by use of two real data sets. In the second application the objective is to analyze the role of bookmakers' odds together with many additional, potentially in uental covariates with respect to a national team's success at European football championships and especially to detect covariates, which are able to explain parts of the information covered by the odds. Therefore a pairwise Poisson model for the number of goals scored by national teams competing in European football championship matches is used. Besides, the GLMM approach allows to incorporate team-specic random eects. Based on the two pre-ceding European football championships a sparse model is obtained that is used to predict all matches of the current tournament resulting in a possible course of the European football championship 2012, see Groll and Abedieh (2013).