Variable selection by regularization methods for generalized mixed models

More about the book

A regression analysis describes the dependency of random variables through a functional relationship, distinguishing between a dependent response variable and one or more independent influence variables. Various model classes and inference methods exist, from conventional linear regression to recent non- and semiparametric models. Generalized regression models provide a consistent framework that includes various approaches, even when response variables are not normally distributed. When repeated measurements are involved, random effects or coefficients can be included, leading to Random Effects Models or Mixed Models. This versatility allows regression procedures to address diverse problems. The dissertation develops regularization techniques for generalized mixed models to perform variable selection, particularly when many potential influence variables are present. It introduces a componentwise boosting technique for generalized linear mixed models based on the likelihood function, iteratively fitting residuals with weak learners, while determining estimator complexity through information criteria. Two approaches for estimating variance components are explored: maximizing the profile likelihood and an approximative EM-algorithm. The boosting concept is then extended to mixed models with ordinal response variables, considering both threshold and sequential models. Additionally, the approach is expanded to additive predictors u