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Oelker, Magret-Ruth; Gertheiss, Jan; Tutz, Gerhard (2014): Regularization and model selection with categorical predictors and effect modifiers in generalized linear models. In: Statistical Modeling, Vol. 14, No. 2: pp. 157-177


Varying-coefficient models with categorical effect modifiers are considered within the framework of generalized linear models. We distinguish between nominal and ordinal effect modifiers, and propose adequate Lasso-type regularization techniques that allow for (1) selection of relevant covariates, and (2) identification of coefficient functions that are actually varying with the level of a potentially effect modifying factor. For computation, a penalized iteratively reweighted least squares algorithm is presented. We investigate large sample properties of the penalized estimates; in simulation studies, we show that the proposed approaches perform very well for finite samples, too. In addition, the presented methods are compared with alternative procedures, and applied to real-world data.