We consider varying-coefficient models with categorial effect modifiers in 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. We investigate the estimators’ large sample properties, and show in simulation studies that the proposed approaches perform very well for finite samples, too. Furthermore, the presented methods are compared with alternative procedures, and applied to real-world medical data.