Oelker, Margret-Ruth; Gertheiss, Jan; Tutz, Gerhard
(6. März 2012):
Regularization and Model Selection with Categorial Predictors and Effect Modifiers in Generalized Linear Models.
Department of Statistics: Technical Reports, Nr. 122
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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.
We investigate large sample properties, and show in simulation studies 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 medical data.
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