Statistical Modelling 14 (2) (2014), 157–177
Regularization and model selection with categorical predictors and effect modifiers in generalized linear models
Margret-Ruth Oelker
Department of Statistics,
Ludwig-Maximilians-Universität Munich,
Germany
e-mail: margret.oelker@stat.uni-muenchen.de
Jan Gertheiss
Department of Animal Sciences,
Georg-August-Universität Göttingen,
Germany
Gerhard Tutz
Department of Statistics,
Ludwig-Maximilians-Universität Munich,
Germany
Abstract:
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.
Keywords:
Categorical predictors; fused Lasso; generalized linear model; variable selection; varying-coefficients
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