Regularization and model selection with categorical predictors and effect modifiers in generalized linear models. (April 2014)

• Record Type: Journal Article
• Authors: Oelker, Margret-Ruth; Gertheiss, Jan; Tutz, Gerhard
• Is Part Of: Statistical modelling. Volume 14:Number 2(2014)
• Page Start: 157
• Page End: 177
• Publication Date: 2014-04
• Subjects: Categorical predictors -- fused Lasso -- generalized linear model -- variable selection -- varying-coefficients; Linear models (Statistics) -- Periodicals; Mathematical models -- Periodicals; Modèles linéaires (Statistique) -- Périodiques; Modèles mathématiques -- Périodiques; Modèle statistique; Modèle linéaire; Modélisation statistique; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 519.5011
• DOI: 10.1177/1471082X13503452
• Languages: English
• ISSNs: 1471-082X

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.