Regularization and Model Selection with Categorial Effect Modifiers

Abstract

The case of continuous effect modifiers in varying-coefficient models has been well investigated. Categorial effect modifiers, however, have been largely neglected. In this paper a regularization technique is proposed that allows for selection of covariates and fusion of categories of categorial effect modifiers in a linear model. It is distinguished between nominal and ordinal variables, since for the latter more economic parametrizations are warranted. The proposed methods are illustrated and investigated in simulation studies and real world data evaluations. Moreover, some asymptotic properties are derived