Regularization and Model Selection with Categorial Effect Modifiers

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.