  Shrinking methods in regression analysis are usually designed for metric
predictors. In this article, however, shrinkage methods for categorial
predictors are proposed. As an application we consider data from the Munich
rent standard, where, for example, urban districts are treated as a categorial
predictor. If independent variables are categorial, some modifications to usual
shrinking procedures are necessary. Two $L_1$-penalty based methods for factor
selection and clustering of categories are presented and investigated. The
first approach is designed for nominal scale levels, the second one for ordinal
predictors. Besides applying them to the Munich rent standard, methods are
illustrated and compared in simulation studies.
