Sparse modeling of categorial explanatory variables

Details Sparse modeling of categorial explanatory variables Sparse modeling of categorial explanatory variables

2011-01-07

arxiv.org/abs/1101.1421v1

Annals of Applied Statistics 2010, Vol. 4, No. 4, 2150-2180

Statistics

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Published in at http://dx.doi.org/10.1214/10-AOAS355 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Ins

Scientific paper

10.1214/10-AOAS355

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.

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