SPARSE MODELING OF CATEGORIAL EXPLANATORY VARIABLES

• 成果类型: Article
• 署名作者: Gertheiss, Jan; Tutz, Gerhard
• 署名单位: University of Munich
• 刊物名称: ANNALS OF APPLIED STATISTICS
• ISSN/ISSBN: 1932-6157
• DOI: 10.1214/10-AOAS355
• 发表日期: 2010
• 页码: 2150-2180
• 关键词: regression; selection; Lasso

摘要

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.