Penalized Regression with Ordinal Predictors

Gertheiss, Jan and Tutz, Gerhard (09. January 2008): Penalized Regression with Ordinal Predictors. Department of Statistics: Technical Reports, No.15

Abstract

Ordered categorial predictors are a common case in regression modeling. In contrast to the case of ordinal response variables, ordinal predictors have been largely neglected in the literature. In this article penalized regression techniques are proposed. Based on dummy coding two types of penalization are explicitly developed; the first imposes a difference penalty, the second is a ridge type refitting procedure. A Bayesian motivation as well as alternative ways of derivation are provided. Simulation studies and real world data serve for illustration and to compare the approach to methods often seen in practice, namely linear regression on the group labels and pure dummy coding. The proposed regression techniques turn out to be highly competitive. On the basis of GLMs the concept is generalized to the case of non-normal outcomes by performing penalized likelihood estimation. The paper is a preprint of an article published in the International Statistical Review. Please use the journal version for citation.

• Item Type: Paper (Technical Report)
• Published in: International Statistical Review, No. 3, Vol. 77, 2009: pp. 345-365.
• Keywords: Bayesian Methodology, Classical Linear Model, Dummy Coding, Generalized Linear Models, Generalized Ridge Regression, Ordinal Predictors, Penalized Likelihood Estimation
• Subjects: Mathematics, Computer Science and Statistics > Statistics > Technical Reports
• Language: English