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Penalized Regression with Ordinal Predictors


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  • Jan Gertheiss
  • Gerhard Tutz
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    Ordered categorial predictors are a common case in regression modelling. In contrast to the case of ordinal response variables, ordinal predictors have been largely neglected in the literature. In this paper, existing methods are reviewed and the use of penalized regression techniques is 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. Also a Bayesian motivation is provided. The concept is generalized to the case of non-normal outcomes within the framework of generalized linear models by applying penalized likelihood estimation. Simulation studies and real world data serve for illustration and to compare the approaches to methods often seen in practice, namely simple linear regression on the group labels and pure dummy coding. Especially the proposed difference penalty turns out to be highly competitive. Copyright (c) 2009 The Authors. Journal compilation (c) 2009 International Statistical Institute.

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    Bibliographic Info

    Article provided by International Statistical Institute in its journal International Statistical Review.

    Volume (Year): 77 (2009)
    Issue (Month): 3 (December)
    Pages: 345-365

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    Handle: RePEc:bla:istatr:v:77:y:2009:i:3:p:345-365

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    Cited by:
    1. Faisal Zahid & Gerhard Tutz, 2013. "Multinomial logit models with implicit variable selection," Advances in Data Analysis and Classification, Springer, vol. 7(4), pages 393-416, December.
    2. Hess, Wolfgang & Persson, Maria & Rubenbauer, Stephanie & Gertheiss, Jan, 2013. "Using Lasso-Type Penalties to Model Time-Varying Covariate Effects in Panel Data Regressions - A Novel Approach Illustrated by the 'Death of Distance' in International Trade," Working Papers 2013:5, Lund University, Department of Economics.


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