Penalized Regression with Ordinal Predictors
Penalized Regression with Ordinal Predictors
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DOI：
10.1111/j.1751-5823.2009.00088.x
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发表时间：
2009-12-01
影响因子：
2
通讯作者：
Tutz, Gerhard
中科院分区：
文献类型：
--
作者：
Gertheiss, Jan;Tutz, Gerhard
P>；有序类别预报器是回归建模中的常见情况。与序数反应变量的情况相比，序数预测变量在文献中基本上被忽略了。本文回顾了现有的方法，并提出了惩罚回归技术的应用。在虚拟编码的基础上，显式地提出了两种惩罚方法：第一种是施加差异惩罚，第二种是脊型改装过程。此外，还提供了贝叶斯动机。通过应用惩罚似然估计，将这一概念推广到广义线性模型框架内非正态结果的情况。模拟研究和真实世界数据用于说明和比较实践中常见的方法，即基团标签上的简单线性回归和纯虚拟编码。特别是拟议的差别处罚被证明是非常有竞争力的。
P>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.