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Ordinal regression

About: Ordinal regression is a research topic. Over the lifetime, 1879 publications have been published within this topic receiving 65431 citations.


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Journal Article
TL;DR: In this article, the authors characterize the Fisher consistency of a rich family of surrogate loss functions used in the context of ordinal regression, including Support Vector Ordinal Regression, ORBoosting and least absolute deviation.
Abstract: Many of the ordinal regression models that have been proposed in the literature can be seen as methods that minimize a convex surrogate of the zero-one, absolute, or squared loss functions. A key property that allows to study the statistical implications of such approximations is that of Fisher consistency. Fisher consistency is a desirable property for surrogate loss functions and implies that in the population setting, i.e., if the probability distribution that generates the data were available, then optimization of the surrogate would yield the best possible model. In this paper we will characterize the Fisher consistency of a rich family of surrogate loss functions used in the context of ordinal regression, including support vector ordinal regression, ORBoosting and least absolute deviation. We will see that, for a family of surrogate loss functions that subsumes support vector ordinal regression and ORBoosting, consistency can be fully characterized by the derivative of a real-valued function at zero, as happens for convex margin-based surrogates in binary classification. We also derive excess risk bounds for a surrogate of the absolute error that generalize existing risk bounds for binary classification. Finally, our analysis suggests a novel surrogate of the squared error loss. We compare this novel surrogate with competing approaches on 9 different datasets. Our method shows to be highly competitive in practice, outperforming the least squares loss on 7 out of 9 datasets.

38 citations

Journal ArticleDOI
TL;DR: This work proposes several scoring procedures for transforming the results of robustness analysis to a univocal recommendation using a preference model in form of an additive value function, and assumes the Decision Maker to provide pairwise comparisons of reference alternatives.

38 citations

Book ChapterDOI
20 May 2008
TL;DR: It is noticed from the results that ordinal regression could be an alternative technique for survival analysis for churn time prediction of mobile customers and state-of-the-art methods for tenure prediction - survival analysis.
Abstract: Customer churn in considered to be a core issue in telecommunication customer relationship management (CRM). Accurate prediction of churn time or customer tenure is important for developing appropriate retention strategies. In this paper, we discuss a method based on ordinal regression to predict churn time or tenure of mobile telecommunication customers. Customer tenure is treated as an ordinal outcome variable and ordinal regression is used for tenure modeling. We compare ordinal regression with the state-of-the-art methods for tenure prediction - survival analysis. We notice from our results that ordinal regression could be an alternative technique for survival analysis for churn time prediction of mobile customers. To the best knowledge of authors, the use of ordinal regression as a potential technique for modeling customer tenure has been attempted for the first time.

37 citations

Journal ArticleDOI
TL;DR: In this paper, a general semi-parametric regression framework for continuous self-rating scales such as the Visual Analog Scale (VAS) used in pain assessment, or the Linear Analog Self-Assessment (LASA) scales in quality of life studies is developed.
Abstract: Ordinal regression analysis is a convenient tool for analyzing ordinal response variables in the presence of covariates. In this paper we extend this methodology to the case of continuous self-rating scales such as the Visual Analog Scale (VAS) used in pain assessment, or the Linear Analog Self-Assessment (LASA) scales in quality of life studies. These scales measure subjects' perception of an intangible quantity, and cannot be handled as ratio variables because of their inherent nonlinearity. We express the likelihood in terms of a function connecting the scale with an underlying continuous latent variable and approximate this function either parametrically or non-parametrically. Then a general semi-parametric regression framework for continuous scales is developed. Two data sets have been analyzed to compare our method to the standard discrete ordinal regression model, and the parametric to the non-parametric versions of the model. The first data set uses VAS data from a study on the efficacy of low-level laser therapy in the treatment of chronic neck pain; the second comes from a study on chemotherapy treatments in advanced breast cancer and looks at the impact of different drugs on patients' quality of life. The continuous formulation of the ordinal regression model has the advantage of no loss of precision due to categorization of the scores and no arbitrary choice of the number and boundaries of categories. The semi-parametric form of the model makes it a flexible method for analysis of continuous ordinal scales.

37 citations

Journal ArticleDOI
TL;DR: New criteria to obtain classification trees for ordinal response variables are introduced and the hereby proposed methods are compared with the ordered twoing criterion via simulations.
Abstract: We introduce new criteria to obtain classification trees for ordinal response variables. At this aim, Breiman et al. (Classification and regression trees. Wadsworth, Belmont, 1984), extended their twoing criterion to the ordinal case. Following CART procedure, we extend the well known Gini---Simpson criterion to the ordinal case. Referring to the exclusivity preference property (introduced by Taylor and Silverman in Stat Comput 3:147---161, 1993, for the nominal case), suitably modified for the ordinal case, a second criterion is introduced. The hereby proposed methods are compared with the ordered twoing criterion via simulations.

37 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023102
2022191
202188
202093
201979
201873