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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 ArticleDOI
TL;DR: An overview of logistic regression models for ordinal data based upon cumulative and conditional probabilities shows how the most popular ordinal regression models, namely the proportional odds model and the continuation ratio model are embedded in the framework of generalized linear models.
Abstract: Although a number of regression models for ordinal responses have been proposed, these models are not widely known and applied in epidemiology and biomedical research. Overviews of these models are either highly technical or consider only a small part of this class of models so that it is difficult to understand the features of the models and to recognize important relations between them. In this paper we give an overview of logistic regression models for ordinal data based upon cumulative and conditional probabilities. We show how the most popular ordinal regression models, namely the proportional odds model and the continuation ratio model, are embedded in the framework of generalized linear models. We describe the characteristics and interpretations of these models and show how the calculations can be performed by means of SAS and S-Plus. We illustrate and compare the methods by applying them to data of a study investigating the effect of several risk factors on diabetic retinopathy. A special aspect is the violation of the usual assumption of equal slopes which makes the correct application of standard models impossible. We show how to use extensions of the standard models to work adequately with this situation.

117 citations

Journal ArticleDOI
TL;DR: Applying several analytic approaches to CAC data to determine the impact of analytic methods on the association with established cardiovascular risk factors and recommend the use of at least two distinct multivariable methods.

117 citations

Journal ArticleDOI
TL;DR: Whether and when fitting multilevel linear models to ordinal outcome data is justified and which estimator to employ when instead fitting multilesvel cumulative logit models to Ordinal data, maximum likelihood (ML), or penalized quasi-likelihood (PQL) is evaluated.
Abstract: Previous research has compared methods of estimation for multilevel models fit to binary data but there are reasons to believe that the results will not always generalize to the ordinal case. This paper thus evaluates (a) whether and when fitting multilevel linear models to ordinal outcome data is justified and (b) which estimator to employ when instead fitting multilevel cumulative logit models to ordinal data, Maximum Likelihood (ML) or Penalized Quasi-Likelihood (PQL). ML and PQL are compared across variations in sample size, magnitude of variance components, number of outcome categories, and distribution shape. Fitting a multilevel linear model to ordinal outcomes is shown to be inferior in virtually all circumstances. PQL performance improves markedly with the number of ordinal categories, regardless of distribution shape. In contrast to binary data, PQL often performs as well as ML when used with ordinal data. Further, the performance of PQL is typically superior to ML when the data includes a small to moderate number of clusters (i.e., ≤ 50 clusters).

116 citations

Proceedings ArticleDOI
18 Jun 1996
TL;DR: Though ordinal measures are presented in the context of stereo, they serve as a general tool for image matching that is applicable to other vision problems such as motion estimation and image registration.
Abstract: We present ordinal measures for establishing image correspondence. Linear correspondence measures like correlation and the sum of squared differences are known to be fragile. Ordinal measures, which are based on relative ordering of intensity values in windows, have demonstrable robustness to depth discontinuities, occlusion and noise. The relative ordering of intensity values in each window is represented by a rank permutation which is obtained by sorting the corresponding intensity data. By using a novel distance metric between the rank permutations, we arrive at ordinal correlation coefficients. These coefficients are independent of absolute intensity scale, i.e. they are normalized measures. Further, since rank permutations are invariant to monotone transformations of the intensity values, the coefficients are unaffected by nonlinear effects like gamma variation between images. We have developed a simple algorithm for their efficient implementation. Experiments suggest the superiority of ordinal measures over existing techniques under non-ideal conditions. Though we present ordinal measures in the context of stereo, they serve as a general tool for image matching that is applicable to other vision problems such as motion estimation and image registration.

116 citations

Journal ArticleDOI
TL;DR: An in-depth study of head pose estimation is conducted and a quaternion-based multiregression loss method achieves state-of-the-art performance on the AFLW2000, AFLW test set, and AFW datasets and is closing the gap with methods that utilize depth information on the BIWI dataset.
Abstract: Head pose estimation has attracted immense research interest recently, as its inherent information significantly improves the performance of face-related applications such as face alignment and face recognition. In this paper, we conduct an in-depth study of head pose estimation and present a multiregression loss function, an $L2$ regression loss combined with an ordinal regression loss, to train a convolutional neural network (CNN) that is dedicated to estimating head poses from RGB images without depth information. The ordinal regression loss is utilized to address the nonstationary property observed as the facial features change with respect to different head pose angles and learn robust features. The $L2$ regression loss leverages these features to provide precise angle predictions for input images. To avoid the ambiguity problem in the commonly used Euler angle representation, we further formulate the head pose estimation problem in quaternions. Our quaternion-based multiregression loss method achieves state-of-the-art performance on the AFLW2000, AFLW test set, and AFW datasets and is closing the gap with methods that utilize depth information on the BIWI dataset.

116 citations


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