Ordinal regression

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

Goodness-of-fit Tests for Ordinal Response Regression Models

Abstract: SUMMARY In this paper, goodness-of-fit test statistics for ordinal regression models are proposed, which have approximate X2-distributions when the model has been correctly specified. The statistics proposed can be viewed as extensions of the Hosmer-Lemeshow statistic to ordinal categorical data and can be easily calculated by using existing statistical software for analysing ordinal response data The methods are illustrated by using data from an arthritis clinical trial comparing the drug auranofin and placebo therapy for the treatment of rheumatoid arthritis, in which the response is a self-assessment of arthritis, classified as poor, fair and good. The covariates of interest are age, gender, treatment and base-line response. A proportional odds model is fitted to the data, and the proposed goodness-of-fit statistics are applied to the fitted model. Also, the small sample properties of the proposed goodness-of-fit statistics are compared in a simulation study.

Robust Ordinal Regression and Stochastic Multiobjective Acceptability Analysis in multiple criteria hierarchy process for the Choquet integral preference model

Abstract: The paper deals with two important issues of Multiple Criteria Decision Aiding: interaction between criteria and hierarchical structure of criteria. To handle interactions, we apply the Choquet integral as a preference model, and to handle the hierarchy of criteria, we apply the recently proposed methodology called Multiple Criteria Hierarchy Process. In addition to dealing with the above issues, we suppose that the preference information provided by the Decision Maker is indirect and has the form of pairwise comparisons of criteria with respect to their importance and pairwise preference comparisons of some pairs of alternatives with respect to some criteria. In consequence, many instances of the Choquet integral are usually compatible with this preference information. These instances are identified and exploited by Robust Ordinal Regression and Stochastic Multiobjective Acceptability Analysis. To illustrate the whole approach, we show its application to a real world decision problem concerning the ranking of universities for a hypothetical Decision Maker.

On the use of heterogeneous thresholds ordinal regression models to account for individual differences in response style

Abstract: This paper proposes a general approach to accounting for individual differences in the extreme response style in statistical models for ordered response categories. This approach uses a hierarchical ordinal regression modeling framework with heterogeneous thresholds structures to account for individual differences in the response style. Markov chain Monte Carlo algorithms for Bayesian inference for models with heterogeneous thresholds structures are discussed in detail. A simulation and two examples based on ordinal probit models are given to illustrate the proposed methodology. The simulation and examples also demonstrate that failing to account for individual differences in the extreme response style can have adverse consequences for statistical inferences.

A general class of hierarchical ordinal regression models with applications to correlated roc analysis

Abstract: The authors discuss a general class of hierarchical ordinal regression models that includes both location and scale parameters, allows link functions to be selected adaptively as finite mixtures of normal cumulative distribution functions, and incorporates flexible correlation structures for the latent scale variables. Exploiting the well-known correspondence between ordinal regression models and parametric ROC (Receiver Operating Characteristic) curves makes it possible to use a hierarchical ROC (HROC) analysis to study multilevel clustered data in diagnostic imaging studies. The authors present a Bayesian approach to model fitting using Markov chain Monte Carlo methods and discuss HROC applications to the analysis of data from two diagnostic radiology studies involving multiple interpreters. RESUME Les auteurs s'interessent a une classe assez vaste de modeles de regression ordinale avec parametres de localisation et d'echelle, laquelle permet la selection adaptative de fonctions de lien s'exprimant comme melanges finis de fonctions de repartition normales et fournit des structures de correlation flexibles pour les variables d'echelle latentes. En exploitant la correspondance bien connue entre les modeles de regression ordinale et les courbes d'efficacite parametriques (CEP) des tests diagnostiques, il est possible d'analyser des donnees d'imagerie medicate diagnostique regroupees a plusieurs niveaux au moyen d'une CEP hieiarchique. Les auteurs decrivent une approche bayesienne pour l'ajustement de tels modeles au moyen des methodes de Monte Carlo a chaǐne de Markov et presentent deux applications concretes concernant l'interpretation de cliches radiologiques