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Showing papers on "Ordinal regression published in 2000"




Journal ArticleDOI
TL;DR: In this article, the Proportional Odds, the Continuation Ratio and the Stereotype models are applied to ordinal data to predict spatial abundance of plant species in a Geographical Information System.
Abstract: . Although ordinal data are not rare in ecology, ecological studies have, until now, seriously neglected the use of specific ordinal regression models. Here, we present three models – the Proportional Odds, the Continuation Ratio and the Stereotype models – that can be successfully applied to ordinal data. Their differences and respective fields of application are discussed. Finally, as an example of application, PO models are used to predict spatial abundance of plant species in a Geographical Information System. It shows that ordinal models give as good a result as binary logistic models for predicting presence-absence, but are additionally able to predict abundance satisfactorily.

178 citations


Journal ArticleDOI
TL;DR: The controversy on the exact definition of an ordinal variable causes problems with regard to defining ordinal association and therefore to the interpretation of many recently designed models for ordinal variables, e.g., structure equation models using polychoric correlations, latent class models and ordinal response models as mentioned in this paper.
Abstract: We present a discussion of the different dimensions of the ongoing controversy about the analysis of ordinal variables. The source of this controversy is traced to the earliest possible stage, measurement theory. Three major approaches in analyzing ordinal variables, called the non-parametric, the parametric, and the underlying variable approach, are identified and the merits and drawbacks of each of these approaches are pointed out. We show that the controversy on the exact definition of an ordinal variable causes problems with regard to defining ordinal association, and therefore to the interpretation of many recently designed models for ordinal variables, e.g., structure equation models using polychoric correlations, latent class models and ordinal response models. We conclude that the discussion with regard to ordinal variable modeling can only be fruitful if one makes a distinction between different types of ordinal variables. Five types of ordinal variables were identified. The problems concerning the analysis of these five types of ordinal variables are solved in some cases and remain a problem for others.

124 citations


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: In this article, a general class of hierarchical ordinal regression models, including 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.
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

88 citations


Journal ArticleDOI
TL;DR: A full-information maximum likelihood method for fitting a multidimensional latent variable model to a set of ordinal observed variables is discussed and is applied to an example dataset concerning attitudes toward technology.
Abstract: A full-information maximum likelihood method for fitting a multidimensional latent variable model to a set of ordinal observed variables is discussed. This method is an implementation of a general ...

78 citations


Journal ArticleDOI
TL;DR: This paper presents and describes an ordinal RRM that includes the possibility that covariate effects vary across the cutpoints of the ordinal outcome, which is particularly useful because a treatment can have varying effects on full versus partial abstinence.
Abstract: In this paper we describe analysis of longitudinal substance use outcomes using random-effects regression models (RRM). Some of the advantages of this approach is that these models allow for incomplete data across time, time-invariant and time-varying covariates, and can estimate individual change across time. Because substance use outcomes are often measured in terms of dichotomous or ordinal categories, our presentation focuses on categorical versions of RRM. Specifically, we present and describe an ordinal RRM that includes the possibility that covariate effects vary across the cutpoints of the ordinal outcome. This latter feature is particularly useful because a treatment can have varying effects on full versus partial abstinence, for example. Data from a smoking cessation study are used to illustrate application of this model for analysis of longitudinal substance use data.

54 citations


Journal ArticleDOI
TL;DR: The final ranking obtained by the Co-plot method differed from that obtained by Zopounidis et al. because the banks are mapped into a partial order according to their (increased) performance to obtain their rating.

49 citations


Journal ArticleDOI
TL;DR: In this paper, the authors compared approaches to modeling ordinal outcome variables, including assumptions, interpretations, and limitations, with data from a multisite HIV prevention intervention and found that most of the approaches were based on assumptions and interpretations.
Abstract: This article compares approaches to modeling ordinal outcome variables, including assumptions, interpretations, and limitations Applications with data from a multisite HIV prevention intervention

40 citations


Journal ArticleDOI
TL;DR: This paper applies the EM algorithm to ordinal regression models to derive ML estimates for ROC curves as a function of covariates, adjusted for covariates affecting the likelihood of being verified.
Abstract: SUMMARY. A receiver operating characteristic (ROC) curve is commonly used to measure the accuracy of a medical test. It is a plot of the true positive fraction (sensitivity) against the false positive fraction (1-specificity) for increasingly stringent positivity criterion. Bias can occur in estimation of an ROC curve if only some of the tested patients are selected for disease verification and if analysis is restricted only to the verified cases. This bias is known as verification bias. In this paper, we address the problem of correcting for verification bias in estimation of an ROC curve when the verification process and efficacy of the diagnostic test depend on covariates. Our method applies the EM algorithm to ordinal regression models to derive ML estimates for ROC curves as a function of covariates, adjusted for covariates affecting the likelihood of being verified. Asymptotic variance estimates are obtained using the observed information matrix of the observed data. These estimates are derived under the missing-at-random assumption, which means that selection for disease verification depends only on the observed data, i.e., the test result and the observed covariates. We also address the issues of model selection and model checking. Finally, we illustrate the proposed method on data from a two-phase study of dementia disorders, where selection for verification depends on the screening test result and age.

Journal ArticleDOI
TL;DR: A smooth regression model is presented for ordinal data with longitudinal dependence structure and cumulative log odds ratios are fitted locally, which allows investigation of how the longitudinal dependence of the ordinal observations changes with time.
Abstract: The paper presents a smooth regression model for ordinal data with longitudinal dependence structure. A marginal model with cumulative logit link (McCullagh 1980) is applied to cope for the ordinal scale and the main and covariate effects in the model are allowed to vary with time. Local fitting is pursued and asymptotic properties of the estimates are discussed. A data example demonstrates the exploratory flavor of the smooth model. In a second step, the longitudinal dependence of the observations is considered. Cumulative log odds ratios are fitted locally which provides insight how the dependence of the ordinal observations changes with time.

Journal ArticleDOI
TL;DR: An algorithm for analyzing ordinal scaling results is described, which applies maximum likelihood estimation of model parameters and the Cramér-Rao bounds of the standard errors of the estimated parameters are calculated.
Abstract: An algorithm for analyzing ordinal scaling results is described. Frequency data on ordinal categories are modeled for unidimensional psychological attributes according to Thurstone’s judgment scaling model. The algorithm applies maximum likelihood estimation of model parameters. The Cramer-Rao bounds of the standard errors of the estimated parameters are calculated, and a stress measure and a goodness-of-fit measure are supplied.

Journal ArticleDOI
TL;DR: Application of this work's methodology to the data offers further support to the conclusions developed earlier using GEE methods yet provides additional insight into the uncertainty levels of the risk estimates.
Abstract: Summary. This paper discusses random effects in censored ordinal regression and presents a Gibbs sampling approach to fit the regression model. A latent structure and its corresponding Bayesian formulation are introduced to effectively deal with heterogeneous and censored ordinal observations. This work is motivated by the need to analyze interval-censored ordinal data from multiple studies in toxicological risk assessment. Application of our methodology to the data offers further support to the conclusions developed earlier using GEE methods yet provides additional insight into the uncertainty levels of the risk estimates.

Journal ArticleDOI
TL;DR: In this paper, a limited information estimator for the multivariate ordinal probit model is developed, which avoids the potential problem of encountering local maxima in the estimation process, which is looming using maximum likelihood.
Abstract: A limited information estimator for the multivariate ordinal probit model is developed. The main advantage of the estimator is that even for high dimensional models, the estimation procedure requires the evaluation of bivariate normal integrals only. The proposed estimator also avoids the potential problem of encountering local maxima in the estimation process, which is looming using maximum likelihood. The performance of the limited information estimator is shown by Monte Carlo experiments to be excellent and it is comparable to that of the maximum likelihood estimator. Finally, an application of the limited information multivariate ordinal probit to model the consumption level of cigarette, alcohol and betel nut is presented.


Journal ArticleDOI
TL;DR: The prediction performance of scoring systems with respect to an ordinal outcome scale is investigated, based on grouped continuous logistic models as well as on an extension of the stereotype logistic regression model.
Abstract: Scoring systems are used in nearly all fields of medicine for evaluation of the state of a disease. The prediction performance of scoring systems with respect to an ordinal outcome scale is investigated, based on grouped continuous logistic models as well as on an extension of the stereotype logistic regression model. The latter is a canonical approach, which allows assessment of properties of outcome categories such as partial and total ordering, distinguishability and allocatability. The approach is applied to a data set of patients with injuries of the head.


Posted Content
TL;DR: In this paper, the authors discuss some problems associated with the application of this technique, such as: if ordinal data are used the traditional significance tests may produce er-roneous results, if non-linear relations exist spurious interaction effects may be found.
Abstract: Moderated regression analysis is generally accepted as the most appropriate way to asses the viability of contingency models. This paper discusses some problems associated with the application of this technique. If interval data are used main effects may not be interpreted. If ordinal data are used the traditional significance tests may produce er-roneous results. If non-linear relations exist spurious interaction effects may be found. The problems surrounding ternative significance tests, measurement instruments. moderated regression analysis are largely solved by using al-mean centering and carefully developed (i.e., highly reliable)

Journal Article
TL;DR: In this paper, a case study of modeling ordinal categorical response data with the MARS method is done to analyze the effect of some personal characteristics and socioeconomic status on the teenage marijuana use.
Abstract: A case study of modeling ordinal categorical response data with the MARS method is done. The study is to analyze the effect of some personal characteristics and socioeconomic status on the teenage marijuana use. The MARS method gave a new insight into the data set.