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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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TL;DR: Results indicate that the proposed BLOR model using the Pólya-Gamma data augmentation approach is a good alternative for analyzing ordinal data in the context of genomic-enabled prediction with the probit or logit link.
Abstract: Most genomic-enabled prediction models developed so far assume that the response variable is continuous and normally distributed. The exception is the probit model, developed for ordered categorical phenotypes. In statistical applications, because of the easy implementation of the Bayesian probit ordinal regression (BPOR) model, Bayesian logistic ordinal regression (BLOR) is implemented rarely in the context of genomic-enabled prediction [sample size (n) is much smaller than the number of parameters (p)]. For this reason, in this paper we propose a BLOR model using the Polya-Gamma data augmentation approach that produces a Gibbs sampler with similar full conditional distributions of the BPOR model and with the advantage that the BPOR model is a particular case of the BLOR model. We evaluated the proposed model by using simulation and two real data sets. Results indicate that our BLOR model is a good alternative for analyzing ordinal data in the context of genomic-enabled prediction with the probit or logit link.

25 citations

Journal ArticleDOI
TL;DR: A procedure which solves the dual of the original linear programming formulation by the dual simplex method with upper bounded variables, in addition to utilizing the special structure of the constraint matrix from the point of view of storage and computation, performs the best in terms of both computational efficiency and storage requirements.
Abstract: The ordinal regression problem is an extension to the standard multiple regression problem in terms of assuming only ordinal properties for the dependent variable (rank order of preferred brands in a product class, academic ranks for students in a class, etc.) while retaining the interval scale assumption for independent (or predictor) variables. The linear programming formulation for obtaining the regression weights for ordinal regression, developed in an earlier paper, is outlined and computational improvements and alternatives which utilize the special structure of this linear program are developed and compared for their computational efficiency and storage requirements. A procedure which solves the dual of the original linear programming formulation by the dual simplex method with upper bounded variables, in addition to utilizing the special structure of the constraint matrix from the point of view of storage and computation, performs the best in terms of both computational efficiency and storage requirements. Using this special procedure, problems with 100 observations and 4 independent variables take less than 1/2 minute, on an average, on the IBM 360/67. Results also show that the linear programming solution procedure for ordinal regression is valid — the correlation coefficient between “true” and predicted values for the dependent variable was greater than .9 for most of the problems tested.

25 citations

Journal ArticleDOI
TL;DR: A family of log-linear models for ordinal data that contain parameters reflecting change patterns to compare treatments relative to change from baseline are proposed and methods for selection of a parsimonious model and for tests of hypotheses concerning treatment differences are described.
Abstract: We propose a family of log-linear models for ordinal data that contain parameters reflecting change patterns to compare treatments relative to change from baseline. Under the most general model, rates of change can depend not only upon the direction of change, but also upon the level of the baseline classification. We describe methods for selection of a parsimonious model and for tests of hypotheses concerning treatment differences. Interpretation of treatment differences in the follow-up response profiles, within baseline strata, employs the concept of stochastic ordering. Data from two clinical trials illustrate the proposed procedure.

25 citations

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.

25 citations

Journal ArticleDOI
TL;DR: In this article, the authors explored the association between Body Mass Index and a set of variables concerning consumer interest toward nutritional information, quality and marketing characteristics of food products, and found that people with excess weight display a high level of interest in nutrition claims, namely, short and immediately recognized messages.

25 citations


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