Ordinal regression

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

Flexible Bayesian Quantile Regression in Ordinal Models

Abstract: This article is motivated by the lack of flexibility in Bayesian quantile regression for ordinal models where the error follows an asymmetric Laplace (AL) distribution. The inflexibility arises because the skewness of the distribution is completely specified when a quantile is chosen. To overcome this shortcoming, we derive the cumulative distribution function (and the moment-generating function) of the generalized asymmetric Laplace (GAL) distribution – a generalization of AL distribution that separates the skewness from the quantile parameter – and construct a working likelihood for the ordinal quantile model. The resulting framework is termed flexible Bayesian quantile regression for ordinal (FBQROR) models. However, its estimation is not straightforward. We address estimation issues and propose an efficient Markov chain Monte Carlo (MCMC) procedure based on Gibbs sampling and joint Metropolis–Hastings algorithm. The advantages of the proposed model are demonstrated in multiple simulation studies and implemented to analyze public opinion on homeownership as the best long-term investment in the United States following the Great Recession.

Visual grading regression with random effects

Abstract: To analyze visual grading experiments, ordinal logistic regression (here called visual grading regression, VGR) may be used in the statistical analysis. In addition to types of imaging or post-processing, the VGR model may include factors such as patient and observer identity, which should be treated as random effects. Standard software does not allow random factors in ordinal logistic regression, but using Generalized Linear Latent And Mixed Models (GLLAMM) this is possible. In a single-image study, 9 radiologists graded 24 cardiac Computed Tomography Angiography (CTA) images with reduced dose without and after post-processing with a 2D adaptive filter, using five image quality criteria. First, standard ordinal logistic regression was carried out, treating filtering, patient and observer identity as fixed effects. The same analysis was then repeated with GLLAMM, treating filtering as a fixed effect and patient and observer identity as random effects. With both approaches, a significant effect (p<0.01) of the filtering was found for all five criteria. No dramatic differences in parameter estimates or significance levels were found between the two approaches. It is concluded that random effects can be appropriately handled in VGR using GLLAMM, but no major differences in the results were found in a preliminary evaluation.

The most representative utility function for non-additive robust ordinal regression

Abstract: Non-additive robust ordinal regression (NAROR) considers Choquet integral or one of its generalizations to represent preferences of a Decision Maker (DM). More precisely, NAROR takes into account all the fuzzy measures which are compatible with the preference information given by the DM and builds two preference relations: possible preference relation, when there is at least one compatible fuzzy measure for which an alternative is preferred to the other, and necessary preference relation, when an alternative is preferred to the other for all compatible fuzzy measures. Although it is interesting to take into consideration all the compatible fuzzy measures, in some decision problems we need to give a value to every alternative and it results necessary to obtain the most representative fuzzy measures among all the compatible ones. The aim of the paper is to propose an algorithm to the DM for selecting the most representative utility function expressed as Choquet integral from which a DM's representation of preferences is obtained.

Deep Ordinal Regression with Label Diversity

Abstract: Regression via classification (RvC) is a common method used for regression problems in deep learning, where the target variable belongs to a set of continuous values. By discretizing the target into a set of non-overlapping classes, it has been shown that training a classifier can improve neural network accuracy compared to using a standard regression approach. However, it is not clear how the set of discrete classes should be chosen and how it affects the overall solution. In this work, we propose that using several discrete data representations simultaneously can improve neural network learning compared to a single representation. Our approach is end-to-end differentiable and can be added as a simple extension to conventional learning methods, such as deep neural networks. We test our method on three challenging tasks and show that our method reduces the prediction error compared to a baseline RvC approach while maintaining a similar model complexity.

A Multivariate Latent Variable Model for Mixed Continuous and Ordinal Responses

Abstract: A joint model fo r multivariate mixed ordinal and continuous responses is presented. In this model the ordinal responses are intercorrelated and also are dependent on the continuous responses. The likelihood is found and modified Pearson residuals, where the correlation between multivariate responses can be taken into account, are presented to find abnormal observations. The model is applied to a medical data, obtained from an observational study on women, where the correlated responses are the ordinal response of osteoporosis of the spine and continuous responses are body mass index and waist. The effect of some covariates on all responses are investigated simultaneously.