Ordinal regression

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

Regression Models for Nominal and Ordinal Outcomes

Abstract: Advances in software make regression models for nominal and ordinal outcomes simple to estimate. The greatest challenge is finding a model that is appropriate for your application and interpreting the results to highlight the key findings from these often complicated, nonlinear models. When choosing a model it is important to realize that ordinal models restrict the relationship between regressors and the probabilities of the outcomes. The classic definition of ordinality assumes ranking on a single attribute, but many seemingly ordinal variables can be ranked on multiple dimensions. In such cases the constraints in ordinal models can lead to incorrect conclusions. Models for nominal outcomes do not impose ordinality, but at the cost of additional parameters. While it is tempting to reduce the number of parameters with stepwise procedures, this risks over-fitting the data. Interpretation of models for nominal and ordinal outcomes uses odds ratios and quantities based on predicted probabilities. Odds ratios do not depend on the values of the regressors, but the meaning of odds ratios in terms of probabilities depends on the values of the regressors. Changes in probabilities have a direct interpretation, but the magnitude of the change depends on the values of all regressors. There is no simple solution to the interpretation of nonlinear models. Interpretation requires detailed post-estimation analyses to determine the most important findings and to find an elegant way to present them. 1 I thank Rich Williams, Andy Fullerton, Tom VanHeuvelen, and Mike Vasseur for their comments. They are not, of course, responsible for my ignoring their advice on some issues.

Multivariate cumulative probit for age estimation using ordinal categorical data.

Abstract: Background: Multivariate ordinal categorical data have figured prominently in the age estimation literature. Unfortunately, the osteological and dental age estimation literature is often disconnected from the statistical literature that provides the underpinnings for rationale analyses.Aim: The aim of the study is to provide an analytical basis for age estimation using multiple ordinal categorical traits.Subjects and methods: Data on ectocranial suture closure from 1152 individuals are analysed in a multivariate cumulative probit model fit using a Markov Chain Monte Carlo (MCMC) method.Results: Twenty-six parameters in a five variable analysis are estimated, including the 10 unique elements of the five × five correlation matrix. The correlation matrix differs substantially from the identity matrix one would assume under conditional independence among the sutures.Conclusion: While the assumption of conditional independence between traits greatly simplifies the use of parametric models in age estima...

Automatic Pain Intensity Estimation using Heteroscedastic Conditional Ordinal Random Fields

Abstract: Automatic pain intensity estimation from facial images is challenging mainly because of high variability in subject-specific pain expressiveness This heterogeneity in the subjects causes their facial appearance to vary significantly when experiencing the same pain level The standard classification methods (eg, SVMs) do not provide a principled way of accounting for this heterogeneity To this end, we propose the heteroscedastic Conditional Ordinal Random Field (CORF) model for automatic estimation of pain intensity This model generalizes the CORF framework for modeling sequences of ordinal variables, by adapting it for heteroscedasticity This is attained by allowing the variance in the ordinal probit model in the CORF to change depending on the input features, resulting in the model able to adapt to the pain expressiveness level specific to each subject Our experimental results on the UNBC Shoulder Pain Database show that modeling heterogeneity in the subjects with the framework of CORFs improves the pain intensity estimation attained by the standard CORF model, and the other commonly used classification models

An Application of Logistic Models to the Analysis of Ordinal Responses

Abstract: Logistic probability models—models linear in the log odds of the outcome event—have found extensive application in modelling of unordered categorical responses. This paper illustrates some extensions of logistic models to the modelling of probabilities of ordinal responses. The extensions arise naturally from discrete probability models for the conditional distribution of the ordinal response, as well as from linear modelling of the log odds of response. Methods of estimation and examination of fit developed for the binary logistic model extend in a straightforward manner to the ordinal models. The models and methods are illustrated in an analysis of the dependence of chronic obstructive respiratory disease prevalence on smoking and age.