Ordinal regression

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

Meaningful aggregation functions mapping ordinal scales into an ordinal scale: a state of the art

Abstract: We present an overview of the meaningful aggregation functions mapping ordinal scales into an ordinal scale. Three main classes are discussed, namely order invariant functions, comparison meaningful functions on a single ordinal scale, and comparison meaningful functions on independent ordinal scales. It appears that the most prominent meaningful aggregation functions are lattice polynomial functions, that is, functions built only on projections and minimum and maximum operations.

Power analysis for trend in ordinal cover classes: implications for long‐term vegetation monitoring

Abstract: Question: We provide a method to calculate the power of ordinal regression models for detecting temporal trends in plant abundance measured as ordinal cover classes. Does power depend on the shape of the unobserved (latent) distribution of percentage cover? How do cover class schemes that differ in the number of categories affect power? Methods: We simulated cover class data by “cutting-up” a continuous logit-beta distributed variable using 7-point and 15-point cover classification schemes. We used Monte Carlo simulation to estimate power for detecting trends with two ordinal models, proportional odds logistic regression (POM) and logistic regression with cover classes re-binned into two categories, a model we term an assessment point model (APM). We include a model fit to the logit-transformed percentage cover data for comparison, which is a latent model. Results: The POM had equal or higher power compared to the APM and latent model, but power varied in complex ways as a function of the assumed latent beta distribution. We discovered that if the latent distribution is skewed, a cover class scheme with more categories might yield higher power to detect trend. Conclusions: Our power analysis method maintains the connection between the observed ordinal cover classes and the unmeasured (latent) percentage cover variable, allowing for a biologically meaningful trend to be defined on the percentage cover scale. Both the shape of the latent beta distribution and the alternative hypothesis should be considered carefully when determining sample size requirements for long-term vegetation monitoring using cover class measurements.

A Comparison of Dierent ROC Measures for Ordinal Regression

Abstract: Ordinal regression learning has characteristics of both multi-class classification and metric regression because labels take ordered, discrete values. In applications of ordinal regression, the misclassification cost among the classes often diers and with dierent misclassification costs the common performance measures are not appropriate. Therefore we extend ROC analysis principles to ordinal regression. We derive an exact expression for the volume under the ROC surface (VUS) spanned by the true positive rates for each class and show its interpretation as the probability that a randomly drawn sequence with one object of each class is correctly ranked. Because the computation of V US has a huge time complexity, we also propose three approximations to this measure. Furthermore, the properties of VUS and its relationship with the approximations are analyzed by simulation. The results demonstrate that optimizing various measures will lead to dierent models.

Citizen Satisfaction: A Multicriteria Satisfaction Analysis

Abstract: Governments across Europe face the challenge of responding to public demand for more valuable, responsive, and efficient and effective services. In this article we will evaluate the public services in Greece. More specifically, this article refers to a citizen's satisfaction web survey for Citizens’ Service Centers. The analysis of the data is based on the MUSA (Multicriteria Satisfaction Analysis) method. MUSA is an ordinal regression model which is based on the principles of multicriteria decision analysis. The method is an instrument to evaluate quantitative global and partial satisfaction levels and to determine the weak and strong points of citizens Service Centers. Furthermore the results of this study will help the Citizens Service Centers to develop more effective services.

Application of Prediction Analysis to Cross Classifications of Ordinal Data

Abstract: Prediction analysis (PA) of cross classifications is characterized as a method for the analysis of local prediction hypotheses, that is, hypotheses that link particular predictor states to particular states of criteria. To evaluate the success of a prediction, PA compares the observed with an expected frequency distribution. The latter is estimated under the assumption of independence between predictors and criteria. When predictors of criteria have ordinal categories, the success of a prediction hypothesis is overestimated if there is a regression of the cell frequencies on the ranks of the variable categories. Using the method of log-linear models, it is shown how ordinal categories can be taken into account in PA. Numerical examples are given from the areas of cognitive development and drug research.