Ordinal regression

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

Kernel Discriminant Learning for Ordinal Regression

Abstract: Ordinal regression has wide applications in many domains where the human evaluation plays a major role. Most current ordinal regression methods are based on Support Vector Machines (SVM) and suffer from the problems of ignoring the global information of the data and the high computational complexity. Linear Discriminant Analysis (LDA) and its kernel version, Kernel Discriminant Analysis (KDA), take into consideration the global information of the data together with the distribution of the classes for classification, but they have not been utilized for ordinal regression yet. In this paper, we propose a novel regression method by extending the Kernel Discriminant Learning using a rank constraint. The proposed algorithm is very efficient since the computational complexity is significantly lower than other ordinal regression methods. We demonstrate experimentally that the proposed method is capable of preserving the rank of data classes in a projected data space. In comparison to other benchmark ordinal regression methods, the proposed method is competitive in accuracy.

Ordinal analysis of time series

Abstract: In order to develop fast and robust methods for extracting qualitative information from non-linear time series, Bandt and Pompe have proposed to consider time series from the pure ordinal viewpoint. On the basis of counting ordinal patterns, which describe the up-and-down in a time series, they have introduced the concept of permutation entropy for quantifying the complexity of a system behind a time series. The permutation entropy only provides one detail of the ordinal structure of a time series. Here we present a method for extracting the whole ordinal information.

Multiple Regression With Discrete Dependent Variables

Abstract: Preface 1. Introduction to Regression Modeling 2. Regression with a Dichotomous Dependent Variable 3. Regression with a Polytomous Dependent Variable 4. Regression with an Ordinal Dependent Variable 5. Regression with a Count Dependent Variable Appendix A: Description of Data Sets Appendix B: Logarithms Glossary

Multilevel Models for Ordinal and Nominal Variables

Abstract: Reflecting the usefulness of multilevel analysis and the importance of categorical outcomes in many areas of research, generalization of multilevel models for categorical outcomes has been an active area of statistical research. For dichotomous response data, several approaches adopting either a logistic or probit regression model and various methods for incorporating and estimating the influence of the random effects have been have discussed and compared some of these models and their estimation procedures. Also, Snijders and Bosker [99, chap. 14] provide a practical summary of the multilevel logistic regression model and the various procedures for estimating its parameters. As these sources indicate, the multilevel logistic regression model is a very popular choice for analysis of dichotomous data. Extending the methods for dichotomous responses to ordinal response data has also been actively Again, developments have been mainly in terms of logistic and probit regression models, and many of these are reviewed in Agresti and Natarajan [5]. Because the proportional odds model described by McCullagh [71], which is based on the logistic regression formulation, is a common choice for analysis of ordinal data, many of the multilevel models for ordinal data are generalizations of this model. The proportional odds model characterizes the ordinal responses in C categories in terms of C−1 cumulative category comparisons, specifically, C−1 cumulative logits (i.e., log odds) of the ordinal responses. In the proportional odds model, the covariate effects are assumed to be the same across these cumulative logits, or proportional across the cumulative odds. As noted by Peterson and Harrell [77], however, examples of non-proportional odds are