Ordinal regression

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

An imputation strategy for incomplete longitudinal ordinal data

Abstract: A new quasi-imputation strategy for correlated ordinal responses is proposed by borrowing ideas from random number generation. The essential idea is collapsing ordinal levels to binary ones and converting correlated binary outcomes to multivariate normal outcomes in a sensible way so that re-conversion to the binary and then ordinal scale, after conducting multiple imputation, yields the original marginal distributions and correlations. This conversion process ensures that the correlations are transformed reasonably, which in turn allows us to take advantage of well-developed imputation techniques for Gaussian outcomes. We use the phrase 'quasi' because the original observations are not guaranteed to be preserved. We present an application using a data set from psychiatric research. We conclude that the proposed method may be a promising tool for handling incomplete longitudinal or clustered ordinal outcomes.

Goodness‐of‐link testing in ordinal regression models

Abstract: McCullagh (1980) presented a comprehensive review of regression models for ordinal response variables. In these models, the functional relationship between the covariates and the response categories is dependent on the link function. This paper shows that discrimination between links is feasible when the response variable is ordinal. Using the log-gamma distribution of Prentice (1974), a generalized link function is constructed which allows discrimination between the probit, log-log, and complementary log-log links. Sample-size considerations are noted, and examples are presented. On peut trouver dans McCullagh (1980) une synthese consciencieuse des modeles de regression concus pour ľanalyse de variables categoriques de type ordinal. Dans de tels modeles, la relation fonctionnelle qui existe entre les variables dependantes et independantes s'exprime par la “fonction de lien”. Dans le present article, nous visons a illustrer comment on peut operer une distinction entre differents genres de liens lorsque la variable dependante est ordinale. Pour ce faire, nous construisons une fonction de lien generalisee a ľaide de la loi log-gamma de Prentice (1974). Cette nouvelle fonction de lien permet alors de distinguer entre les liens probit, log-log et log-log complementaire. Nous insistons en outre sur ľimportance de tenir compte de la taille echantionnalle et nous presentons des exemples.

Exploitation of pairwise class distances for ordinal classification

Abstract: Ordinal classification refers to classification problems in which the classes have a natural order imposed on them because of the nature of the concept studied. Some ordinal classification approaches perform a projection from the input space to one-dimensional latent space that is partitioned into a sequence of intervals one for each class. Class identity of a novel input pattern is then decided based on the interval its projection falls into. This projection is trained only indirectly as part of the overall model fitting. As with any other latent model fitting, direct construction hints one may have about the desired form of the latent model can prove very useful for obtaining high-quality models. The key idea of this letter is to construct such a projection model directly, using insights about the class distribution obtained from pairwise distance calculations. The proposed approach is extensively evaluated with 8 nominal and ordinal classifiers methods, 10 real-world ordinal classification data sets, and 4 different performance measures. The new methodology obtained the best results in average ranking when considering three of the performance metrics, although significant differences are found for only some of the methods. Also, after observing other methods of internal behavior in the latent space, we conclude that the internal projections do not fully reflect the intraclass behavior of the patterns. Our method is intrinsically simple, intuitive, and easily understandable, yet highly competitive with state-of-the-art approaches to ordinal classification.