Ordinal regression

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

A study of the effect of dichotomizing ordinal data upon modeling

Abstract: Investigators in health services research often analyze ordinal outcome data as if it were dichotomous by collapsing outcomes into two groups and using standard logistic regression, rather than an alternate discrete model. This paper assesses the degree to which parameters are inaccurately estimated and ower is lost when this is done. Simulations with a five level ordinal outcome variable demonstrated that the loss of precision and power can be very pronounced. Parameter estimates were especially poor in the presence of moderately sparse data, while the loss of power was most evident with balanced data. Polychotomous models are also examined and discussed. An example using length of hospital stay data grouped into discrete outcome levels is given.

From circular ordinal regression to multilabel classification

Abstract: Several applications domains like wind forecasting in meteorology and robot control in robotics demand for learning algorithms that are able to make discrete directional predictions. We refer to this problem setting as circular ordinal regression, since it shares the same properties as traditional ordinal regression, namely the need for a specific model structure and order-preserving loss functions. This article gives a detailed introduction to the topic and proposes two methods. The first one is a circular support vector approach (cSVM), parameterized with only two vectors. The second method converts circular ordinal regression to a multilabel classification approach that takes the circular ranking into account by minimizing the Hamming loss. We also present initial empirical results based on two toy examples and a real-life application in the area of brain-computer interfaces.

Are ordinal models useful for classification

Abstract: There is recent interest in classification procedures intended for use only when the response is ordinal. Ordinal response, however, is evident in the parameters estimated by either multinomial logistic or normal discriminant analyses, both of which classify either ordinal or non-ordinal responses. Further, there may be harm in applying ordinal models inappropriately and ample opportunity to assume mistakenly ordinality in real data sets. Therefore, it becomes important to ascertain whether there is benefit obtained in the appropriate application of ordinal models. This paper presents the results of a simulation study designed to compare classification accuracy of various models. We show that ordinal models classify less accurately than the multinomial logistic and normal discriminant procedures under a variety of circumstances. Until further studies become available, we presently conclude that ordinal models confer no advantage when the main purpose of the analysis is classification.

When is it Better to Compare than to Score

Abstract: When eliciting judgements from humans for an unknown quantity, one often has the choice of making direct-scoring (cardinal) or comparative (ordinal) measurements. In this paper we study the relative merits of either choice, providing empirical and theoretical guidelines for the selection of a measurement scheme. We provide empirical evidence based on experiments on Amazon Mechanical Turk that in a variety of tasks, (pairwise-comparative) ordinal measurements have lower per sample noise and are typically faster to elicit than cardinal ones. Ordinal measurements however typically provide less information. We then consider the popular Thurstone and Bradley-Terry-Luce (BTL) models for ordinal measurements and characterize the minimax error rates for estimating the unknown quantity. We compare these minimax error rates to those under cardinal measurement models and quantify for what noise levels ordinal measurements are better. Finally, we revisit the data collected from our experiments and show that fitting these models confirms this prediction: for tasks where the noise in ordinal measurements is sufficiently low, the ordinal approach results in smaller errors in the estimation.

Robust Ranking of Universities Evaluated by Hierarchical and Interacting Criteria

Abstract: In this chapter, we present a methodology of decision aiding that helps to build a ranking of a finite set of alternatives evaluated by a family of hierarchically structured criteria. The presentation has a tutorial character, and takes as an example the ranking of universities. Each university is generally evaluated on several aspects, such as quality of faculty and research output. Moreover, their performance on these macro-criteria can be further detailed by evaluation on some subcriteria. To take into account the hierarchical structure of criteria presented as a tree, the multiple criteria hierarchy process will be applied. The aggregation of the university performances will be done by the Choquet integral preference model that is able to take into account the possible negative and positive interactions between the criteria at hand. On the basis of an indirect preference information supplied by the decision maker in terms of pairwise comparisons of some universities, or comparison of some criteria in terms of their importance and their interaction, the robust ordinal regression and the stochastic multicriteria acceptability analysis will be used. They will provide the decision maker some robust recommendations presented in the form of necessary and possible preference relations between universities, and in the form of a distribution of possible rank positions got by each of them, taking into account all preference models compatible with the available preference information. The methodology will be presented step by step on a sample of some European universities.