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Ordinal regression

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


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Reference EntryDOI
15 Apr 2003
TL;DR: The authors discusses statistical methods that make use of ordinal information, including ordinal measures of correlation and group comparisons, and a discussion of the relation between ordinal correlations and multiple regression.
Abstract: This chapter discusses statistical methods that make use of ordinal information. There are two main sections, the first covers ordinal measures of correlation and the second covers ordinal measures for group comparisons. The correlation section focuses on descriptive and inferential methods for the bivariate case. There is also a discussion of the comparison of ordinal correlations and a type of ordinal multiple regression. The group comparison section focuses on dominance analysis using the delta measure. Two-group and multiple-group situations are discussed as well as factorial designs and designs with correlated data. The methods of the chapter have many desirable properties that argue for their general use. Much data in the social sciences has only ordinal justification and ordinal methods are based on operations consistent with ordinal data. Many research questions in the social sciences are ordinal in nature and ordinal methods provide answers to ordinal questions. The ordinal methods have the advantage of invariance under monotonic transformations so that results obtained on raw data are exactly the same under any order-preserving transformation. Finally, the ordinal methods have desirable statistical qualities, including few distributional assumptions, resistance to extreme values, and applicability to nonlinear but monotonic relationships. Keywords: concordance; delta; distribution-free; dominance; nonparametric; ordinal; tau

54 citations

Journal ArticleDOI
TL;DR: It is shown how the previously introduced weighted ordinal means can be obtained without exploiting the formal similarity of the structure of continuous t-conorms on [0,1] and divisible ordinal t- Conorms.

54 citations

Journal ArticleDOI
TL;DR: In this article, an ordered-response logit (ORL) model is proposed to capture the ordinal properties of categorical dependent variables, and it is shown that ORL improves interpretability of the estimated coefficients and enhances parsimony over the multinomial logit model in cases where it is reasonable to expect that the underlying categories are indeed ordinal.

53 citations

Journal ArticleDOI
TL;DR: A new procedure for generating samples from ordinal random variables with a prespecified correlation matrix and marginal distributions is proposed and its features are examined and compared with those of its main competitors.
Abstract: The increasing use of ordinal variables in different fields has led to the introduction of new statistical methods for their analysis. The performance of these methods needs to be investigated under a number of experimental conditions. Procedures to simulate from ordinal variables are then required. In this article, we deal with simulation from multivariate ordinal random variables. We propose a new procedure for generating samples from ordinal random variables with a prespecified correlation matrix and marginal distributions. Its features are examined and compared with those of its main competitors. A software implementation in R is also provided along with examples of its application.

53 citations

Journal ArticleDOI
01 Jan 2013
TL;DR: The Dominance-based Rough Set Approach (DRSA) is applied to a recently proposed MCDA methodology, called Robust Ordinal Regression, providing a very useful interpretation of the preference relations in terms of decision rules.
Abstract: We propose to apply the Dominance-based Rough Set Approach (DRSA) on the results of multiple criteria decision aiding (MCDA) methods, in order to explain their recommendations in terms of rules involving conditions on evaluation criteria. The rules represent a decision model which is transparent and easy to interpret for the DM. In fact, decision rules give arguments to justify and explain the decision and, in a learning perspective, they can be the starting point for an interactive procedure for analyzing and constructing the DM's preferences. It enables his/her understanding of the conditions for the suggested recommendation, and provides useful information about the role of particular criteria or their subsets. DRSA can be used in junction with any MCDA method producing a classification result or a preference relation in the set of alternatives. In this paper, we apply DRSA to a recently proposed MCDA methodology, called Robust Ordinal Regression (ROR). The ROR approach to MCDA, also called disaggregation-aggregation approach, aims at inferring parameters of a preference model representing some holistic preference comparisons of alternatives provided by the decision maker (DM). Contrary to the usual ordinal regression approaches to MCDA, ROR takes into account the whole set of possible value of preference model parameters compatible with the DM's preference information, to work out a final recommendation. In consequence, ROR gives a recommendation in terms of necessary and possible consequences of the application of all the compatible sets of parameter values to the considered set of alternatives. UTAGMS and GRIP methods apply this approach, considering general monotonic additive value functions, and produce as a result the necessary and possible preference relations. In this paper we show how DRSA completes the decision aiding process started with ROR, providing a very useful interpretation of the preference relations in terms of decision rules. Highlights? We apply the Dominance-based Rough Set Approach (DRSA) on the results of MCDA methods. ? DRSA completes the decision aiding process started with Robust Ordinal Regression. ? DRSA explains necessary and possible preference relations in terms of decision rules. ? Decision rules are useful for an interactive construction of DM's preferences. ? DRSA can be used in this way with any MCDA method to explain their recommendations.

52 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023102
2022191
202188
202093
201979
201873