An ordinal evaluation of categorical judgement data by random utilities and a corresponding correlation analysis

Autor(en): Suck, R
Stichwörter: biorders; categorical judgement; Mathematical Methods In Social Sciences; Mathematics; Mathematics, Interdisciplinary Applications; order polytope; polyhedral combinatorics; Psychology; Psychology, Mathematical; random utility representations; REPRESENTATIONS; Social Sciences, Mathematical Methods; SYSTEMS; THEOREM
Erscheinungsdatum: 2005
Herausgeber: ACADEMIC PRESS INC ELSEVIER SCIENCE
Journal: JOURNAL OF MATHEMATICAL PSYCHOLOGY
Volumen: 49
Ausgabe: 6
Startseite: 489
Seitenende: 497
Zusammenfassung: 
Categorical judgement data are analyzed along the lines of random utility theory. A class of orders is introduced (categorical weak orders); their characteristic vectors are regarded as points in a Euclidean space; their convex hull forms a polytope whose facets are fully characterized. This polytope is shown to correspond to an order polytope. Furthermore, its relation to the biorder polytope is pointed out. The convex representations of a given point of the polytope are discussed. The impact of these results on the methods of analyzing data arising from a categorical judgement procedure is outlined. In particular, some consequences are drawn with respect to the usual evaluation of correlations of such data. (c) 2005 Elsevier Inc. All rights reserved.
ISSN: 00222496
DOI: 10.1016/j.jmp.2005.08.004

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