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Remarks on the Identifiability of Thurstonian Ranking Models: Case V, Case III, or Neither?

Published online by Cambridge University Press:  01 January 2025

Rung-Ching Tsai
Rung-Ching Tsai*
Affiliation:
University of Illinois, Champaign-Urbana
*
Requests for reprints should be sent to Rung-Ching Tsai, Department of Psychology, University of Illinois, 603 E. Daniel, Champaign, IL 61820. E-Mail: [email protected].
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Abstract

It is well-known that the representations of the Thurstonian Case III and Case V models for paired comparison data are not unique. Similarly, when analyzing ranking data, other equivalent covariance structures can substitute for those given by Thurstone in these cases. That is, we may more broadly define the family of covariance structures satisfying Case III and Case V conditions. This paper introduces the notion of equivalence classes which defines a more meaningful partition of the covariance structures of the Thurstonian ranking models. In addition, the equivalence classes of Case V and Case III are completely characterized.

Keywords

Thurstonian modelsidentifiabilityranking data
Type
Original Paper
Information
Psychometrika , Volume 65 , Issue 2 , June 2000 , pp. 233 - 240
Copyright
Copyright © 2000 The Psychometric Society

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Footnotes

The author gratefully acknowledges the valuable feedback from Ulf Böckenholt and the Associate Editor. The author would also like to thank River Chiang and three reviewers for their helpful comments and suggestions.

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