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Remarks on the Identifiability of Thurstonian Paired Comparison Models Under Multiple Judgment

Published online by Cambridge University Press:  01 January 2025

Rung-Ching Tsai
Rung-Ching Tsai*
Affiliation:
National Taiwan Normal University
*
Requests for reprints should be sent to Rung-Ching Tsai, Department of Mathematics, National Taiwan Normal University, No. 88, Sec. 4, Ting-Zhou Road, Taipei 116, Taiwan. E-Mail: rtsai@math.ntnu.edu.tw
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Abstract

It is well-known that the representations of the Thurstonian models for difference judgment data are not unique. It has been shown that equivalence classes can be formed to provide a more meaningful partition of the covariance structures of the Thurstonian ranking models. In this paper, we examine the equivalence relations between Thurstonian covariance structure models for paired comparison data obtained under multiple judgment and discuss their implications on the general identification constraints and methods to check for parameter identifiability in restricted models.

Keywords

Thurstonian paired comparison modelsidentifiabilitymultiple judgment
Type
Article
Information
Psychometrika , Volume 68 , Issue 3 , September 2003 , pp. 361 - 372
Copyright
Copyright © 2003 The Psychometric Society

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Footnotes

The author is indebted to Ulf Böckenholt and Albert Maydeu-Olivares for their significant comments and suggestions which led to considerable improvement in this article.

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