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Modeling Within-Subject Dependencies in Ordinal Paired Comparison Data

Published online by Cambridge University Press:  01 January 2025

Ulf Böckenholt  and
William R. Dillon
Ulf Böckenholt*
Affiliation:
University of Illinois
William R. Dillon*
Affiliation:
Southern Methodist University
*
Requests for reprints should be sent to Ulf Böckenholt, Department of Psychology, University of Illinois, Champaign, IL 61820, or to William R. Dillon, School of Business, Southern Methodist University, Dallas, TX 75275.
Requests for reprints should be sent to Ulf Böckenholt, Department of Psychology, University of Illinois, Champaign, IL 61820, or to William R. Dillon, School of Business, Southern Methodist University, Dallas, TX 75275.
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Abstract

This paper presents two probabilistic models based on the logistic and the normal distribution for the analysis of dependencies in individual paired comparison judgments. It is argued that a core assumption of latent class choice models, independence of individual decisions, may not be well-suited for the analysis of paired comparison data. Instead, the analysis and interpretation of paired comparison data may be much simplified by allowing for within-person dependencies that result from repeated evaluations of the same options in different pairs. Moreover, by relating dependencies among the individual-level responses to (in)consistencies in the judgmental process, we show that the proposed graded paired comparison models reduce to ranking models under certain conditions. Three applications are presented to illustrate the approach.

Keywords

repeated measurementsrankingsintransitivitiesThurstonian models
Type
Original Paper
Information
Psychometrika , Volume 62 , Issue 3 , September 1997 , pp. 411 - 434
Copyright
Copyright © 1997 The Psychometric Society

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Footnotes

This research was partially supported by NSF grant SBR-9409531. The authors are grateful to the reviewers, Alan Agresti and Herbert Hoijtink for their helpful comments on this research.

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