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A Note on Stochastic Ordering of the Latent Trait Using the Sum of Polytomous Item Scores

Published online by Cambridge University Press:  01 January 2025

L. Andries van der Ark  and
Wicher P. Bergsma
L. Andries van der Ark*
Affiliation:
Tilburg University
Wicher P. Bergsma
Affiliation:
London School of Economics
*
Requests for reprints should be sent to L. Andries van der Ark, Department of Methodology and Statistics, Faculty of Social and Behavioral Sciences, Tilburg University, 5000 LE, Tilburg, The Netherlands. E-mail: a.vdark@uvt.nl
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Abstract

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In contrast to dichotomous item response theory (IRT) models, most well-known polytomous IRT models do not imply stochastic ordering of the latent trait by the total test score (SOL). This has been thought to make the ordering of respondents on the latent trait using the total test score questionable and throws doubt on the justifiability of using nonparametric polytomous IRT models for ordinal measurement. We show that a broad class of polytomous IRT models has a weaker form of SOL, denoted weak SOL, and argue that weak SOL justifies ordering respondents on the latent trait using the total test score and, therefore, the use of nonparametric polytomous IRT models for ordinal measurement.

Keywords

Latent traitmonotone likelihood rationonparametric item response theoryordinal measurementpolytomous item response theorypolytomous itemsstochastic orderingtotal test score
Type
Original Paper
Information
Psychometrika , Volume 75 , Issue 2 , June 2010 , pp. 272 - 279
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NC
This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Copyright
Copyright © 2010 The Psychometric Society

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