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Polytomous Latent Scales for the Investigation of the Ordering of Items

Published online by Cambridge University Press:  01 January 2025

Rudy Ligtvoet ,
L. Andries van der Ark ,
Wicher P. Bergsma  and
Klaas Sijtsma
Rudy Ligtvoet*
Affiliation:
University of Amsterdam
L. Andries van der Ark
Affiliation:
Tilburg University
Wicher P. Bergsma
Affiliation:
London School of Economics
Klaas Sijtsma
Affiliation:
Tilburg University
*
Requests for reprints should be sent to Rudy Ligtvoet, Faculty of Social and Behavioural Sciences, University of Amsterdam, Nieuwe Prinsengracht 130, 1018 VZ Amsterdam, The Netherlands. E-mail: [email protected]
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Abstract

We propose three latent scales within the framework of nonparametric item response theory for polytomously scored items. Latent scales are models that imply an invariant item ordering, meaning that the order of the items is the same for each measurement value on the latent scale. This ordering property may be important in, for example, intelligence testing and person-fit analysis. We derive observable properties of the three latent scales that can each be used to investigate in real data whether the particular model adequately describes the data. We also propose a methodology for analyzing test data in an effort to find support for a latent scale, and we use two real-data examples to illustrate the practical use of this methodology.

Keywords

increasingness in transpositioninvariant item orderinglatent scalesmanifest invariant item orderingnonparametric IRT modelspolytomous IRT models
Type
Original Paper
Information
Psychometrika , Volume 76 , Issue 2 , April 2011 , pp. 200 - 216
Copyright
Copyright © 2011 The Psychometric Society

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