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Nonparametric Polytomous IRT Models for Invariant Item Ordering, with Results for Parametric Models

Published online by Cambridge University Press:  01 January 2025

Klaas Sijtsma  and
Bas T. Hemker
Klaas Sijtsma*
Affiliation:
Tilburg University
Bas T. Hemker
Affiliation:
CITO National Institute for Educational Measurement
*
Requests for reprints should be sent to Klaas Sijtsma, Department of Research Methodology, Faculty of Social Sciences, Tilburg University, PO Box 90153, 5000 LE Tilburg, THE NETHERLANDS. E-mail: k.sijtsma@kub.nl
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Abstract

It is often considered desirable to have the same ordering of the items by difficulty across different levels of the trait or ability. Such an ordering is an invariant item ordering (IIO). An IIO facilitates the interpretation of test results. For dichotomously scored items, earlier research surveyed the theory and methods of an invariant ordering in a nonparametric IRT context. Here the focus is on polytomously scored items, and both nonparametric and parametric IRT models are considered.

The absence of the IIO property in two nonparametric polytomous IRT models is discussed, and two nonparametric models are discussed that imply an IIO. A method is proposed that can be used to investigate whether empirical data imply an IIO. Furthermore, only two parametric polytomous IRT models are found to imply an IIO. These are the rating scale model (Andrich, 1978) and a restricted rating scale version of the graded response model (Muraki, 1990). Well-known models, such as the partial credit model (Masters, 1982) and the graded response model (Samejima, 1969), do no imply an IIO.

Keywords

invariant item orderingitem response theorynonparametric polytomous IRT modelsparametric polytomous IRT models
Type
Original Paper
Information
Psychometrika , Volume 63 , Issue 2 , June 1998 , pp. 183 - 200
Copyright
Copyright © 1998 The Psychometric Society

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