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Nonparametric polytomous IRT models for invariant item ordering, with results for parametric models

Authors
  • Sijtsma, Klaas1
  • Hemker, Bas T.2
  • 1 Tilburg University, Department of Research Methodology, Faculty of Social Sciences, Tilburg, 5000 LE, The Netherlands , Tilburg
  • 2 Cito National Institute for Educational Measurement, The Netherlands
Type
Published Article
Journal
Psychometrika
Publisher
Springer-Verlag
Publication Date
Jun 01, 1998
Volume
63
Issue
2
Pages
183–200
Identifiers
DOI: 10.1007/BF02294774
Source
Springer Nature
Keywords
License
Yellow

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 twononparametric 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 twoparametric 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.

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