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The Person Response Function as a Tool in Person-Fit Research

Published online by Cambridge University Press:  01 January 2025

Klaas Sijtsma  and
Rob R. Meijer
Klaas Sijtsma*
Affiliation:
Tilburg University
Rob R. Meijer
Affiliation:
University of Twente
*
Requests for reprints should be sent to Klaas Sijtsma, Department of Research Methodology, FSW, Tilburg University, PO Box 90153, 5000 LE Tilburg, The Netherlands. E-Mail: k.sijtsma@kub.nl
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Abstract

Item responses that do not fit an item response theory (IRT) model may cause the latent trait value to be inaccurately estimated. In the past two decades several statistics have been proposed that can be used to identify nonfitting item score patterns. These statistics all yield scalar values. Here, the use of the person response function (PRF) for identifying nonfitting item score patterns was investigated. The PRF is a function and can be used for diagnostic purposes. First, the PRF is defined in a class of IRT models that imply an invariant item ordering. Second, a person-fit method proposed by Trabin & Weiss (1983) is reformulated in a nonparametric IRT context assuming invariant item ordering, and statistical theory proposed by Rosenbaum (1987a) is adapted to test locally whether a PRF is nonincreasing. Third, a simulation study was conducted to compare the use of the PRF with the person-fit statistic ZU3. It is concluded that the PRF can be used as a diagnostic tool in person-fit research.

Keywords

appropriateness measurementinvariant item orderingnonparametric item response theoryperson-fit methodperson response function
Type
Articles
Information
Psychometrika , Volume 66 , Issue 2 , June 2001 , pp. 191 - 207
Copyright
Copyright © 2001 The Psychometric Society

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Footnotes

The authors are grateful to Coen A. Bernaards for preparing the figures used in this article, and to Wilco H.M. Emons for checking the calculations.

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