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Multiple Equating of Separate IRT Calibrations

Published online by Cambridge University Press:  01 January 2025

Michela Battauz Open the ORCID record for Michela Battauz [Opens in a new window]
Michela Battauz*
Affiliation:
University of Udine
*
Correspondence should be made to Michela Battauz, Department of Economics and Statistics, University of Udine,Udine, Italy. Email: [email protected]; http://people.uniud.it/page/michela.battauz
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Abstract

When test forms are calibrated separately, item response theory parameters are not comparable because they are expressed on different measurement scales. The equating process includes the conversion of item parameter estimates on a common scale and the determination of comparable test scores. Various statistical methods have been proposed to perform equating between two test forms. This paper provides a generalization to multiple test forms of the mean-geometric mean, the mean-mean, the Haebara, and the Stocking–Lord methods. The proposed methods estimate simultaneously the equating coefficients that permit the scale transformation of the parameters of all forms to the scale of the base form. Asymptotic standard errors of the equating coefficients are derived. A simulation study is presented to illustrate the performance of the methods.

Keywords

equating coefficientsHaebaraitem response theorylinkingmean-geometric meanmean-meanstandard errorsStocking–Lord
Type
Original paper
Information
Psychometrika , Volume 82 , Issue 3 , September 2017 , pp. 610 - 636
Copyright
Copyright © 2016 The Psychometric Society

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