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equateIRT: An R Package for IRT Test Equating

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  • Battauz, Michela

Abstract

The R package equateIRT implements item response theory (IRT) methods for equating different forms composed of dichotomous items. In particular, the IRT models included are the three-parameter logistic model, the two-parameter logistic model, the one-parameter logistic model and the Rasch model. Forms can be equated when they present common items (direct equating) or when they can be linked through a chain of forms that present common items in pairs (indirect or chain equating). When two forms can be equated through different paths, a single conversion can be obtained by averaging the equating coefficients. The package calculates direct and chain equating coefficients. The averaging of direct and chain coefficients that link the same two forms is performed through the bisector method. Furthermore, the package provides analytic standard errors of direct, chain and average equating coefficients.

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  • Battauz, Michela, 2015. "equateIRT: An R Package for IRT Test Equating," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 68(i07).
    • Handle: RePEc:jss:jstsof:v:068:i07
    DOI: http://hdl.handle.net/10.18637/jss.v068.i07
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    References listed on IDEAS

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    1. R. Bock & Murray Aitkin, 1981. "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 443-459, December.
    2. Chalmers, R. Philip, 2012. "mirt: A Multidimensional Item Response Theory Package for the R Environment," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i06).
    3. Ogasawara, Haruhiko, 2000. "Asymptotic Standard Errors of IRT Equating Coefficients Using Moments," 商学討究 (Shogaku Tokyu), Otaru University of Commerce, vol. 51(1), pages 1-23.
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    Cited by:

    1. Michela Battauz, 2017. "Multiple Equating of Separate IRT Calibrations," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 610-636, September.
    2. Alexander Robitzsch, 2024. "Estimation of Standard Error, Linking Error, and Total Error for Robust and Nonrobust Linking Methods in the Two-Parameter Logistic Model," Stats, MDPI, vol. 7(3), pages 1-21, June.
    3. John Patrick Lalor & Pedro Rodriguez, 2023. "py-irt : A Scalable Item Response Theory Library for Python," INFORMS Journal on Computing, INFORMS, vol. 35(1), pages 5-13, January.
    4. Michelle D. Barrett & Wim J. van der Linden, 2019. "Estimating Linking Functions for Response Model Parameters," Journal of Educational and Behavioral Statistics, , vol. 44(2), pages 180-209, April.
    5. Michela Battauz, 2019. "On Wald tests for differential item functioning detection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(1), pages 103-118, March.
    6. Michela Battauz, 2023. "Testing for differences in chain equating," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(2), pages 134-145, May.
    7. Björn Andersson & Marie Wiberg, 2017. "Item Response Theory Observed-Score Kernel Equating," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 48-66, March.

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