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Linking Item Response Model Parameters

Author

Listed:
  • Wim J. Linden

    (CTB/McGraw-Hill Education)

  • Michelle D. Barrett

    (CTB/McGraw-Hill Education)

Abstract

With a few exceptions, the problem of linking item response model parameters from different item calibrations has been conceptualized as an instance of the problem of test equating scores on different test forms. This paper argues, however, that the use of item response models does not require any test score equating. Instead, it involves the necessity of parameter linking due to a fundamental problem inherent in the formal nature of these models—their general lack of identifiability. More specifically, item response model parameters need to be linked to adjust for the different effects of the identifiability restrictions used in separate item calibrations. Our main theorems characterize the formal nature of these linking functions for monotone, continuous response models, derive their specific shapes for different parameterizations of the 3PL model, and show how to identify them from the parameter values of the common items or persons in different linking designs.

Suggested Citation

  • Wim J. Linden & Michelle D. Barrett, 2016. "Linking Item Response Model Parameters," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 650-673, September.
    • Handle: RePEc:spr:psycho:v:81:y:2016:i:3:d:10.1007_s11336-015-9469-6
    DOI: 10.1007/s11336-015-9469-6
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    References listed on IDEAS

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    Cited by:

    1. Haruhiko Ogasawara, 2021. "Maximization of Some Types of Information for Unidentified Item Response Models with Guessing Parameters," Psychometrika, Springer;The Psychometric Society, vol. 86(2), pages 544-563, June.
    2. Hao Wu, 2016. "A Note on the Identifiability of Fixed-Effect 3PL Models," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 1093-1097, December.
    3. 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.
    4. Stefano Noventa & Andrea Spoto & Jürgen Heller & Augustin Kelava, 2019. "On a Generalization of Local Independence in Item Response Theory Based on Knowledge Space Theory," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 395-421, June.
    5. Leah M. Feuerstahler, 2019. "Metric Transformations and the Filtered Monotonic Polynomial Item Response Model," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 105-123, March.

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