IDEAS home Printed from https://ideas.repec.org/a/bla/stanee/v77y2023i2p134-145.html

Testing for differences in chain equating

Author

Listed:
  • Michela Battauz

Abstract

The comparability of the scores obtained in different forms of a test is certainly an essential requirement. This paper proposes a statistical test for the detection of noncomparable scores based on item response theory (IRT) methods. When the IRT model is fit separately for different forms of a test, the item parameter estimates are expressed on different measurement scales. The first step to obtain comparable scores is to convert the item parameters to a common metric using two constants, called equating coefficients. The equating coefficients can be estimated for two forms with common items, or derived through a chain of forms. The proposal of this paper is a statistical test to verify whether the scale conversions provided by the equating coefficients are as expected when the assumptions of the model are satisfied, hence leading to comparable scores. The method is illustrated through simulation studies and a real‐data example.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:stanee:v:77:y:2023:i:2:p:134-145
    DOI: 10.1111/stan.12277
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/stan.12277
    Download Restriction: no
    File URL: https://libkey.io/10.1111/stan.12277?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Haruhiko Ogasawara, 2003. "Asymptotic standard errors of irt observed-score equating methods," Psychometrika, Springer;The Psychometric Society, vol. 68(2), pages 193-211, June.
    2. Yi-Hsuan Lee & Alina Davier, 2013. "Monitoring Scale Scores over Time via Quality Control Charts, Model-Based Approaches, and Time Series Techniques," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 557-575, July.
    3. 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.
    4. Michela Battauz, 2017. "Multiple Equating of Separate IRT Calibrations," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 610-636, September.
    5. 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).
    6. Battauz, Michela, 2015. "equateIRT: An R Package for IRT Test Equating," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 68(i07).
    7. Michela Battauz, 2013. "IRT Test Equating in Complex Linkage Plans," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 464-480, July.
    8. Yi-Hsuan Lee & Shelby Haberman, 2013. "Harmonic Regression and Scale Stability," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 815-829, October.
    9. Michela Battauz, 2015. "Factors affecting the variability of IRT equating coefficients," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(2), pages 85-101, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Alexander Robitzsch, 2023. "Linking Error in the 2PL Model," J, MDPI, vol. 6(1), pages 1-27, January.
    4. Björn Andersson & Marie Wiberg, 2017. "Item Response Theory Observed-Score Kernel Equating," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 48-66, March.
    5. Alexander Robitzsch, 2024. "Extensions to Mean–Geometric Mean Linking," Mathematics, MDPI, vol. 13(1), pages 1-14, December.
    6. 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.
    7. Melissa Gladstone & Gillian Lancaster & Gareth McCray & Vanessa Cavallera & Claudia R. L. Alves & Limbika Maliwichi & Muneera A. Rasheed & Tarun Dua & Magdalena Janus & Patricia Kariger, 2021. "Validation of the Infant and Young Child Development (IYCD) Indicators in Three Countries: Brazil, Malawi and Pakistan," IJERPH, MDPI, vol. 18(11), pages 1-19, June.
    8. Björn Andersson & Tao Xin, 2021. "Estimation of Latent Regression Item Response Theory Models Using a Second-Order Laplace Approximation," Journal of Educational and Behavioral Statistics, , vol. 46(2), pages 244-265, April.
    9. Zhehan Jiang & Jonathan Templin, 2019. "Gibbs Samplers for Logistic Item Response Models via the Pólya–Gamma Distribution: A Computationally Efficient Data-Augmentation Strategy," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 358-374, June.
    10. Michela Battauz, 2013. "IRT Test Equating in Complex Linkage Plans," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 464-480, July.
    11. Michela Battauz, 2015. "Factors affecting the variability of IRT equating coefficients," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(2), pages 85-101, May.
    12. Yoav Bergner & Peter Halpin & Jill-Jênn Vie, 2022. "Multidimensional Item Response Theory in the Style of Collaborative Filtering," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 266-288, March.
    13. Xue Wang & Jing Lu & Jiwei Zhang, 2025. "A Metropolis–Hastings Robbins–Monro algorithm via variational inference for estimating the multidimensional graded response model: a calculationally efficient estimation scheme to deal with complex test structures," Computational Statistics, Springer, vol. 40(3), pages 1253-1284, March.
    14. Sara Fernandes & Guillaume Fond & Xavier Zendjidjian & Pierre Michel & Karine Baumstarck & Christophe Lançon & Ludovic Samalin & Pierre-Michel Llorca & Magali Coldefy & Pascal Auquier & Laurent Boyer , 2022. "Development and Calibration of the PREMIUM Item Bank for Measuring Respect and Dignity for Patients with Severe Mental Illness," Post-Print hal-03649277, HAL.
    15. Felix Zimmer & Clemens Draxler & Rudolf Debelak, 2023. "Power Analysis for the Wald, LR, Score, and Gradient Tests in a Marginal Maximum Likelihood Framework: Applications in IRT," Psychometrika, Springer;The Psychometric Society, vol. 88(4), pages 1249-1298, December.
    16. Yunxiao Chen & Xiaoou Li & Siliang Zhang, 2019. "Joint Maximum Likelihood Estimation for High-Dimensional Exploratory Item Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 124-146, March.
    17. Chanjin Zheng & Shaoyang Guo & Justin L Kern, 2021. "Fast Bayesian Estimation for the Four-Parameter Logistic Model (4PLM)," SAGE Open, , vol. 11(4), pages 21582440211, October.
    18. Alexander Robitzsch, 2021. "A Comprehensive Simulation Study of Estimation Methods for the Rasch Model," Stats, MDPI, vol. 4(4), pages 1-23, October.
    19. Peter W. Rijn & Usama S. Ali & Hyo Jeong Shin & Sean-Hwane Joo, 2024. "Adjusted Residuals for Evaluating Conditional Independence in IRT Models for Multistage Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 89(1), pages 317-346, March.
    20. R. Philip Chalmers, 2018. "Model-Based Measures for Detecting and Quantifying Response Bias," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 696-732, September.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:stanee:v:77:y:2023:i:2:p:134-145. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0039-0402 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.