IDEAS home Printed from https://ideas.repec.org/a/gam/jstats/v7y2024i3p36-612d1419601.html
   My bibliography  Save this article

Estimation of Standard Error, Linking Error, and Total Error for Robust and Nonrobust Linking Methods in the Two-Parameter Logistic Model

Author

Listed:
  • Alexander Robitzsch

    (IPN—Leibniz Institute for Science and Mathematics Education, Olshausenstraße 62, 24118 Kiel, Germany
    Centre for International Student Assessment (ZIB), Olshausenstraße 62, 24118 Kiel, Germany)

Abstract

The two-parameter logistic (2PL) item response theory model is a statistical model for analyzing multivariate binary data. In this article, two groups are brought onto a common metric using the 2PL model using linking methods. The linking methods of mean–mean linking, mean–geometric–mean linking, and Haebara linking are investigated in nonrobust and robust specifications in the presence of differential item functioning (DIF). M-estimation theory is applied to derive linking errors for the studied linking methods. However, estimated linking errors are prone to sampling error in estimated item parameters, thus resulting in artificially increased the linking error estimates in finite samples. For this reason, a bias-corrected linking error estimate is proposed. The usefulness of the modified linking error estimate is demonstrated in a simulation study. It is shown that a simultaneous assessment of the standard error and linking error in a total error must be conducted to obtain valid statistical inference. In the computation of the total error, using the bias-corrected linking error estimate instead of the usually employed linking error provides more accurate coverage rates.

Suggested Citation

  • 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.
  • Handle: RePEc:gam:jstats:v:7:y:2024:i:3:p:36-612:d:1419601
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2571-905X/7/3/36/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2571-905X/7/3/36/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. Michela Battauz, 2017. "Multiple Equating of Separate IRT Calibrations," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 610-636, September.
    3. Alexander Robitzsch, 2023. "Linking Error in the 2PL Model," J, MDPI, vol. 6(1), pages 1-27, January.
    4. Alexander Robitzsch, 2023. "Comparing Robust Linking and Regularized Estimation for Linking Two Groups in the 1PL and 2PL Models in the Presence of Sparse Uniform Differential Item Functioning," Stats, MDPI, vol. 6(1), pages 1-17, January.
    5. Francesco Bartolucci, 2007. "A class of multidimensional IRT models for testing unidimensionality and clustering items," Psychometrika, Springer;The Psychometric Society, vol. 72(2), pages 141-157, June.
    6. Fumiko Samejima, 2000. "Logistic positive exponent family of models: Virtue of asymmetric item characteristic curves," Psychometrika, Springer;The Psychometric Society, vol. 65(3), pages 319-335, September.
    7. Dale Ballou, 2009. "Test Scaling and Value-Added Measurement," Education Finance and Policy, MIT Press, vol. 4(4), pages 351-383, October.
    8. Zeileis, Achim, 2006. "Object-oriented Computation of Sandwich Estimators," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 16(i09).
    9. Battauz, Michela, 2015. "equateIRT: An R Package for IRT Test Equating," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 68(i07).
    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.
    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. Alexander Robitzsch, 2023. "Linking Error in the 2PL Model," J, MDPI, vol. 6(1), pages 1-27, January.
    2. 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.
    3. Michela Battauz, 2017. "Multiple Equating of Separate IRT Calibrations," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 610-636, September.
    4. Alexander Robitzsch, 2024. "Bias-Reduced Haebara and Stocking–Lord Linking," J, MDPI, vol. 7(3), pages 1-12, September.
    5. Alexander Robitzsch, 2020. "L p Loss Functions in Invariance Alignment and Haberman Linking with Few or Many Groups," Stats, MDPI, vol. 3(3), pages 1-38, August.
    6. Heleno Bolfarine & Jorge Luis Bazan, 2010. "Bayesian Estimation of the Logistic Positive Exponent IRT Model," Journal of Educational and Behavioral Statistics, , vol. 35(6), pages 693-713, December.
    7. Dylan Molenaar & Conor Dolan & Paul Boeck, 2012. "The Heteroscedastic Graded Response Model with a Skewed Latent Trait: Testing Statistical and Substantive Hypotheses Related to Skewed Item Category Functions," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 455-478, July.
    8. Björn Andersson & Marie Wiberg, 2017. "Item Response Theory Observed-Score Kernel Equating," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 48-66, March.
    9. Dylan Molenaar, 2015. "Heteroscedastic Latent Trait Models for Dichotomous Data," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 625-644, September.
    10. Daniel M. Bolt & Xiangyi Liao, 2022. "Item Complexity: A Neglected Psychometric Feature of Test Items?," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1195-1213, December.
    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. Ping Chen & Chun Wang, 2021. "Using EM Algorithm for Finite Mixtures and Reformed Supplemented EM for MIRT Calibration," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 299-326, March.
    13. 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.
    14. 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.
    15. Padilla, Juan L. & Azevedo, Caio L.N. & Lachos, Victor H., 2018. "Multidimensional multiple group IRT models with skew normal latent trait distributions," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 250-268.
    16. Ying Cheng & Ke-Hai Yuan, 2010. "The Impact of Fallible Item Parameter Estimates on Latent Trait Recovery," Psychometrika, Springer;The Psychometric Society, vol. 75(2), pages 280-291, June.
    17. Koedel Cory & Leatherman Rebecca & Parsons Eric, 2012. "Test Measurement Error and Inference from Value-Added Models," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 12(1), pages 1-37, November.
    18. Alberto Maydeu-Olivares & Rosa Montaño, 2013. "How Should We Assess the Fit of Rasch-Type Models? Approximating the Power of Goodness-of-Fit Statistics in Categorical Data Analysis," Psychometrika, Springer;The Psychometric Society, vol. 78(1), pages 116-133, January.
    19. Carolina Navarro & Luis Ayala & José Labeaga, 2010. "Housing deprivation and health status: evidence from Spain," Empirical Economics, Springer, vol. 38(3), pages 555-582, June.
    20. Seth Gershenson, 2016. "Performance Standards and Employee Effort: Evidence From Teacher Absences," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 35(3), pages 615-638, June.

    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:gam:jstats:v:7:y:2024:i:3:p:36-612:d:1419601. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.