IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v81y2016i3d10.1007_s11336-015-9469-6.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-015-9469-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11336-015-9469-6?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Thom Luijben, 1991. "Equivalent models in covariance structure analysis," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 653-665, December.
    2. Gerhard Fischer, 2004. "Remarks on “equivalent linear logistic test models” by Bechger, Verstralen, and Verhelst (2002)," Psychometrika, Springer;The Psychometric Society, vol. 69(2), pages 305-315, June.
    3. Javier Revuelta, 2009. "Identifiability and Equivalence of GLLIRM Models," Psychometrika, Springer;The Psychometric Society, vol. 74(2), pages 257-272, June.
    4. Ernesto San Martín & Jean-Marie Rolin & Luis Castro, 2013. "Identification of the 1PL Model with Guessing Parameter: Parametric and Semi-parametric Results," Psychometrika, Springer;The Psychometric Society, vol. 78(2), pages 341-379, April.
    5. Gunter Maris & Timo Bechger, 2004. "Equivalent MIRID models," Psychometrika, Springer;The Psychometric Society, vol. 69(4), pages 627-639, December.
    6. Gabrielsen, Arne, 1978. "Consistency and identifiability," Journal of Econometrics, Elsevier, vol. 8(2), pages 261-263, October.
    7. San Martin, Ernesto & Jara, Alejandro & Rolin, Jean-Marie & Mouchart, Michel, 2011. "On the Bayesian nonparametric generalization of IRT-type models," LIDAM Reprints ISBA 2011012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    9. Richmond, J, 1974. "Identifiability in Linear Models," Econometrica, Econometric Society, vol. 42(4), pages 731-736, July.
    10. Timo Bechger & Huub Verstralen & Norman Verhelst, 2002. "Equivalent linear logistic test models," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 123-136, March.
    11. Ernesto San Martín & Alejandro Jara & Jean-Marie Rolin & Michel Mouchart, 2011. "On the Bayesian Nonparametric Generalization of IRT-Type Models," Psychometrika, Springer;The Psychometric Society, vol. 76(3), pages 385-409, July.
    12. Timo Bechger & Norman Verhelst & Huub Verstralen, 2001. "Identifiability of nonlinear logistic test models," Psychometrika, Springer;The Psychometric Society, vol. 66(3), pages 357-371, September.
    13. Rung-Ching Tsai, 2000. "Remarks on the identifiability of thurstonian ranking models: Case V, case III, or neither?," Psychometrika, Springer;The Psychometric Society, vol. 65(2), pages 233-240, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    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. 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.

    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. Ernesto Martín & Jorge González & Francis Tuerlinckx, 2015. "On the Unidentifiability of the Fixed-Effects 3PL Model," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 450-467, June.
    2. Ernesto San Martín & Jean-Marie Rolin & Luis Castro, 2013. "Identification of the 1PL Model with Guessing Parameter: Parametric and Semi-parametric Results," Psychometrika, Springer;The Psychometric Society, vol. 78(2), pages 341-379, April.
    3. Javier Revuelta, 2009. "Identifiability and Equivalence of GLLIRM Models," Psychometrika, Springer;The Psychometric Society, vol. 74(2), pages 257-272, June.
    4. S. Rabe-Hesketh & A. Skrondal, 2001. "Parameterization of Multivariate Random Effects Models for Categorical Data," Biometrics, The International Biometric Society, vol. 57(4), pages 1256-1263, December.
    5. Spanos, Aris, 1990. "The simultaneous-equations model revisited : Statistical adequacy and identification," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 87-105.
    6. Sally Paganin & Christopher J. Paciorek & Claudia Wehrhahn & Abel Rodríguez & Sophia Rabe-Hesketh & Perry de Valpine, 2023. "Computational Strategies and Estimation Performance With Bayesian Semiparametric Item Response Theory Models," Journal of Educational and Behavioral Statistics, , vol. 48(2), pages 147-188, April.
    7. Justin L. Kern & Steven Andrew Culpepper, 2020. "A Restricted Four-Parameter IRT Model: The Dyad Four-Parameter Normal Ogive (Dyad-4PNO) Model," Psychometrika, Springer;The Psychometric Society, vol. 85(3), pages 575-599, September.
    8. Yuqi Gu & Gongjun Xu, 2019. "The Sufficient and Necessary Condition for the Identifiability and Estimability of the DINA Model," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 468-483, June.
    9. Javier Revuelta, 2010. "Estimating Difficulty from Polytomous Categorical Data," Psychometrika, Springer;The Psychometric Society, vol. 75(2), pages 331-350, June.
    10. Xin-Yuan Song & Zhao-Hua Lu & Jing-Heng Cai & Edward Ip, 2013. "A Bayesian Modeling Approach for Generalized Semiparametric Structural Equation Models," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 624-647, October.
    11. Nguimkeu, Pierre & Denteh, Augustine & Tchernis, Rusty, 2019. "On the estimation of treatment effects with endogenous misreporting," Journal of Econometrics, Elsevier, vol. 208(2), pages 487-506.
    12. Kocięcki, Andrzej & Kolasa, Marcin, 2023. "A solution to the global identification problem in DSGE models," Journal of Econometrics, Elsevier, vol. 236(2).
    13. Carvalho Lopes, Celia Mendes & Bolfarine, Heleno, 2012. "Random effects in promotion time cure rate models," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 75-87, January.
    14. Neusser, Klaus, 2016. "A topological view on the identification of structural vector autoregressions," Economics Letters, Elsevier, vol. 144(C), pages 107-111.
    15. Orazio Attanasio & Sarah Cattan & Emla Fitzsimons & Costas Meghir & Marta Rubio-Codina, 2020. "Estimating the Production Function for Human Capital: Results from a Randomized Controlled Trial in Colombia," American Economic Review, American Economic Association, vol. 110(1), pages 48-85, January.
    16. Chrysanthos Dellarocas & Charles A. Wood, 2008. "The Sound of Silence in Online Feedback: Estimating Trading Risks in the Presence of Reporting Bias," Management Science, INFORMS, vol. 54(3), pages 460-476, March.
    17. Xiaohong Chen & Victor Chernozhukov & Sokbae Lee & Whitney K. Newey, 2014. "Local Identification of Nonparametric and Semiparametric Models," Econometrica, Econometric Society, vol. 82(2), pages 785-809, March.
    18. Naimoli, Antonio & Storti, Giuseppe, 2019. "Heterogeneous component multiplicative error models for forecasting trading volumes," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1332-1355.
    19. Daeyoung Kim & Bruce Lindsay, 2015. "Empirical identifiability in finite mixture models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(4), pages 745-772, August.
    20. Andrew Chesher & Adam Rosen, 2015. "Characterizations of identified sets delivered by structural econometric models," CeMMAP working papers 63/15, Institute for Fiscal Studies.

    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:spr:psycho:v:81:y:2016:i:3:d:10.1007_s11336-015-9469-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.