IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v80y2015i2p450-467.html
   My bibliography  Save this article

On the Unidentifiability of the Fixed-Effects 3PL Model

Author

Listed:
  • Ernesto Martín
  • Jorge González
  • Francis Tuerlinckx

Abstract

The paper offers a general review of the basic concepts of both statistical model and parameter identification, and revisits the conceptual relationships between parameter identification and both parameter interpretability and properties of parameter estimates. All these issues are then exemplified for the 1PL, 2PL, and 1PL-G fixed-effects models. For the 3PL model, however, we provide a theorem proving that the item parameters are not identified, do not have an empirical interpretation and that it is not possible to obtain consistent and unbiased estimates of them. Copyright The Psychometric Society 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:psycho:v:80:y:2015:i:2:p:450-467
    DOI: 10.1007/s11336-014-9404-2
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11336-014-9404-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11336-014-9404-2?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. San Martin, Ernesto & Rolin, Jean-Marie, 2013. "Identification of parametric Rasch-type models," LIDAM Reprints ISBA 2013002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Jing Cao & S. Stokes, 2008. "Bayesian IRT Guessing Models for Partial Guessing Behaviors," Psychometrika, Springer;The Psychometric Society, vol. 73(2), pages 209-230, June.
    3. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    4. Guido Pino & Ernesto Martín & Jorge González & Paul Boeck, 2008. "On the Relationships between Sum Score Based Estimation and Joint Maximum Likelihood Estimation," Psychometrika, Springer;The Psychometric Society, vol. 73(1), pages 145-151, March.
    5. Gabrielsen, Arne, 1978. "Consistency and identifiability," Journal of Econometrics, Elsevier, vol. 8(2), pages 261-263, October.
    6. 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).
    7. 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.
    8. Abderrahim Oulhaj & Michel Mouchart, 2003. "Partial sufficiency with connection to the identification problem," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 267-283.
    9. Javier Revuelta, 2010. "Estimating Difficulty from Polytomous Categorical Data," Psychometrika, Springer;The Psychometric Society, vol. 75(2), pages 331-350, June.
    10. 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.
    11. Lancaster, Tony, 2000. "The incidental parameter problem since 1948," Journal of Econometrics, Elsevier, vol. 95(2), pages 391-413, April.
    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. 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.
    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. Sandip Sinharay & Jens Ledet Jensen, 2019. "Higher-Order Asymptotics and Its Application to Testing the Equality of the Examinee Ability Over Two Sets of Items," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 484-510, June.
    4. Paula Fariña & Jorge González & Ernesto San Martín, 2019. "The Use of an Identifiability-Based Strategy for the Interpretation of Parameters in the 1PL-G and Rasch Models," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 511-528, June.
    5. Page, Garritt L. & San Martin, Ernesto & Torres Irribarra, David & Van Bellegem, Sébastien, 2024. "Temporally Dynamic, Cohort-Varying Value-Added Models," LIDAM Discussion Papers CORE 2024009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Garritt L. Page & Ernesto San Martín & David Torres Irribarra & Sébastien Van Bellegem, 2024. "Temporally Dynamic, Cohort-Varying Value-Added Models," Psychometrika, Springer;The Psychometric Society, vol. 89(3), pages 1074-1103, September.

    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 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.
    2. Wim J. Linden & Michelle D. Barrett, 2016. "Linking Item Response Model Parameters," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 650-673, September.
    3. Garritt L. Page & Ernesto San Martín & David Torres Irribarra & Sébastien Van Bellegem, 2024. "Temporally Dynamic, Cohort-Varying Value-Added Models," Psychometrika, Springer;The Psychometric Society, vol. 89(3), pages 1074-1103, September.
    4. Page, Garritt L. & San Martin, Ernesto & Torres Irribarra, David & Van Bellegem, Sébastien, 2024. "Temporally Dynamic, Cohort-Varying Value-Added Models," LIDAM Discussion Papers CORE 2024009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Bai, Jushan, 2024. "Likelihood approach to dynamic panel models with interactive effects," Journal of Econometrics, Elsevier, vol. 240(1).
    6. Yu-Wei Chang & Nan-Jung Hsu & Rung-Ching Tsai, 2017. "Unifying Differential Item Functioning in Factor Analysis for Categorical Data Under a Discretization of a Normal Variant," Psychometrika, Springer;The Psychometric Society, vol. 82(2), pages 382-406, June.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Cho, Seo-young & Vadlamannati, Krishna Chaitanya, 2010. "Compliance for big brothers: An empirical analysis on the impact of the anti-trafficking protocol," University of Göttingen Working Papers in Economics 118, University of Goettingen, Department of Economics.
    13. 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.
    14. Cavit Pakel & Neil Shephard & Kevin Sheppard, 2009. "Nuisance parameters, composite likelihoods and a panel of GARCH models," Economics Papers 2009-W12, Economics Group, Nuffield College, University of Oxford.
    15. Eric Hillebrand & Huiyu Huang & Tae-Hwy Lee & Canlin Li, 2018. "Using the Entire Yield Curve in Forecasting Output and Inflation," Econometrics, MDPI, vol. 6(3), pages 1-27, August.
    16. Le, Huyen T.K. & Buehler, Ralph & Fan, Yingling & Hankey, Steve, 2020. "Expanding the positive utility of travel through weeklong tracking: Within-person and multi-environment variability of ideal travel time," Journal of Transport Geography, Elsevier, vol. 84(C).
    17. Kocięcki, Andrzej & Kolasa, Marcin, 2023. "A solution to the global identification problem in DSGE models," Journal of Econometrics, Elsevier, vol. 236(2).
    18. Kato, Kengo & F. Galvao, Antonio & Montes-Rojas, Gabriel V., 2012. "Asymptotics for panel quantile regression models with individual effects," Journal of Econometrics, Elsevier, vol. 170(1), pages 76-91.
    19. 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.
    20. Neusser, Klaus, 2016. "A topological view on the identification of structural vector autoregressions," Economics Letters, Elsevier, vol. 144(C), pages 107-111.

    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:80:y:2015:i:2:p:450-467. 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.