IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v71y2006i2d10.1007_s11336-004-1175-8.html
   My bibliography  Save this article

Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities

Author

Listed:
  • Carol M. Woods

    (Washington University in St. Louis
    Washington University)

  • David Thissen

    (University of North Carolina at Chapel Hill)

Abstract

The purpose of this paper is to introduce a new method for fitting item response theory models with the latent population distribution estimated from the data using splines. A spline-based density estimation system provides a flexible alternative to existing procedures that use a normal distribution, or a different functional form, for the population distribution. A simulation study shows that the new procedure is feasible in practice, and that when the latent distribution is not well approximated as normal, two-parameter logistic (2PL) item parameter estimates and expected a posteriori scores (EAPs) can be improved over what they would be with the normal model. An example with real data compares the new method and the extant empirical histogram approach.

Suggested Citation

  • Carol M. Woods & David Thissen, 2006. "Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities," Psychometrika, Springer;The Psychometric Society, vol. 71(2), pages 281-301, June.
    • Handle: RePEc:spr:psycho:v:71:y:2006:i:2:d:10.1007_s11336-004-1175-8
    DOI: 10.1007/s11336-004-1175-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-004-1175-8
    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/s11336-004-1175-8?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.

    Citations

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


    Cited by:

    1. Ke-Hai Yuan & Ying Cheng & Jeff Patton, 2014. "Information Matrices and Standard Errors for MLEs of Item Parameters in IRT," Psychometrika, Springer;The Psychometric Society, vol. 79(2), pages 232-254, April.
    2. 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.
    3. Scott Monroe, 2021. "Testing Latent Variable Distribution Fit in IRT Using Posterior Residuals," Journal of Educational and Behavioral Statistics, , vol. 46(3), pages 374-398, June.
    4. Yang Liu & Ji Seung Yang, 2018. "Bootstrap-Calibrated Interval Estimates for Latent Variable Scores in Item Response Theory," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 333-354, June.
    5. Xi Wang & Yang Liu, 2020. "Detecting Compromised Items Using Information From Secure Items," Journal of Educational and Behavioral Statistics, , vol. 45(6), pages 667-689, December.
    6. 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.
    7. James O. Ramsay & Marie Wiberg, 2017. "A Strategy for Replacing Sum Scoring," Journal of Educational and Behavioral Statistics, , vol. 42(3), pages 282-307, June.
    8. Bianconcini, Silvia & Cagnone, Silvia, 2012. "Estimation of generalized linear latent variable models via fully exponential Laplace approximation," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 183-193.
    9. James Ramsay & Marie Wiberg & Juan Li, 2020. "Full Information Optimal Scoring," Journal of Educational and Behavioral Statistics, , vol. 45(3), pages 297-315, June.
    10. Ying Cheng & Cheng Liu & John Behrens, 2015. "Standard Error of Ability Estimates and the Classification Accuracy and Consistency of Binary Decisions," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 645-664, September.
    11. Andrej Srakar & Vesna Čopič & Miroslav Verbič, 2018. "European cultural statistics in a comparative perspective: index of economic and social condition of culture for the EU countries," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 42(2), pages 163-199, May.
    12. Longjuan Liang & Michael W. Browne, 2015. "A Quasi-Parametric Method for Fitting Flexible Item Response Functions," Journal of Educational and Behavioral Statistics, , vol. 40(1), pages 5-34, February.
    13. Steven P. Reise & Han Du & Emily F. Wong & Anne S. Hubbard & Mark G. Haviland, 2021. "Matching IRT Models to Patient-Reported Outcomes Constructs: The Graded Response and Log-Logistic Models for Scaling Depression," Psychometrika, Springer;The Psychometric Society, vol. 86(3), pages 800-824, September.
    14. Shaobo Jin & Fan Yang-Wallentin, 2017. "Asymptotic Robustness Study of the Polychoric Correlation Estimation," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 67-85, March.
    15. Christopher J. Urban & Daniel J. Bauer, 2021. "A Deep Learning Algorithm for High-Dimensional Exploratory Item Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 1-29, March.
    16. 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.
    17. Marie Wiberg & James O. Ramsay & Juan Li, 2019. "Optimal Scores: An Alternative to Parametric Item Response Theory and Sum Scores," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 310-322, March.
    18. Yang Liu, 2020. "A Riemannian Optimization Algorithm for Joint Maximum Likelihood Estimation of High-Dimensional Exploratory Item Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 439-468, June.
    19. Li Cai, 2010. "A Two-Tier Full-Information Item Factor Analysis Model with Applications," Psychometrika, Springer;The Psychometric Society, vol. 75(4), pages 581-612, December.
    20. J. R. Lockwood & Katherine E. Castellano & Benjamin R. Shear, 2018. "Flexible Bayesian Models for Inferences From Coarsened, Group-Level Achievement Data," Journal of Educational and Behavioral Statistics, , vol. 43(6), pages 663-692, December.

    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:71:y:2006:i:2:d:10.1007_s11336-004-1175-8. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.