IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v84y2019i2d10.1007_s11336-019-09667-4.html
   My bibliography  Save this article

Restricted Recalibration of Item Response Theory Models

Author

Listed:
  • Yang Liu

    (University of Maryland)

  • Ji Seung Yang

    (University of Maryland)

  • Alberto Maydeu-Olivares

    (University of South Carolina
    University of Barcelona)

Abstract

In item response theory (IRT), it is often necessary to perform restricted recalibration (RR) of the model: A set of (focal) parameters is estimated holding a set of (nuisance) parameters fixed. Typical applications of RR include expanding an existing item bank, linking multiple test forms, and associating constructs measured by separately calibrated tests. In the current work, we provide full statistical theory for RR of IRT models under the framework of pseudo-maximum likelihood estimation. We describe the standard error calculation for the focal parameters, the assessment of overall goodness-of-fit (GOF) of the model, and the identification of misfitting items. We report a simulation study to evaluate the performance of these methods in the scenario of adding a new item to an existing test. Parameter recovery for the focal parameters as well as Type I error and power of the proposed tests are examined. An empirical example is also included, in which we validate the pediatric fatigue short-form scale in the Patient-Reported Outcome Measurement Information System (PROMIS), compute global and local GOF statistics, and update parameters for the misfitting items.

Suggested Citation

  • Yang Liu & Ji Seung Yang & Alberto Maydeu-Olivares, 2019. "Restricted Recalibration of Item Response Theory Models," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 529-553, June.
    • Handle: RePEc:spr:psycho:v:84:y:2019:i:2:d:10.1007_s11336-019-09667-4
    DOI: 10.1007/s11336-019-09667-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-019-09667-4
    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/s11336-019-09667-4?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. 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. Shelby J. Haberman & Sandip Sinharay, 2013. "Generalized Residuals for General Models for Contingency Tables With Application to Item Response Theory," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1435-1444, December.
    3. William Meredith, 1993. "Measurement invariance, factor analysis and factorial invariance," Psychometrika, Springer;The Psychometric Society, vol. 58(4), pages 525-543, December.
    4. Harry Joe & Albert Maydeu-Olivares, 2006. "On the asymptotic distribution of Pearson’s X 2 in cross-validation samples," Psychometrika, Springer;The Psychometric Society, vol. 71(3), pages 587-592, September.
    5. Cees Glas, 1999. "Modification indices for the 2-PL and the nominal response model," Psychometrika, Springer;The Psychometric Society, vol. 64(3), pages 273-294, September.
    6. 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.
    7. Cees Glas, 1988. "The derivation of some tests for the rasch model from the multinomial distribution," Psychometrika, Springer;The Psychometric Society, vol. 53(4), pages 525-546, December.
    8. Shelby Haberman & Sandip Sinharay & Kyong Chon, 2013. "Assessing Item Fit for Unidimensional Item Response Theory Models Using Residuals from Estimated Item Response Functions," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 417-440, July.
    9. Eric Bradlow & Howard Wainer & Xiaohui Wang, 1999. "A Bayesian random effects model for testlets," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 153-168, June.
    10. Maydeu-Olivares, Albert & Joe, Harry, 2005. "Limited- and Full-Information Estimation and Goodness-of-Fit Testing in 2n Contingency Tables: A Unified Framework," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1009-1020, September.
    11. Albert Maydeu-Olivares & Harry Joe, 2006. "Limited Information Goodness-of-fit Testing in Multidimensional Contingency Tables," Psychometrika, Springer;The Psychometric Society, vol. 71(4), pages 713-732, December.
    12. 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.
    13. Mark Reiser, 1996. "Analysis of residuals for the multionmial item response model," Psychometrika, Springer;The Psychometric Society, vol. 61(3), pages 509-528, September.
    14. Harry Joe & Alberto Maydeu-Olivares, 2010. "A General Family of Limited Information Goodness-of-Fit Statistics for Multinomial Data," Psychometrika, Springer;The Psychometric Society, vol. 75(3), pages 393-419, September.
    15. Stephen Schilling & R. Bock, 2005. "High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature," Psychometrika, Springer;The Psychometric Society, vol. 70(3), pages 533-555, September.
    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. 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.

    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. 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.
    2. 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.
    3. Wu, Jianmin & Bentler, Peter M., 2013. "Limited information estimation in binary factor analysis: A review and extension," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 392-403.
    4. Mark Reiser & Silvia Cagnone & Junfei Zhu, 2023. "An Extended GFfit Statistic Defined on Orthogonal Components of Pearson’s Chi-Square," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 208-240, March.
    5. Vassilis Vasdekis & Silvia Cagnone & Irini Moustaki, 2012. "A Composite Likelihood Inference in Latent Variable Models for Ordinal Longitudinal Responses," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 425-441, July.
    6. Nuo Xi & Michael W. Browne, 2014. "Contributions to the Underlying Bivariate Normal Method for Factor Analyzing Ordinal Data," Journal of Educational and Behavioral Statistics, , vol. 39(6), pages 583-611, December.
    7. Albert Maydeu-Olivares & Harry Joe, 2006. "Limited Information Goodness-of-fit Testing in Multidimensional Contingency Tables," Psychometrika, Springer;The Psychometric Society, vol. 71(4), pages 713-732, December.
    8. 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.
    9. Katsikatsou, Myrsini & Moustaki, Irini & Yang-Wallentin, Fan & Jöreskog, Karl G., 2012. "Pairwise likelihood estimation for factor analysis models with ordinal data," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4243-4258.
    10. Molenaar, Dylan & Tuerlinckx, Francis & van der Maas, Han L. J., 2015. "Fitting Diffusion Item Response Theory Models for Responses and Response Times Using the R Package diffIRT," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 66(i04).
    11. C. Glas & Anna Dagohoy, 2007. "A Person Fit Test For Irt Models For Polytomous Items," Psychometrika, Springer;The Psychometric Society, vol. 72(2), pages 159-180, June.
    12. Michael Edwards, 2010. "A Markov Chain Monte Carlo Approach to Confirmatory Item Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 75(3), pages 474-497, September.
    13. 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.
    14. Shing-On Leung, 2008. "A Three-Dimensional Latent Variable Model for Attitude Scales," Sociological Methods & Research, , vol. 37(1), pages 135-154, August.
    15. Jochen Ranger & Kay Brauer, 2022. "On the Generalized S − X 2 –Test of Item Fit: Some Variants, Residuals, and a Graphical Visualization," Journal of Educational and Behavioral Statistics, , vol. 47(2), pages 202-230, April.
    16. Yang Liu & Jan Hannig, 2017. "Generalized Fiducial Inference for Logistic Graded Response Models," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1097-1125, December.
    17. Salim Moussa, 2016. "A two-step item response theory procedure for a better measurement of marketing constructs," Journal of Marketing Analytics, Palgrave Macmillan, vol. 4(1), pages 28-50, March.
    18. 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.
    19. Ji Seung Yang & Xiaying Zheng, 2018. "Item Response Data Analysis Using Stata Item Response Theory Package," Journal of Educational and Behavioral Statistics, , vol. 43(1), pages 116-129, February.
    20. Jules Ellis, 2014. "An Inequality for Correlations in Unidimensional Monotone Latent Variable Models for Binary Variables," Psychometrika, Springer;The Psychometric Society, vol. 79(2), pages 303-316, April.

    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:84:y:2019:i:2:d:10.1007_s11336-019-09667-4. 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.