IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v89y2024i2d10.1007_s11336-024-09960-x.html
   My bibliography  Save this article

Efficient Corrections for Standardized Person-Fit Statistics

Author

Listed:
  • Kylie Gorney

    (Michigan State University)

  • Sandip Sinharay

    (Educational Testing Service)

  • Carol Eckerly

    (Educational Testing Service)

Abstract

Many popular person-fit statistics belong to the class of standardized person-fit statistics, T, and are assumed to have a standard normal null distribution. However, in practice, this assumption is incorrect since T is computed using (a) an estimated ability parameter and (b) a finite number of items. Snijders (Psychometrika 66(3):331–342, 2001) developed mean and variance corrections for T to account for the use of an estimated ability parameter. Bedrick (Psychometrika 62(2):191–199, 1997) and Molenaar and Hoijtink (Psychometrika 55(1):75–106, 1990) developed skewness corrections for T to account for the use of a finite number of items. In this paper, we combine these two lines of research and propose three new corrections for T that simultaneously account for the use of an estimated ability parameter and the use of a finite number of items. The new corrections are efficient in that they only require the analysis of the original data set and do not require the simulation or analysis of any additional data sets. We conducted a detailed simulation study and found that the new corrections are able to control the Type I error rate while also maintaining reasonable levels of power. A real data example is also included.

Suggested Citation

  • Kylie Gorney & Sandip Sinharay & Carol Eckerly, 2024. "Efficient Corrections for Standardized Person-Fit Statistics," Psychometrika, Springer;The Psychometric Society, vol. 89(2), pages 569-591, June.
    • Handle: RePEc:spr:psycho:v:89:y:2024:i:2:d:10.1007_s11336-024-09960-x
    DOI: 10.1007/s11336-024-09960-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-024-09960-x
    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/s11336-024-09960-x?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. Kevin Carl P. Santos & Jimmy Torre & Matthias Davier, 2020. "Adjusting Person Fit Index for Skewness in Cognitive Diagnosis Modeling," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 399-420, July.
    2. Matthias Davier & Ivo Molenaar, 2003. "A person-fit index for polytomous rasch models, latent class models, and their mixture generalizations," Psychometrika, Springer;The Psychometric Society, vol. 68(2), pages 213-228, June.
    3. Maxwell Hong & Lizhen Lin & Ying Cheng, 2021. "Asymptotically Corrected Person Fit Statistics for Multidimensional Constructs with Simple Structure and Mixed Item Types," Psychometrika, Springer;The Psychometric Society, vol. 86(2), pages 464-488, June.
    4. Sandip Sinharay, 2016. "Asymptotically Correct Standardization of Person-Fit Statistics Beyond Dichotomous Items," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 992-1013, December.
    5. Ivo Molenaar & Herbert Hoijtink, 1990. "The many null distributions of person fit indices," Psychometrika, Springer;The Psychometric Society, vol. 55(1), pages 75-106, March.
    6. Thomas Warm, 1989. "Weighted likelihood estimation of ability in item response theory," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 427-450, September.
    7. Tom Snijders, 2001. "Asymptotic null distribution of person fit statistics with estimated person parameter," Psychometrika, Springer;The Psychometric Society, vol. 66(3), pages 331-342, September.
    8. 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.
    9. Kylie Gorney & James A. Wollack & Sandip Sinharay & Carol Eckerly, 2023. "Using Item Scores and Distractors to Detect Item Compromise and Preknowledge," Journal of Educational and Behavioral Statistics, , vol. 48(5), pages 636-660, October.
    10. Kikumi Tatsuoka, 1984. "Caution indices based on item response theory," Psychometrika, Springer;The Psychometric Society, vol. 49(1), pages 95-110, March.
    11. Edward Bedrick, 1997. "Approximating the conditional distribution of person FIT indexes for checking the rasch model," Psychometrika, Springer;The Psychometric Society, vol. 62(2), pages 191-199, June.
    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. Maxwell Hong & Lizhen Lin & Ying Cheng, 2021. "Asymptotically Corrected Person Fit Statistics for Multidimensional Constructs with Simple Structure and Mixed Item Types," Psychometrika, Springer;The Psychometric Society, vol. 86(2), pages 464-488, June.
    2. Zhongtian Lin & Tao Jiang & Frank Rijmen & Paul Wamelen, 2024. "Asymptotically Correct Person Fit z-Statistics For the Rasch Testlet Model," Psychometrika, Springer;The Psychometric Society, vol. 89(4), pages 1230-1260, December.
    3. Kevin Carl P. Santos & Jimmy Torre & Matthias Davier, 2020. "Adjusting Person Fit Index for Skewness in Cognitive Diagnosis Modeling," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 399-420, July.
    4. Sandip Sinharay, 2016. "Asymptotically Correct Standardization of Person-Fit Statistics Beyond Dichotomous Items," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 992-1013, December.
    5. David Magis & Gilles Raîche & Sébastien Béland, 2012. "A Didactic Presentation of Snijders’s lz* Index of Person Fit With Emphasis on Response Model Selection and Ability Estimation," Journal of Educational and Behavioral Statistics, , vol. 37(1), pages 57-81, February.
    6. Xiang Liu & James Yang & Hui Soo Chae & Gary Natriello, 2020. "Power Divergence Family of Statistics for Person Parameters in IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 502-525, June.
    7. 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.
    8. Martin Biehler & Heinz Holling & Philipp Doebler, 2015. "Saddlepoint Approximations of the Distribution of the Person Parameter in the Two Parameter Logistic Model," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 665-688, September.
    9. 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.
    10. Sandip Sinharay, 2015. "Assessment of Person Fit for Mixed-Format Tests," Journal of Educational and Behavioral Statistics, , vol. 40(4), pages 343-365, August.
    11. Ogasawara, Haruhiko, 2013. "Asymptotic cumulants of ability estimators using fallible item parameters," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 144-162.
    12. Sandip Sinharay, 2016. "Person Fit Analysis in Computerized Adaptive Testing Using Tests for a Change Point," Journal of Educational and Behavioral Statistics, , vol. 41(5), pages 521-549, October.
    13. Matthias Davier & Ivo Molenaar, 2003. "A person-fit index for polytomous rasch models, latent class models, and their mixture generalizations," Psychometrika, Springer;The Psychometric Society, vol. 68(2), pages 213-228, June.
    14. Sandip Sinharay, 2017. "Detection of Item Preknowledge Using Likelihood Ratio Test and Score Test," Journal of Educational and Behavioral Statistics, , vol. 42(1), pages 46-68, February.
    15. 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.
    16. Rob R. Meijer & Jorge N. Tendeiro, 2012. "The Use of the lz and lz* Person-Fit Statistics and Problems Derived From Model Misspecification," Journal of Educational and Behavioral Statistics, , vol. 37(6), pages 758-766, December.
    17. Sukaesi Marianti & Jean-Paul Fox & Marianna Avetisyan & Bernard P. Veldkamp & Jesper Tijmstra, 2014. "Testing for Aberrant Behavior in Response Time Modeling," Journal of Educational and Behavioral Statistics, , vol. 39(6), pages 426-451, December.
    18. Yang Liu & Jan Hannig & Abhishek Pal Majumder, 2019. "Second-Order Probability Matching Priors for the Person Parameter in Unidimensional IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 701-718, September.
    19. Xiang Liu & Zhuangzhuang Han & Matthew S. Johnson, 2018. "The UMP Exact Test and the Confidence Interval for Person Parameters in IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 182-202, March.
    20. Karl Klauer, 1991. "An exact and optimal standardized person test for assessing consistency with the rasch model," Psychometrika, Springer;The Psychometric Society, vol. 56(2), pages 213-228, 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:spr:psycho:v:89:y:2024:i:2:d:10.1007_s11336-024-09960-x. 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.