IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v79y2014i2p232-254.html
   My bibliography  Save this article

Information Matrices and Standard Errors for MLEs of Item Parameters in IRT

Author

Listed:
  • Ke-Hai Yuan
  • Ying Cheng
  • Jeff Patton

Abstract

The paper clarifies the relationship among several information matrices for the maximum likelihood estimates (MLEs) of item parameters. It shows that the process of calculating the observed information matrix also generates a related matrix that is the middle piece of a sandwich-type covariance matrix. Monte Carlo results indicate that standard errors (SEs) based on the observed information matrix are robust to many, but not all, conditions of model/distribution misspecifications. SEs based on the sandwich-type covariance matrix perform most consistently across conditions. Results also suggest that SEs based on other matrices are either not consistent or perform not as robust as those based on the sandwich-type covariance matrix or the observed information matrix. Copyright The Psychometric Society 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:psycho:v:79:y:2014:i:2:p:232-254
    DOI: 10.1007/s11336-013-9334-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11336-013-9334-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11336-013-9334-4?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. William Stout, 1987. "A nonparametric approach for assessing latent trait unidimensionality," Psychometrika, Springer;The Psychometric Society, vol. 52(4), pages 589-617, December.
    2. 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.
    3. Jinming Zhang & William Stout, 1999. "The theoretical detect index of dimensionality and its application to approximate simple structure," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 213-249, June.
    4. Ogasawara, Haruhiko, 2010. "Asymptotic expansions for the pivots using log-likelihood derivatives with an application in item response theory," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2149-2167, October.
    5. David Thissen & Howard Wainer, 1982. "Some standard errors in item response theory," Psychometrika, Springer;The Psychometric Society, vol. 47(4), pages 397-412, December.
    6. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    7. Robert Mislevy, 1986. "Bayes modal estimation in item response models," Psychometrika, Springer;The Psychometric Society, vol. 51(2), pages 177-195, June.
    8. Carol 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.
    9. 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.
    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. 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.
    2. Alexander Robitzsch, 2023. "Linking Error in the 2PL Model," J, MDPI, vol. 6(1), pages 1-27, January.
    3. 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.
    4. Wenchao Ma & Jimmy de la Torre, 2019. "Category-Level Model Selection for the Sequential G-DINA Model," Journal of Educational and Behavioral Statistics, , vol. 44(1), pages 45-77, February.
    5. Michel Philipp & Carolin Strobl & Jimmy de la Torre & Achim Zeileis, 2018. "On the Estimation of Standard Errors in Cognitive Diagnosis Models," Journal of Educational and Behavioral Statistics, , vol. 43(1), pages 88-115, February.
    6. Peter W. Rijn & Usama S. Ali, 2018. "A Generalized Speed–Accuracy Response Model for Dichotomous Items," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 109-131, March.
    7. Yang Liu & Jan Hannig, 2016. "Generalized Fiducial Inference for Binary Logistic Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 81(2), pages 290-324, June.
    8. Christian Ritzel & Gabriele Mack & Marco Portmann & Katja Heitkämper & Nadja El Benni, 2020. "Empirical evidence on factors influencing farmers’ administrative burden: A structural equation modeling approach," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-16, October.

    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. 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.
    2. 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.
    3. 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.
    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. Ogasawara, Haruhiko, 2013. "Asymptotic cumulants of ability estimators using fallible item parameters," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 144-162.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. A. Béguin & C. Glas, 2001. "MCMC estimation and some model-fit analysis of multidimensional IRT models," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 541-561, December.
    13. Edward Ip & Yuchung Wang & Paul Boeck & Michel Meulders, 2004. "Locally dependent latent trait model for polytomous responses with application to inventory of hostility," Psychometrika, Springer;The Psychometric Society, vol. 69(2), pages 191-216, June.
    14. Douglas L. Steinley & M. J. Brusco, 2019. "Using an Iterative Reallocation Partitioning Algorithm to Verify Test Multidimensionality," Journal of Classification, Springer;The Classification Society, vol. 36(3), pages 397-413, October.
    15. Vitoratou, Silia & Ntzoufras, Ioannis & Moustaki, Irini, 2016. "Explaining the behavior of joint and marginal Monte Carlo estimators in latent variable models with independence assumptions," LSE Research Online Documents on Economics 57685, London School of Economics and Political Science, LSE Library.
    16. Björn Andersson & Tao Xin, 2021. "Estimation of Latent Regression Item Response Theory Models Using a Second-Order Laplace Approximation," Journal of Educational and Behavioral Statistics, , vol. 46(2), pages 244-265, April.
    17. 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.
    18. Paul Holland, 1990. "On the sampling theory roundations of item response theory models," Psychometrika, Springer;The Psychometric Society, vol. 55(4), pages 577-601, December.
    19. Haruhiko Ogasawara, 2013. "Asymptotic properties of the Bayes modal estimators of item parameters in item response theory," Computational Statistics, Springer, vol. 28(6), pages 2559-2583, 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:79:y:2014:i:2:p:232-254. 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.