IDEAS home Printed from https://ideas.repec.org/a/sae/jedbes/v46y2021i3p374-398.html
   My bibliography  Save this article

Testing Latent Variable Distribution Fit in IRT Using Posterior Residuals

Author

Listed:
  • Scott Monroe

    (14707University of Massachusetts Amherst)

Abstract

This research proposes a new statistic for testing latent variable distribution fit for unidimensional item response theory (IRT) models. If the typical assumption of normality is violated, then item parameter estimates will be biased, and dependent quantities such as IRT score estimates will be adversely affected. The proposed statistic compares the specified latent variable distribution to the sample average of latent variable posterior distributions commonly used in IRT scoring. Formally, the statistic is an instantiation of a generalized residual and is thus asymptotically distributed as standard normal. Also, the statistic naturally complements residual-based item-fit statistics, as both are conditional on the latent trait, and can be presented with graphical plots. In addition, a corresponding unconditional statistic, which controls for multiple comparisons, is proposed. The statistics are evaluated using a simulation study, and empirical analyses are provided.

Suggested Citation

  • 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.
    • Handle: RePEc:sae:jedbes:v:46:y:2021:i:3:p:374-398
    DOI: 10.3102/1076998620953764
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.3102/1076998620953764
    Download Restriction: no
    File URL: https://libkey.io/10.3102/1076998620953764?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
    ---><---

    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. Robert Gibbons & Donald Hedeker, 1992. "Full-information item bi-factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 57(3), pages 423-436, September.
    4. 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.
    5. 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.
    6. 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.
    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. Carmen Köhler & Alexander Robitzsch & Johannes Hartig, 2020. "A Bias-Corrected RMSD Item Fit Statistic: An Evaluation and Comparison to Alternatives," Journal of Educational and Behavioral Statistics, , vol. 45(3), pages 251-273, 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.
    10. Robert Mislevy, 1984. "Estimating latent distributions," Psychometrika, Springer;The Psychometric Society, vol. 49(3), pages 359-381, September.
    11. Scott Monroe, 2019. "Estimation of Expected Fisher Information for IRT Models," Journal of Educational and Behavioral Statistics, , vol. 44(4), pages 431-447, August.
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Gregory Camilli & Jean-Paul Fox, 2015. "An Aggregate IRT Procedure for Exploratory Factor Analysis," Journal of Educational and Behavioral Statistics, , vol. 40(4), pages 377-401, August.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Li Cai, 2010. "Metropolis-Hastings Robbins-Monro Algorithm for Confirmatory Item Factor Analysis," Journal of Educational and Behavioral Statistics, , vol. 35(3), pages 307-335, June.
    15. 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.
    16. Azevedo, Caio L.N. & Andrade, Dalton F. & Fox, Jean-Paul, 2012. "A Bayesian generalized multiple group IRT model with model-fit assessment tools," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4399-4412.
    17. 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.
    18. Azevedo, Caio L.N. & Bolfarine, Heleno & Andrade, Dalton F., 2011. "Bayesian inference for a skew-normal IRT model under the centred parameterization," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 353-365, January.
    19. Javier Revuelta, 2010. "Estimating Difficulty from Polytomous Categorical Data," Psychometrika, Springer;The Psychometric Society, vol. 75(2), pages 331-350, June.
    20. 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.

    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:sae:jedbes:v:46:y:2021:i:3:p:374-398. 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: SAGE Publications (email available below). General contact details of provider: .

    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.