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Modeling Differential Item Functioning Using a Generalization of the Multiple-Group Bifactor Model

Author

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  • Minjeong Jeon

    (University of California, Berkeley)

  • Frank Rijmen

    (Educational Testing Service)

  • Sophia Rabe-Hesketh

    (University of California, Berkeley and Institute of Education, University of London)

Abstract

The authors present a generalization of the multiple-group bifactor model that extends the classical bifactor model for categorical outcomes by relaxing the typical assumption of independence of the specific dimensions. In addition to the means and variances of all dimensions, the correlations among the specific dimensions are allowed to differ between groups. By including group-specific difficulty parameters, the model can be used to assess differential item functioning (DIF) for testlet-based tests. The model encompasses various item response models for polytomous data by allowing for different link functions, and it includes testlet and second-order models as special cases. Importantly, by assuming that the testlet dimensions are conditionally independent given the general dimension, the authors show, using a graphical model framework, that the integration over all latent variables can be carried out through a sequence of computations in two-dimensional subspaces, making full-information maximum likelihood estimation feasible for high-dimensional problems and large datasets. The importance of relaxing the orthogonality assumption and allowing for a different covariance structure of the dimensions for each group is demonstrated in the context of the assessment of DIF. Through a simulation study, it is shown that ignoring between-group differences in the structure of the multivariate latent space can result in substantially biased estimates of DIF.

Suggested Citation

  • Minjeong Jeon & Frank Rijmen & Sophia Rabe-Hesketh, 2013. "Modeling Differential Item Functioning Using a Generalization of the Multiple-Group Bifactor Model," Journal of Educational and Behavioral Statistics, , vol. 38(1), pages 32-60, February.
    • Handle: RePEc:sae:jedbes:v:38:y:2013:i:1:p:32-60
    DOI: 10.3102/1076998611432173
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    References listed on IDEAS

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    1. Robin Shealy & William Stout, 1993. "A model-based standardization approach that separates true bias/DIF from group ability differences and detects test bias/DTF as well as item bias/DIF," Psychometrika, Springer;The Psychometric Society, vol. 58(2), pages 159-194, June.
    2. Sun, Xiaoqian & Sun, Dongchu, 2005. "Estimation of the Cholesky decomposition of the covariance matrix for a conditional independent normal model," Statistics & Probability Letters, Elsevier, vol. 73(1), pages 1-12, June.
    3. Karl Holzinger & Frances Swineford, 1937. "The Bi-factor method," Psychometrika, Springer;The Psychometric Society, vol. 2(1), pages 41-54, March.
    4. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 149-174, June.
    5. Edward Ip, 2002. "Locally dependent latent trait model and the dutch identity revisited," Psychometrika, Springer;The Psychometric Society, vol. 67(3), pages 367-386, September.
    6. Lauritzen, Steffen L., 1995. "The EM algorithm for graphical association models with missing data," Computational Statistics & Data Analysis, Elsevier, vol. 19(2), pages 191-201, February.
    7. Robert Gibbons & Donald Hedeker, 1992. "Full-information item bi-factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 57(3), pages 423-436, September.
    8. Frank Rijmen & Kristof Vansteelandt & Paul Boeck, 2008. "Latent Class Models for Diary Method Data: Parameter Estimation by Local Computations," Psychometrika, Springer;The Psychometric Society, vol. 73(2), pages 167-182, June.
    9. William Meredith, 1993. "Measurement invariance, factor analysis and factorial invariance," Psychometrika, Springer;The Psychometric Society, vol. 58(4), pages 525-543, December.
    10. Sandip Sinharay & Neil J. Dorans, 2010. "Two Simple Approaches to Overcome a Problem With the Mantel-Haenszel Statistic: Comments on Wang, Bradlow, Wainer, and Muller (2008)," Journal of Educational and Behavioral Statistics, , vol. 35(4), pages 474-488, August.
    11. Nambury Raju, 1988. "The area between two item characteristic curves," Psychometrika, Springer;The Psychometric Society, vol. 53(4), pages 495-502, December.
    12. Johan Braeken & Francis Tuerlinckx & Paul Boeck, 2007. "Copula Functions for Residual Dependency," Psychometrika, Springer;The Psychometric Society, vol. 72(3), pages 393-411, September.
    13. 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.
    14. Rabe-Hesketh, Sophia & Skrondal, Anders & Pickles, Andrew, 2005. "Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects," Journal of Econometrics, Elsevier, vol. 128(2), pages 301-323, October.
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    Cited by:

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    2. Ward, Jeffrey T. & Ray, James V. & Fox, Kathleen A., 2018. "Exploring differences in self-control across sex, race, age, education, and language: Considering a bifactor MIMIC model," Journal of Criminal Justice, Elsevier, vol. 56(C), pages 29-42.
    3. Frank Rijmen & Minjeong Jeon & Matthias von Davier & Sophia Rabe-Hesketh, 2014. "A Third-Order Item Response Theory Model for Modeling the Effects of Domains and Subdomains in Large-Scale Educational Assessment Surveys," Journal of Educational and Behavioral Statistics, , vol. 39(4), pages 235-256, August.
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    5. Minjeong Jeon & Paul Boeck & Jevan Luo & Xiangrui Li & Zhong-Lin Lu, 2021. "Modeling Within-Item Dependencies in Parallel Data on Test Responses and Brain Activation," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 239-271, March.

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