IDEAS home Printed from https://ideas.repec.org/a/sae/jedbes/v38y2013i1p32-60.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.3102/1076998611432173
    Download Restriction: no
    File URL: https://libkey.io/10.3102/1076998611432173?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. 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.
    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. Li Cai, 2015. "Lord–Wingersky Algorithm Version 2.0 for Hierarchical Item Factor Models with Applications in Test Scoring, Scale Alignment, and Model Fit Testing," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 535-559, June.
    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.
    4. Minjeong Jeon & Sophia Rabe-Hesketh, 2016. "An autoregressive growth model for longitudinal item analysis," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 830-850, September.
    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.

    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. 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.
    2. Nana Kim & Daniel M. Bolt & James Wollack, 2022. "Noncompensatory MIRT For Passage-Based Tests," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 992-1009, September.
    3. Yunxiao Chen & Xiaoou Li & Jingchen Liu & Zhiliang Ying, 2018. "Robust Measurement via A Fused Latent and Graphical Item Response Theory Model," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 538-562, September.
    4. Minjeong Jeon & Sophia Rabe-Hesketh, 2016. "An autoregressive growth model for longitudinal item analysis," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 830-850, September.
    5. Stefano Noventa & Andrea Spoto & Jürgen Heller & Augustin Kelava, 2019. "On a Generalization of Local Independence in Item Response Theory Based on Knowledge Space Theory," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 395-421, June.
    6. Chen, Yunxiao & Li, Xiaoou & Liu, Jingchen & Ying, Zhiliang, 2018. "Robust measurement via a fused latent and graphical item response theory model," LSE Research Online Documents on Economics 103181, London School of Economics and Political Science, LSE Library.
    7. 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.
    8. 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.
    9. Li Cai, 2015. "Lord–Wingersky Algorithm Version 2.0 for Hierarchical Item Factor Models with Applications in Test Scoring, Scale Alignment, and Model Fit Testing," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 535-559, June.
    10. Joachim Büschken & Thomas Otter & Greg M. Allenby, 2013. "The Dimensionality of Customer Satisfaction Survey Responses and Implications for Driver Analysis," Marketing Science, INFORMS, vol. 32(4), pages 533-553, July.
    11. Jeanne A. Teresi & Chun Wang & Marjorie Kleinman & Richard N. Jones & David J. Weiss, 2021. "Differential Item Functioning Analyses of the Patient-Reported Outcomes Measurement Information System (PROMIS®) Measures: Methods, Challenges, Advances, and Future Directions," Psychometrika, Springer;The Psychometric Society, vol. 86(3), pages 674-711, September.
    12. 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.
    13. Marino, Maria Francesca & Alfó, Marco, 2016. "Gaussian quadrature approximations in mixed hidden Markov models for longitudinal data: A simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 193-209.
    14. 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.
    15. Aristidis Nikoloulopoulos & Harry Joe, 2015. "Factor Copula Models for Item Response Data," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 126-150, March.
    16. Victoria T. Tanaka & George Engelhard & Matthew P. Rabbitt, 2020. "Using a Bifactor Model to Measure Food Insecurity in Households with Children," Journal of Family and Economic Issues, Springer, vol. 41(3), pages 492-504, September.
    17. Jean-Paul Fox & Cees Glas, 2001. "Bayesian estimation of a multilevel IRT model using gibbs sampling," Psychometrika, Springer;The Psychometric Society, vol. 66(2), pages 271-288, June.
    18. Chun Wang & Steven W. Nydick, 2020. "On Longitudinal Item Response Theory Models: A Didactic," Journal of Educational and Behavioral Statistics, , vol. 45(3), pages 339-368, June.
    19. 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.
    20. Sun-Joo Cho & Paul Boeck & Susan Embretson & Sophia Rabe-Hesketh, 2014. "Additive Multilevel Item Structure Models with Random Residuals: Item Modeling for Explanation and Item Generation," Psychometrika, Springer;The Psychometric Society, vol. 79(1), pages 84-104, 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:38:y:2013:i:1:p:32-60. 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.