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A Multilevel Mixture IRT Model With an Application to DIF

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  • Sun-Joo Cho
  • Allan S. Cohen

Abstract

Mixture item response theory models have been suggested as a potentially useful methodology for identifying latent groups formed along secondary, possibly nuisance dimensions. In this article, we describe a multilevel mixture item response theory (IRT) model (MMixIRTM) that allows for the possibility that this nuisance dimensionality may function differently at different levels. A MMixIRT model is described that enables simultaneous detection of differences in latent class composition at both examinee and school levels. The MMixIRTM can be viewed as a combination of an IRT model, an unrestricted latent class model, and a multilevel model. A Bayesian estimation of the MMixIRTM is described including analysis of label switching, use of priors, and model selection strategies. Results of a simulation study indicated that the generated parameters were recovered very well for the conditions considered. Use of MMixIRTM also was illustrated with the standardized mathematics test.

Suggested Citation

  • Sun-Joo Cho & Allan S. Cohen, 2010. "A Multilevel Mixture IRT Model With an Application to DIF," Journal of Educational and Behavioral Statistics, , vol. 35(3), pages 336-370, June.
    • Handle: RePEc:sae:jedbes:v:35:y:2010:i:3:p:336-370
    DOI: 10.3102/1076998609353111
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    References listed on IDEAS

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    1. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
    2. 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.
    3. Robert Mislevy & Norman Verhelst, 1990. "Modeling item responses when different subjects employ different solution strategies," Psychometrika, Springer;The Psychometric Society, vol. 55(2), pages 195-215, June.
    4. Paul Boeck, 2008. "Random Item IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 533-559, December.
    5. Bates, Douglas M. & DebRoy, Saikat, 2004. "Linear mixed models and penalized least squares," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 1-17, October.
    6. Sophia Rabe-Hesketh & Anders Skrondal & Andrew Pickles, 2004. "Generalized multilevel structural equation modeling," Psychometrika, Springer;The Psychometric Society, vol. 69(2), pages 167-190, June.
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    Cited by:

    1. Meredith Langi & Minjeong Jeon, 2023. "Identifying and Supporting Academically Low-Performing Schools in a Developing Country: An Application of a Specialized Multilevel IRT Model to PISA-D Assessment Data," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 332-356, March.
    2. Sun-Joo Cho & Allan Cohen & Brian Bottge, 2013. "Detecting Intervention Effects Using a Multilevel Latent Transition Analysis with a Mixture IRT Model," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 576-600, July.
    3. Silvia Bacci & Michela Gnaldi, 2015. "A classification of university courses based on students’ satisfaction: an application of a two-level mixture item response model," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 927-940, May.
    4. Elizabeth Ayers & Sophia Rabe-Hesketh & Rebecca Nugent, 2013. "Incorporating Student Covariates in Cognitive Diagnosis Models," Journal of Classification, Springer;The Classification Society, vol. 30(2), pages 195-224, July.
    5. Wallin, Gabriel & Chen, Yunxiao & Moustaki, Irini, 2024. "DIF analysis with unknown groups and anchor items," LSE Research Online Documents on Economics 121991, London School of Economics and Political Science, LSE Library.
    6. David Andrich & Curt Hagquist, 2012. "Real and Artificial Differential Item Functioning," Journal of Educational and Behavioral Statistics, , vol. 37(3), pages 387-416, June.

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