IDEAS home Printed from https://ideas.repec.org/a/sae/jedbes/v35y2010i3p336-370.html
   My bibliography  Save this article

A Multilevel Mixture IRT Model With an Application to DIF

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.3102/1076998609353111
    Download Restriction: no
    File URL: https://libkey.io/10.3102/1076998609353111?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. 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. 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.
    4. 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.
    5. Paul Boeck, 2008. "Random Item IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 533-559, December.
    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.
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    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.

    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. Sijia Huang & Li Cai, 2024. "Cross-Classified Item Response Theory Modeling With an Application to Student Evaluation of Teaching," Journal of Educational and Behavioral Statistics, , vol. 49(3), pages 311-341, June.
    2. Anders Skrondal & Sophia Rabe‐Hesketh, 2007. "Latent Variable Modelling: A Survey," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 712-745, December.
    3. Royce Anders & William Batchelder, 2015. "Cultural Consensus Theory for the Ordinal Data Case," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 151-181, March.
    4. Minjeong Jeon & Sophia Rabe-Hesketh, 2012. "Profile-Likelihood Approach for Estimating Generalized Linear Mixed Models With Factor Structures," Journal of Educational and Behavioral Statistics, , vol. 37(4), pages 518-542, August.
    5. Alexander Robitzsch, 2020. "L p Loss Functions in Invariance Alignment and Haberman Linking with Few or Many Groups," Stats, MDPI, vol. 3(3), pages 1-38, August.
    6. Dylan Molenaar, 2015. "Heteroscedastic Latent Trait Models for Dichotomous Data," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 625-644, September.
    7. Margot Bennink & Marcel A. Croon & Jos Keuning & Jeroen K. Vermunt, 2014. "Measuring Student Ability, Classifying Schools, and Detecting Item Bias at School Level, Based on Student-Level Dichotomous Items," Journal of Educational and Behavioral Statistics, , vol. 39(3), pages 180-202, June.
    8. Cho, S.-J. & Rabe-Hesketh, S., 2011. "Alternating imputation posterior estimation of models with crossed random effects," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 12-25, January.
    9. Mariagiulia Matteucci & Bernard Veldkamp, 2015. "The approach of power priors for ability estimation in IRT models," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 917-926, May.
    10. Hanneke Geerlings & Cees Glas & Wim Linden, 2011. "Modeling Rule-Based Item Generation," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 337-359, April.
    11. 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.
    12. 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.
    13. Sophia Rabe-Hesketh & Anders Skrondal, 2007. "Multilevel and Latent Variable Modeling with Composite Links and Exploded Likelihoods," Psychometrika, Springer;The Psychometric Society, vol. 72(2), pages 123-140, June.
    14. Li Cai, 2010. "High-dimensional Exploratory Item Factor Analysis by A Metropolis–Hastings Robbins–Monro Algorithm," Psychometrika, Springer;The Psychometric Society, vol. 75(1), pages 33-57, March.
    15. Bengt Muthén & Tihomir Asparouhov, 2018. "Recent Methods for the Study of Measurement Invariance With Many Groups," Sociological Methods & Research, , vol. 47(4), pages 637-664, November.
    16. Quinn N. Lathrop & Ying Cheng, 2017. "Item Cloning Variation and the Impact on the Parameters of Response Models," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 245-263, March.
    17. Ryan Mullins & Raj Agnihotri, 2022. "Digital selling: organizational and managerial influences for frontline readiness and effectiveness," Journal of the Academy of Marketing Science, Springer, vol. 50(4), pages 800-821, July.
    18. Yao, Weixin & Wei, Yan & Yu, Chun, 2014. "Robust mixture regression using the t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 116-127.
    19. Jeong Eun Lee & Christian Robert, 2013. "Imortance Sampling Schemes for Evidence Approximation in Mixture Models," Working Papers 2013-42, Center for Research in Economics and Statistics.
    20. Aßmann, Christian & Boysen-Hogrefe, Jens & Pape, Markus, 2012. "The directional identification problem in Bayesian factor analysis: An ex-post approach," Kiel Working Papers 1799, Kiel Institute for the World Economy (IfW Kiel).

    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:35:y:2010:i:3:p:336-370. 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.