IDEAS home Printed from https://ideas.repec.org/a/sae/somere/v47y2018i4p637-664.html
   My bibliography  Save this article

Recent Methods for the Study of Measurement Invariance With Many Groups

Author

Listed:
  • Bengt Muthén
  • Tihomir Asparouhov

Abstract

This article reviews and compares recently proposed factor analytic and item response theory approaches to the study of invariance across groups. Two methods are described and contrasted. The alignment method considers the groups as a fixed mode of variation, while the random-intercept, random-loading two-level method considers the groups as a random mode of variation. Both maximum likelihood and Bayesian analyses are applied. A survey of close to 50,000 subjects in 26 countries is used as an illustration. In addition, the two methods are studied by Monte Carlo simulations. A list of considerations for choosing between the two methods is presented.

Suggested Citation

  • 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.
    • Handle: RePEc:sae:somere:v:47:y:2018:i:4:p:637-664
    DOI: 10.1177/0049124117701488
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/0049124117701488
    Download Restriction: no
    File URL: https://libkey.io/10.1177/0049124117701488?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. N. Longford & B. Muthén, 1992. "Factor analysis for clustered observations," Psychometrika, Springer;The Psychometric Society, vol. 57(4), pages 581-597, December.
    2. Harvey Goldstein & Roderick McDonald, 1988. "A general model for the analysis of multilevel data," Psychometrika, Springer;The Psychometric Society, vol. 53(4), pages 455-467, December.
    3. 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.
    4. Martijn G. De Jong & Jan-Benedict E. M. Steenkamp & Jean-Paul Fox, 2007. "Relaxing Measurement Invariance in Cross-National Consumer Research Using a Hierarchical IRT Model," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 34(2), pages 260-278, June.
    5. Robert Jennrich, 2006. "Rotation to Simple Loadings Using Component Loss Functions: The Oblique Case," Psychometrika, Springer;The Psychometric Society, vol. 71(1), pages 173-191, March.
    6. Paul Boeck, 2008. "Random Item IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 533-559, December.
    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. 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.
    2. 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.
    3. Jean-Paul Fox & Joris Mulder & Sandip Sinharay, 2017. "Bayes Factor Covariance Testing in Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 979-1006, December.
    4. Asim Ansari & Kamel Jedidi & Sharan Jagpal, 2000. "A Hierarchical Bayesian Methodology for Treating Heterogeneity in Structural Equation Models," Marketing Science, INFORMS, vol. 19(4), pages 328-347, August.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Hanneke Geerlings & Cees Glas & Wim Linden, 2011. "Modeling Rule-Based Item Generation," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 337-359, April.
    10. 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.
    11. de Jong, M.G., 2006. "Response bias in international marketing research," Other publications TiSEM 5d4031be-97b5-4db3-962b-2, Tilburg University, School of Economics and Management.
    12. Ling Peng & Geng Cui & Yuho Chung & Chunyu Li, 2019. "A multi-facet item response theory approach to improve customer satisfaction using online product ratings," Journal of the Academy of Marketing Science, Springer, vol. 47(5), pages 960-976, September.
    13. Ke-Hai Yuan & Peter Bentler, 2004. "On the asymptotic distributions of two statistics for two-level covariance structure models within the class of elliptical distributions," Psychometrika, Springer;The Psychometric Society, vol. 69(3), pages 437-457, September.
    14. 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.
    15. Ke-Hai Yuan & Peter Bentler, 2002. "On normal theory based inference for multilevel models with distributional violations," Psychometrika, Springer;The Psychometric Society, vol. 67(4), pages 539-561, December.
    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. Conti, Gabriella & Frühwirth-Schnatter, Sylvia & Heckman, James J. & Piatek, Rémi, 2014. "Bayesian exploratory factor analysis," Journal of Econometrics, Elsevier, vol. 183(1), pages 31-57.
    18. Wang, Luming & Finn, Adam, 2014. "A psychometric theory that measures up to marketing reality: An adapted Many Faceted IRT model," Australasian marketing journal, Elsevier, vol. 22(2), pages 93-102.
    19. Martijn G. de Jong & Jan-Benedict E. M. Steenkamp & Bernard P. Veldkamp, 2009. "A Model for the Construction of Country-Specific Yet Internationally Comparable Short-Form Marketing Scales," Marketing Science, INFORMS, vol. 28(4), pages 674-689, 07-08.
    20. 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.

    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:somere:v:47:y:2018:i:4:p:637-664. 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.