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Alternatives to Weighted Item Fit Statistics for Establishing Measurement Invariance in Many Groups

Author

Listed:
  • Sean Joo

    (University of Kansas)

  • Montserrat Valdivia
  • Dubravka Svetina Valdivia
  • Leslie Rutkowski

    (Indiana University Bloomington)

Abstract

Evaluating scale comparability in international large-scale assessments depends on measurement invariance (MI). The root mean square deviation (RMSD) is a standard method for establishing MI in several programs, such as the Programme for International Student Assessment and the Programme for the International Assessment of Adult Competencies. Previous research showed that the RMSD was unable to detect departures from MI when the latent trait distribution was far from item difficulty. In this study, we developed three alternative approaches to the original RMSD: equal, item information, and b -norm weighted RMSDs. Specifically, we considered the item-centered normalized weight distributions to compute the item characteristic curve difference in the RMSD procedure more efficiently. We further compared all methods’ performance via a simulation study and the item information and b -norm weighted RMSDs showed the most promising results. An empirical example is demonstrated, and implications for researchers are discussed.

Suggested Citation

  • Sean Joo & Montserrat Valdivia & Dubravka Svetina Valdivia & Leslie Rutkowski, 2024. "Alternatives to Weighted Item Fit Statistics for Establishing Measurement Invariance in Many Groups," Journal of Educational and Behavioral Statistics, , vol. 49(3), pages 465-493, June.
    • Handle: RePEc:sae:jedbes:v:49:y:2024:i:3:p:465-493
    DOI: 10.3102/10769986231183326
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    References listed on IDEAS

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    1. Carmen Köhler & Alexander Robitzsch & Johannes Hartig, 2020. "A Bias-Corrected RMSD Item Fit Statistic: An Evaluation and Comparison to Alternatives," Journal of Educational and Behavioral Statistics, , vol. 45(3), pages 251-273, June.
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