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A comparative study on di erential item functioning detection of three approaches to measurement equivalence
Journal of the Korean Data & Information Science Society 2021;32:227-41
Published online January 31, 2021;
© 2021 Korean Data and Information Science Society.

Jungkyu Park1 · Sunho Jung2

1Department of Psychology, Kyungpook National University
2School of Management, Kyung Hee University
Correspondence to: 1Assistant professor, Department of Psychology, Kyungpook National University, Daegu 41566, Korea.
2Corresponding author: Associate professor, School of Management, Kyung Hee University, Seoul 02447, Korea. E-mail:
Received October 27, 2020; Revised December 1, 2020; Accepted December 2, 2020.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
This article compares three approaches for testing measurement equivalence in terms of detecting di erential item functioning. These approaches include mean and covari- ance structure (MACS), con rmatory factor analysis with ordered categorical variables (ordinal CFA), and item response theory (IRT) model. With the growing interest in measurement invariance in latent variable models, several studies have been mainly conducted to compare the factor analytic approach with the item response theory ap- proach. However, these studies have practical limitations due to unrealistic assumptions about observed variables and parameter nonequivalence. For a meaningful comparison between the factor analytic and item response methods, ordinal CFA is considered an- other alternative approach to measurement invariance in the present study. The results of the simulation study validate that the ordinal CFA approach presented in ated Type I error rates compared with the MACS and IRT methods in overall conditions, while the statistical power of ordinal CFA were not higher than those of MACS but much higher than those of the IRT model throughout most conditions.
Keywords : Confirmatory factor analysis, item response theory model, mean and covariance structure, measurement invariance.