A comparative study on differential item functioning detection of three approaches to measurement equivalence
Jungkyu Park, Sunho Jung · Journal of the Korean Data and Information Science Society · 2021
This article compares three approaches for testing measurement equivalence in terms of detecting differential item functioning. These approaches include mean and covariance structure (MACS), confirmatory 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 approach. 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 another alternative approach to measurement invariance in the present study. The results of the simulation study validate that the ordinal CFA approach presented inflated 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.