Type I error and power of the mean and covariance structure confirmatory factor analysis for differential item functioning detection: Methodological issues and resolutions

Abstract

Recently, mean and covariance structure (MACS) confirmatory factor analysis (CFA) has been widely used to detect items with differential item functioning (DIF). Although how we define the scale does not impact overall model fit or tests for whether or not a given level of measurement equivalence holds, different scaling methods can lead to different conclusions when a researcher locates DIF in a scale. This dissertation evaluates the MACS analysis for DIF detection by means of a Monte Carlo simulation. The simulation results indicate that three statistically equivalent scaling methods provide different outcomes of DIF analysis. In addition, Bonferroni-correction improves the accuracy of the analysis, notably when a scale (or an anchor) is contaminated by DIF. Based on the previous and current simulation studies, this dissertation offers practical guidance for researchers who attempt to evaluate measurement equivalence using CFA.