Main Article Content
Mixture distribution, Multilevel mixture item response theory, Latent class, Differential item functioning, Bias
In this study, performance of differential item functioning (DIF) methods was compared under 36 different conditions based on latent classes and manifest groups. In the study, simulation conditions such as DIFcontaining item rate, reference-focal group rate, DIF effect size and overlap ratio of manifest groups and latent classes were taken into consideration. To examine DIF, the Mantel–Haenszel (MH) method, which is a method related to the manifest group variable, was used within the framework of classical test theory and Lord’s x2 method and item response theory. Latent classes were determined using the model of multilevel mixture item response theory (MMIRT). Results show that data fit the MMIRT model with larger effect size and with a higher number of items containing DIF. When DIF effect size was 1.0, the power of MMIRT was found to be higher and the type I error rate was found to be lower in all overlap and DIF-containing item rates and reference-focal group conditions. While the rate of overlap was 90%, the power of MH and Lord’s x2 methods and type I errors were at acceptable levels under all conditions. It was observed that the power of MH and Lord’s x2 methods decreased as a result of a decrease in the overlap ratio for manifest groups and latent classes.