Abstract

This study investigated the impact of misspecifying the source of differential item functioning on detection accuracy using a factor mixture model that incorporates covariates, when both observed DIF (ODIF), caused by known group membership, and latent DIF (LDIF), caused by latent class membership, coexist within a single test. DIF type, magnitude, and sample size were systematically varied to evaluate model performance in terms of class enumeration accuracy, detection power, Type I error rate, and parameter bias. The results showed that the model including both LDIF and ODIF (L&ODIF model) yielded the highest accuracy in estimating the number of latent classes, while the ODIF-only model showed very low estimation accuracy. The detection power for LDIF was highest in the L&ODIF model, whereas ODIF detection was most accurate in the ODIF-only model. The L&ODIF model demonstrated lower Type I error rates in most conditions, and parameter bias remained within or slightly above acceptable levels. These findings suggest that when both types of DIF are present, applying a factor mixture model capable of detecting LDIF and ODIF simultaneously can improve detection accuracy.