Testing for Nonuniform Differential Item Functioning With Multiple Indicator Multiple Cause Models

In extant literature, multiple indicator multiple cause (MIMIC) models have been presented for identifying items that display uniform differential item functioning (DIF) only, not nonuniform DIF. This article addresses, for apparently the first time, the use of MIMIC models for testing both uniform and nonuniform DIF with categorical indicators. A latent variable interaction is added to the MIMIC model to test for nonuniform DIF. The approach is tested in simulations with small focal-group N and illustrated with an empirical example using a scale about agoraphobic cognitions. MIMIC-interaction models are compared with MIMIC models without the interaction as well as likelihood ratio DIF testing using item response theory (IRT-LR-DIF). The most important finding is that when the latent moderated structural equations approach is used to estimate the interaction, the Type I error in MIMIC-interaction DIF models is severely inflated.