Detecting Multidimensional Differential Item Functioning with the Multiple Indicators Multiple Causes Model, the Item Response Theory Likelihood Ratio Test, and Logistic Regression

Differential item functioning (DIF) is typically evaluated in educational assessments with a simple structure in which items are associated with a single latent trait. This study aims to extend the investigation of DIF for multidimensional assessments with a nonsimple structure in which items can be associated with two or more latent traits. A simulation study was conducted with the multidimensional extensions of the item response theory likelihood ratio (IRT-LR) test, the multiple indicators multiple causes (MIMIC) model, and logistic regression for detecting uniform and nonuniform DIF in multidimensional assessments. The results indicated that the IRT-LR test outperformed the MIMIC and logistic regression approaches in detecting nonuniform DIF. When detecting uniform DIF, the MIMIC and logistic regression approaches appeared to perform better than the IRT-LR test in short tests, while the performances of all three approaches were very similar in longer tests. Type I error rates for logistic regression were severely inflated compared to the other two approaches. The IRT-LR test appears to be a more balanced and powerful method than the MIMIC and logistic regression approaches in detecting DIF in multidimensional assessments with a nonsimple structure.