Multidimensional Polytomous DIF Detection Methods – A Monte Carlo Simulation Study

Abstract

The study compared the effectiveness of four methods for detecting differential item functioning (DIF) in polytomous multidimensional data with a simple structure: the item response theory likelihood ratio test (IRT-LR), two ordinal logistic regression approaches (using raw scores vs. latent trait estimates as the matching variable), and the multidimensional MIMIC-interaction method. Data were generated under a two-dimensional graded response model with 28 five-category items. Simulation conditions manipulated DIF type (uniform, nonuniform), DIF magnitude (0, 0.3, 0.6), group size ratio (1:1, 3:1), latent trait correlation (ρ = 0, 0.5), and the presence of group impact, yielding 40 conditions with 100 replications each. Across conditions, IRT-LR and both logistic regression approaches generally maintained Type I error within acceptable limits, whereas the MIMIC-interaction model showed inflated Type I error in the presence of impact. All methods demonstrated high power for moderate uniform DIF, but detection rates declined substantially for low DIF and for nonuniform DIF. Logistic regression with latent trait estimates showed the most stable overall performance, combining adequate Type I error control with comparatively high power across conditions. Logistic regression with raw scores demonstrated relatively stronger performance for moderate nonuniform DIF. In contrast, IRT-LR exhibited lower power despite conservative Type I error control. Results suggest that regression-based approaches, particularly logistic regression using latent trait estimates, provide robust performance for DIF detection in multidimensional polytomous assessments under simple structure.