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As a class of discrete latent variable models, cognitive diagnostic models have been widely researched in education, psychology, and many other disciplines. Detecting and eliminating differential item functioning (DIF) items from cognitive diagnostic tests is of great importance for test fairness and validity. A Monte Carlo study with varying manipulated factors was carried out to investigate the performance of the Mantel-Haenszel (MH), logistic regression (LR), and Wald tests based on item-wise information, cross-product information, observed information, and sandwich-type covariance matrices (denoted by  W  d ,  W  XPD ,  W  Obs , and  W  Sw , respectively) for DIF detection. The results showed that (1) the  W  XPD  and LR methods had the best performance in controlling Type I error rates among the six methods investigated in this study and (2) under the uniform DIF condition, when the item quality was high or medium, the power of  W  XPD ,  W  Obs , and  W  Sw  was comparable with or superior to that of MH and LR, but when the item quality was low,  W  XPD ,  W  Obs , and  W  Sw  were less powerful than MH and LR. Under the non-uniform DIF condition, the power of  W  XPD ,  W  Obs , and  W  Sw  was comparable with or higher than that of LR.

A Comparison of Differential Item Functioning Detection Methods in Cognitive Diagnostic Models