Detecting Differential Item Functioning Using Cognitive Diagnosis Models: Applications of the Wald Test and Likelihood Ratio Test in a University Entrance Examination

ABSTRACT The present study aims to examine gender differential item functioning (DIF) in the reading comprehension section of a high stakes test using cognitive diagnosis models. Based on the multiple-group generalized deterministic, noisy “and” gate (MG G-DINA) model, the Wald test and likelihood ratio test are used to detect DIF. The flagged items are further inspected to find the attributes they measure, and the probabilities of correct response are checked across latent profiles to gain insights into the potential reasons for the occurrence of DIF. In addition, attribute and latent class prevalence are examined across males and females. The three items displaying large DIF involve three attributes, namely Vocabulary, Main Idea, and Details. The results indicate that females have lower probabilities of correct response across all latent profiles, and fewer females have mastered all the attributes. Moreover, the findings show that the same attribute mastery profiles are prevalent across genders. Finally, the results of the DIF analysis are used to select models that could replace the complex MG G-DINA without significant loss of information.