Assessment of differential item functioning and differential attribute functioning under cognitive diagnosis models

Cognitive diagnosis models (CDMs) are developed to assess respondents’ binary status (mastery or non-mastery) on a set of fine-grained attributes. As CDMs get popular, issues on differential item functioning (DIF) and differential attribute functioning (DAF) have attracted more and more research attention. DIF and DAF occur when people with the same latent trait level but from different groups have different response probabilities to an item. This study proposes two methods to detect DIF and DAF for CDMs. These methods are applied to the deterministic inputs, noisy “and” gate (DINA) model, and simulation studies demonstrate performance and usefulness of the new methods for DIF and DAF assessment.