Modeling the influence of interactions among subgroups on differential item functioning detection using the likelihood ratio test and the item response theory approach

Differential item functioning (DIF) analysis is usually conducted with an interested variable one by one. It means that a common procedure only concerns a main effect of a demographic variable on items and ignores complex interactions among them. The study examined the impact of ignoring an interaction among group memberships using a simple scenario: Two 2-level demographic variables (e.g., gender and country) forming four subgroups were involved in DIF detection. Different patterns of DIF among subgroups were simulated and examined by three DIF detection methods, including analyzing either one variable only, both variables at the same time, and an interaction. Factors such as IRT model, test length, sample size, and DIF size were manipulated. Simulations were carried out by using WinBUGS. Findings suggested that the DIF item can be precisely detected if the critical variable(s) or interaction was considered. In addition, disregarding the interaction resulted in a lower true positive rate, but did not increase the false positive rate.