Differential item functioning detection across multiple groups

Differential item functioning (DIF) can be investigated by estimating item response theory (IRT) parameters separately for different respondent groups, thus allowing for the detection of discrepancies in parameter estimates across groups. However, before comparing the estimates, it is necessary to convert them to a common metric due to the constraints required to identify the model. These processes influence each other, as the presence of DIF items affects the estimation of scale conversion. This paper proposes a novel method that simultaneously performs scale conversion and DIF detection. By doing so, the estimated scale conversion automatically takes into account the presence of DIF. The differences of the item parameter estimates across groups can be explained through variables at the within-group item level or by the group itself. Penalized likelihood estimation is used to perform an automatic selection of the item parameters that differ in some groups. Real-data applications and simulation studies show the good performance of the proposal.