Assessing and explaining differential item functioning using logistic mixed models

Although differential item functioning (DIF) theory traditionally focuses on the behavior of individual items in two (or a few) specific groups, in educational measurement contexts, it is often plausible to regard the set of items as a random sample from a broader category. This article presents logistic mixed models that can be used to model uniform DIF, treating the item effects and their interaction with groups (DIF) as random. In a similar way, the group effects can be modeled as random instead of fixed, if the groups can be considered a random sample from a population of groups. The models can, furthermore, be adapted easily for modeling DIF over individual persons rather than over groups, or for modeling the differential functioning of groups of items instead of individual items. It is shown that the logistic mixed model approach is not only a comprehensive and economical way to detect these different kinds of DIF, it also encourages us to explore possible explanations of DIF by including group or item covariates in the model.