Bayesian Covariance Modeling of Differential Item Functioning

In a Bayesian modeling approach for differential item functioning (DIF), the dependence structure of (non-)uniform DIF is represented by a structured covariance matrix. Item-group interactions (uniform DIF) but also item-specific person-group interactions (non-uniform DIF) are represented by additional correlations in (latent) item responses. DIF in discriminations and difficulties is modeled simultaneously across items and multiple groups in the covariance matrix, making it possible to examine (non-)uniform DIF without needing anchor item(s) or multiple-step procedures. The modeling framework is very efficient, avoids the computation of any interaction parameter, and requires only a single covariance parameter for the DIF assessment of an item parameter for any number of groups. This supports a simultaneous non-uniform DIF analysis of all items, even for small sample sizes. The proposed DIF procedure is applied to PISA data, where the advantages of the method are illustrated and compared to a multiple-group IRT analysis.