Simultaneous multifactor DIF analysis and detection in Item Response Theory

In this paper, two integrated Bayesian models for differential item functioning (DIF) analysis in item response theory (IRT) models are proposed and compared. The model is integrated in the sense of modelling the responses along with the DIF determination, thus allowing DIF detection and DIF explanation in a simultaneous setup. DIF occurs because item characteristics may change according to grouping factors and its explanation is provided in the form of mixed models. Practical situations may lead to the simultaneous consideration of a number of factors. This gives rise to an extended class of models also introduced in this paper. The hypothesis of multifactorial DIF with possibly different explanations for each factor or combination of factors is also introduced. Important practical issues concerning identifiability of the models and the convergence of MCMC algorithms are discussed and illustrated in simulated examples. A real data set analysis of a Mathematics exam applied nationally to Brazilian elementary school students is performed considering two DIF factors: geographical region and type of school. The results highlight the relevance of the proposed methodology and of each of its model components to address important issues in educational studies and testing.