Differential item and test functioning

This chapter focuses on differential item functioning (DIF) and differential test functioning (DTF) methods for dominance models, extending these approaches to ideal point models is an important area for future research. It describes effect size indices for DIF and DTF. In principle, the item response theory (IRT) approach to DIF and DTF should be preferred for discrete item responses, whether dichotomously scored or polytomously scored. The chapter also describes Thissen, Steinberg, and Wainer's likelihood ratio (LR) approach to the IRT study of DIF. Similar to the IRT methods for identifying DIF, the confirmatory factor analysis (CFA) approach relies on chi-square tests and empirically derived rules of thumb for identifying nonequivalence. The chapter presents an example of the study of DIF with IRT and CFA. An important consideration is that CFA is a dominance model: CFA assumes a linear relation between the latent trait and response variables.