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Goodness of fit for item response theory (IRT) models in a frequentist and Bayesian framework are evaluated. The assumptions that are targeted are differential item functioning (DIF), local independence (LI), and the form of the item characteristics curve (ICC) in the one-, two-, and three parameter logistic models. It is shown that a Lagrange multiplier (LM) test, which is a frequentist based approach,...
Item bias or differential item functioning (DIF) has an important impact on the fairness of psychological and educational testing. In this paper, DIF is seen as a lack of fit to an item response (IRT) model. Inferences about the presence and importance of DIF require a process of so-called test purification where items with DIF are identified using statistical tests and DIF is modeled using group-specific...
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