Item Response Theory

9Differential Item Functioning

An approximate answer to the right problem is worth a good deal more than an exact answer to an approximate problem.

(Source: John Tukey)

9.1 Introduction

Differential item functioning (DIF) occurs when individuals who are at the same level on the construct(s) being assessed, but are from different subpopulations, have unequal probabilities of attaining a given score on a given item. Methods for investigating DIF have been developed for both dichotomously and polytomously scored items. These methods may be classified by whether they condition on an unobserved or observed variable. Item response theory (IRT), logistic regression, and Mantel–Haenszel procedures for dichotomously scored responses and their extensions to polytomous responses are currently the most widely used methods for detecting DIF. Thissen et al. (1993) introduced the IRT approach to DIF detection. The IRT approach usually involves the comparison of two models, a compact model (with common parameters between the different subpopulations) and an augmented model where a subset of the parameters are allowed to vary across the subgroups. Most procedures involve fitting the model twice per hypothesis, once for the compact model and once for the augmented model, resulting in considerable computational complexity. Woods et al. (2013) have described an approach suitable for assessing DIF for multidimensional IRT models that can be adapted to the bifactor model. We generally refer ...