Testing Differential Item Functioning Without Predefined Anchor Items Using Robust Regression

Abstract

Differential item functioning (DIF) occurs when the probability of endorsing an item differs across groups for individuals with the same latent trait level. The presence of DIF items may jeopardize the validity of an instrument; therefore, it is crucial to identify DIF items in routine operations of educational assessment. While DIF detection procedures based on item response theory (IRT) have been widely used, a majority of IRT-based DIF tests assume predefined anchor (i.e., DIF-free) items. Not only is this assumption strong, but violations to it may also lead to erroneous inferences, for example, an inflated Type I error rate. We propose a general framework to define the effect sizes of DIF without a priori knowledge of anchor items. In particular, we quantify DIF by item-specific residuals from a regression model fitted to the true item parameters in respective groups. Moreover, the null distribution of the proposed test statistic using robust estimator can be derived analytically or approximated numerically even when there is a mix of DIF and non-DIF items, which yields asymptotically justified statistical inference. The Type I error rate and the power performance of the proposed procedure are evaluated and compared with the conventional likelihood-ratio DIF tests in a Monte Carlo experiment. Our simulation study has shown promising results in controlling Type I error rate and power of detecting DIF items. Even when there is a mix of DIF and non-DIF items, the true and false alarm rate can be well controlled when a robust regression estimator is used.