How Are the Form and Magnitude of DIF Effects in Multiple-Choice Items Determined by Distractor-Level Invariance Effects?

Abstract

This article explores how the magnitude and form of differential item functioning (DIF) effects in multiple-choice items are determined by the underlying differential distractor functioning (DDF) effects, as modeled under the nominal response model. The results of a numerical investigation indicated that (a) the presence of one or more nonzero DDF effects implies a nonzero DIF effect; (b) the magnitude of the DDF effects creates an upper bound to the magnitude of the resulting DIF effect; (c) the presence of a large DDF effect does not necessarily imply a large DIF effect; (d) under the condition of constant DDF effects the resulting DIF effect is independent of other item properties (i.e., location and discrimination parameters), but under the condition of varying DDF effects the resulting DIF effect magnitude is dependent on other item properties; and (e) although crossing DIF can only exist with divergent (varying in sign) DDF effects, divergent DDF effects do not always yield crossing DIF. Implications of these findings for evaluating DIF effects and interpreting the causes of DIF effects are discussed.