Explaining Crossing DIF in Polytomous Items Using Differential Step Functioning Effects

Abstract

Crossing, or intersecting, differential item functioning (DIF) is a form of nonuniform DIF that exists when the sign of the between-group difference in expected item performance changes across the latent trait continuum. The presence of crossing DIF presents a problem for many statistics developed for evaluating DIF because positive and negative conditional between-group differences in expected item score can cancel to yield a negligible between-group difference when aggregated across the latent trait continuum. As a result, many DIF detection statistics are insensitive to DIF that is crossing in nature. Currently, little is known about why crossing DIF occurs in polytomous items. This study demonstrates that crossing DIF in polytomous items can be explained by the presence of differential step functioning (DSF) effects that vary in sign across the steps of the polytomous item, suggesting that crossing DIF is caused by the presence of one or more secondary factors that yield a relative advantage for different groups at different steps of the polytomous item. Using this result, this study describes how to use the pattern of the DSF effects to (a) target the search for secondary traits responsible for a crossing DIF effect, (b) identify situations where certain DIF statistics will lead to the conclusion of no DIF despite a substantial crossing DIF effect, and (c) generate realistic crossing DIF effects in simulation research.