Modeling DIF for Simulations: Continuous or Categorical Secondary Trait?

Abstract

For DIF studies, item responses are often simulated using a unidimensional item response theory (IRT) model, with the item difficulty varying by group for the DIF item(s). This implies that the item is easier for all members of one group. However, many researchers may want to conceptualize DIF as a continuous factor; in this conceptualization, one group finds the DIF item easier on average, but this is not true for all group members. Multidimensional IRT models allow item responses to be generated to correspond to this perspective. Data were simulated under both unidimensional and multidimensional models and effect sizes were estimated from the resulting item responses using the Mantel-Haenszel DIF procedure. The bias and empirical standard errors of the effect sizes were virtually identical. Thus, practitioners using observed-score methods of DIF detection can trust results from DIF simulation studies regardless of the underlying model used to create the data.