The Simultaneous Factorial Analysis of Differential Item Functioning

Conventional one-factor differential item functioning (DIF) analysis is extended to factorial DIF analysis where multiple factors (e.g., ethnicity and gender) with multiple groups in each are compared simultaneously. By adopting the formulation of factorial analysis of variance, DIF is parameterized and partitioned into main effects and interaction effects. DIF parameters and the item difficulties for all items are simultaneously estimated. This simultaneous estimation procedure was compared with the consecutive estimation procedure where DIF is detected one item at a time in terms of parameter recovery and power of DIF detection through a simulation study. The results show that only the simultaneous factorial estimation procedure yields unbiased estimates and reasonable power of DIF detection. A real data set of ten dichotomous items and 1055 subjects was analyzed to illustrate implications and applications of the proposed modeling.