Assessing Differential Item Functioning in Multiple Grouping Variables with Factorial Logistic Regression

Differential item functioning (DIF) can occur among multiple grouping variables (e.g., gender and ethnicity). For such cases, one can either examine DIF one grouping variable at a time or combine all the grouping variables into a single grouping variable in a test without a substantial meaning. These two approaches, analogous to one-way analysis of variance (ANOVA), are less efficient than an approach that considers all the grouping variables simultaneously and decomposes the DIF effect into main effects of individual grouping variables and their interactions, which is analogous to factorial ANOVA. In this study, the idea of factorial ANOVA was applied to the logistic regression method for the assessment of uniform and nonuniform DIF, and the performance of this approach was evaluated with simulations. The results indicated that the proposed factorial approach outperformed conventional approaches when there was interaction between grouping variables; the larger the DIF effect size, the higher the power of detection; the more DIF items in the anchored test, the worse the DIF assessment. Given the promising results, the factorial logistic regression method is recommended for the assessment of uniform and nonuniform DIF when there are multiple grouping variables.