Digital Module 38: Differential Item Functioning by Multiple Variables Using Moderated Nonlinear Factor Analysis

Module Abstract When investigating potential bias in educational test items via differential item functioning (DIF) analysis, researchers have historically been limited to comparing two groups of students at a time. The recent introduction of Moderated Nonlinear Factor Analysis (MNLFA) generalizes Item Response Theory models to extend the assessment of DIF to an arbitrary number of background variables. This facilitates more complex analyses such as DIF across more than two groups (e.g. low/middle/high socioeconomic status), across more than one background variable (e.g. DIF by race/ethnicity and gender), across non‐categorical background variables (e.g. DIF by parental income), and more. Framing MNLFA as a generalization of the two‐parameter logistic IRT model, we introduce the model with an emphasis on the parameters representing DIF versus impact; describe the current state of the art for estimating MNLFA models; and illustrate the application of MNLFA in a scenario where one wants to test for DIF across two background variables at once.