Item Group Covariates

We propose and study an extension of moderated nonlinear factor analysis that models covariate effects—that is, differential item functioning (DIF)—at the level of item groups rather than, or in addition to, individual items. This allows for a more theory-driven approach to DIF and measurement invariance testing in which researchers can form and test hypotheses about why items differ in how they function across an arbitrary number of categorical or continuous covariates. As a motivating example, we demonstrate gender effects on a developmental measure where scores that assume invariance overstate boys’ cognitive development and understate their fine and gross motor development, with opposite implications for girls. Simulation demonstrates the empirical identifiability and predictable statistical performance of the proposed model, and additional empirical examples demonstrate the approach’s substantial flexibility.

Materials:

• Preprint: Making Room for Theory in DIF and Measurement Invariance Analysis with Covariate Effects on Groups of Items