A Comparison of Uniform DIF Effect Size Estimators Under the MIMIC and Rasch Models

Abstract

The Rasch model, a member of a larger group of models within item response theory, is widely used in empirical studies. Detection of uniform differential item functioning (DIF) within the Rasch model typically employs null hypothesis testing with a concomitant consideration of effect size (e.g., signed area [SA]). Parametric equivalence between confirmatory factor analysis under the multiple indicators, multiple causes (MIMIC) model and the Rasch model has been established. Unlike the Rasch approach to DIF, however, the parallel MIMIC approach to DIF detection has relied exclusively on null hypothesis testing. This study derived an effect size estimator for DIF under the MIMIC model (MIMIC-ES) and then investigated the ability of MIMIC-ES to correctly estimate the magnitude of DIF as compared to the SA approach under the Rasch model (Rasch-ES) in a Monte Carlo study. Variables manipulated were sample size, mean ability difference, DIF size, number of DIF items, and item difficulty levels. Results indicated that MIMIC-ES performed well when there was no mean ability difference. When mean ability difference was present, MIMIC-ES became increasingly imprecise and unstable when the sample size was small for all DIF sizes and number of DIF items. MIMIC-ES outperformed Rasch-ES when the number of DIF items reached 30%.