A Bayesian Moderated Nonlinear Factor Analysis Approach for DIF Detection under Violation of the Equal Variance Assumption

Research has shown that multiple-indicator multiple-cause (MIMIC) models can result in inflated Type I error rates in detecting differential item functioning (DIF) when the assumption of equal latent variance is violated. This study explains how the violation of the equal variance assumption adversely impacts the detection of nonuniform DIF and how it can be addressed through moderated nonlinear factor analysis (MNLFA) model via Bayesian estimation approach to overcome limitations from the restrictive assumption. The Bayesian MNLFA approach suggested in this study better control Type I errors by freely estimating latent factor variances across different groups. Our experimentation with simulated data demonstrates that the BMNFA models outperform the existing MIMIC models, in terms of Type I error control as well as parameter recovery. The results suggest that the MNLFA models have the potential to be a superior choice to the existing MIMIC models, especially in situations where the assumption of equal latent variance assumption is not likely to hold.