Anchor Detection Strategy in Moderated Non-Linear Factor Analysis for Differential Item Functioning (DIF)

Ensuring measurement invariance is crucial for fair psychological and educational assessments, particularly in detecting Differential Item Functioning (DIF). Moderated Non-linear Factor Analysis (MNLFA) provides a flexible framework for detecting DIF by modeling item parameters as functions of observed covariates. However, a significant challenge in MNLFA-based DIF detection is anchor item selection, as improperly chosen anchors can bias results. This study proposes a refined constrained-baseline anchor detection approach utilizing information criteria (IC) for model selection. The proposed three-step procedure sequentially identifies potential DIF items through the Bayesian Information Criterion (BIC) and Weighted Information Criterion (WIC), followed by DIF-free anchor items using the Akaike Information Criterion (AIC). The method's effectiveness in controlling Type I error rates while maintaining statistical power is evaluated through simulation studies and empirical data analysis. Comparisons with regularization approaches demonstrate the proposed method's accuracy and computational efficiency.