Residual‐Based DIF Detection as a Model‐Agnostic Framework: A Comparison of Parametric, Semi‐Parametric, and Nonparametric Methods

Residual‐based methods provide a computationally efficient way to screen items for differential item functioning (DIF) using residuals from a fitted measurement model. Within this broader family, the residual‐based differential item functioning (RDIF) statistics represent an established approach that summarizes DIF evidence through group comparisons of raw residuals, squared residuals, and their joint combination. However, the relative behavior of RDIF compared with more flexible residual‐based procedures remains unclear, especially under less ideal conditions such as shorter tests, skewed ability distributions, sample imbalance, difficult item profiles, and nonlinear DIF. The present study compares three complementary procedures within a unified residual‐based framework: RDIF as a parametric method, spline likelihood‐ratio (Spline‐LR) as a semi‐parametric method, and mutual information (MI) as a nonparametric method. Two simulation studies were conducted in a two‐group DIF setting. The first adapted standard RDIF benchmark conditions, whereas the second served as a targeted stress test. Across the simulations, RDIF provided a strong and robust benchmark, showing stable error‐control behavior under both conventional and less ideal conditions. Spline‐LR and MI showed higher sensitivity under some complex DIF conditions, but these gains were accompanied by substantial losses in specificity and precision. Overall, the findings indicate that greater flexibility in modeling residual dependence does not necessarily improve item‐level DIF decisions and that RDIF provides the more reliable basis for routine screening under the conditions examined.