Halpin's differential test functioning via robust linking: A comparison of bisquare and L0 loss functions

Differential test functioning (DTF) assesses, within an item response model, whether differential item functioning (DIF) affects the test as a whole. A recent contribution by Halpin (2025, arXiv) introduced a DTF statistic defined as the difference between a robust linking method based on the bisquare loss function and a nonrobust linking method such as mean–mean linking. The present article applies this statistic in the context of robust mean–geometric mean linking using the 𝐿0 loss function and compares it with Halpin’s original bisquare-loss approach. Alternative confidence interval estimation methods are evaluated for statistical inference for the DTF statistic. The findings indicate that the 𝐿0 loss function yields a smaller bias in the group mean estimate under several conditions than the bisquare loss function. However, the DTF statistic is estimated more precisely with the bisquare than with the 𝐿0 loss function. Moreover, the most satisfactory statistical inference is obtained from bias-corrected bootstrap and basic bootstrap confidence intervals based on a parametric rather than nonparametric bootstrap.