Computational aspects of L0 linking in the Rasch model

The 𝐿0 linking approach replaces the 𝐿2 loss function in mean–mean linking under the Rasch model with the 𝐿0 loss function. Using the 𝐿0 loss function offers the advantage of potential robustness against fixed differential item functioning effects. However, its nondifferentiability necessitates differentiable approximations to ensure feasible and computationally stable estimation. This article examines alternative specifications of two approximations, each controlled by a tuning parameter 𝜀 that determines the approximation error. Results demonstrate that the optimal 𝜀 value minimizing the RMSE of the linking parameter estimate depends on the magnitude of DIF effects, the number of items, and the sample size. A data-driven selection of 𝜀 outperformed a fixed 𝜀 across all conditions in both a numerical illustration and a simulation study.