Mean-geometric mean (MGM) linking is a widely used method for linking two groups within the two-parameter logistic (2PL) item response model. However, the presence of differential item functioning (DIF) can lead to biased parameter estimates using the traditional MGM method. To address this, alternative linking methods based on robust loss functions have been proposed. In this article, the conventional L2 loss function is compared with the L0.5 and L0 loss functions in MGM linking. Our results suggest that robust loss functions are preferable when dealing with outlying DIF effects, with the L0 function showing particular advantages in tests with larger item sets and sample sizes. Additionally, a simulation study demonstrates that defining MGM linking based on item intercepts rather than item difficulties leads to more accurate linking parameter estimates. Finally, robust Haberman linking slightly outperforms robust MGM linking in two-group comparisons.