In the social sciences, the performance of two groups is frequently compared based on a cognitive test involving binary items. Item response models are often utilized for comparing the two groups. However, the presence of differential item functioning (DIF) can impact group comparisons. In order to avoid the biased estimation of groups, appropriate statistical methods for handling differential item functioning are required. This article compares the performance-regularized estimation and several robust linking approaches in three simulation studies that address the one-parameter logistic (1PL) and two-parameter logistic (2PL) models, respectively. It turned out that robust linking approaches are at least as effective as the regularized estimation approach in most of the conditions in the simulation studies.