Based on concerns about the item response theory (IRT) linking approach used in the Programme for International Student Assessment (PISA) until 2012 as well as the desire to include new, more complex, interactive items with the introduction of computer-based assessments, alternative IRT linking methods were implemented in the 2015 PISA round. The new linking method represents a concurrent calibration using all available data, enabling us to find item parameters that maximize fit across all groups and allowing us to investigate measurement invariance across groups. Apart from the Rasch model that historically has been used in PISA operational analyses, we compared our method against more general IRT models that can incorporate item-by-country interactions. The results suggest that our proposed method holds promise not only to provide a strong linkage across countries and cycles but also to serve as a tool for investigating measurement invariance.