This paper studies the forms of model misspecification that are likely to persist when compared with competing models. I consider an agent using a subjective model to learn about an action-dependent outcome distribution. Aware of potential model misspecification, she uses a threshold rule to switch between models according to how well they fit the data. A model is globally robust if it can persist against every finite set of competing models and is locally robust if it can persist against every finite set of nearby competing models. The main result provides simple characterizations of globally robust and locally robust models based on the set of Berk-Nash equilibria they induce. I then apply the results to examples including risk underestimation, overconfidence, and incorrect beliefs about market demand.