In empirical modeling, an important desiderata for deeming theoretical entities and processes as real is that they can be reproducible in a statistical sense. Current day crises regarding replicability in science intertwines with the question of how statistical methods link data to statistical and substantive theories and models. Different answers to this question have important methodological consequences for inference, which are intertwined with a contrast between the ontological commitments of the two types of models. The key to untangling them is (...) the realization that behind every substantive model there is a statistical model that pertains exclusively to the probabilistic assumptions imposed on the data. It is not that the methodology determines whether to be a realist about entities and processes in a substantive field. It is rather that the substantive and statistical models refer to different entities and processes, and therefore call for different criteria of adequacy. (shrink)