Social network data collected from digital sources is increasingly being used to gain insights into human behavior. However, while these observable networks constitute an empirical ground truth, the individuals within the network can perceive the network’s structure differently—and they often act on these perceptions. As such, we argue that there is a distinct gap between the data used to model behaviors in a network, and the data internalized by people when they actually engage in behaviors. We find that statistical analyses of observable network structure do not consistently take these discrepancies into account, and this omission may lead to inaccurate inferences about hypothesized network mechanisms. To remedy this issue, we apply techniques of robust optimization to statistical models for social network analysis. Using robust maximum likelihood, we derive an estimation technique that immunizes inference to errors such as false positives and false negatives, without knowing a priori the source or realized magnitude of the error. We demonstrate the efficacy of our methodology on real social network datasets and simulated data. Our contributions extend beyond the social network context, as perception gaps may exist in many other economic contexts.