Previous research on hit-and-run crashes employed regression methods or machine learning techniques. However, regression methods necessitate preestablished model formulations, making it challenging to accommodate intricate nonlinear effects. In contrast, machine learning methods are characterized as black box systems, lacking interpretability. Thus, we propose an innovative analytical framework that combines data-driven machine learning algorithms with emerging interpretation techniques. The complex nonlinear effects of various factors on hit-and-run crashes are investigated by employing post hoc interpretation techniques, specifically, Shapley Additive exPlanations and accumulated local effect. The results demonstrate that machine learning algorithms are superior in accounting for complex relationships among influencing factors and identifying hit-and-run crashes. The quantitative importance of various factors is estimated and compared to reveal key determinants such as visibility, road location, and accident liability. The complex effects of different factors on hit-and-run crashes are unveiled, delineating quantitative piecewise nonlinear patterns. These patterns, which are difficult to capture using conventional regression models with predefined formulations, shed light on the nuanced dynamics of hit-and-run crashes. This research offers quantitative analysis and data-supported insights for transportation agencies and police departments to proactively mitigate hit-and-run crashes.