The gravity model is a classical spatial interaction model for estimating geographical flows between regions, such as trade and migration. A key to enhancing the model performance is addressing the fixed effects (FE) to capture unobserved group-based characteristics. Traditionally, this is done by grouping flows sharing the same origin or destination. However, it ignores the fact that FE of flows are directional and spatially heterogeneous, e.g., for the same origin (destination), the FE vary among destinations (origins). In this study, we propose a new method that addresses FE of flows based on higher-order origin-destination (OD) pairs. Specifically, we estimate FE by grouping flows that share the same OD dyad at an upper geographic level, e.g., all county-level migration flows from California to Florida are grouped to estimate their FE. We conducted two case studies using U.S. migration flows and for-hire vehicle trips in New York City. The results prove that our method can enhance the model performance. More importantly, our results demonstrate that the FE based on higher-order OD pairs can reveal the directionality, reciprocity, regionality, and temporal regularity of geographical flows. This insight helps us achieve a deeper understanding of the space-time mechanisms underlying spatial interaction phenomena. [ABSTRACT FROM AUTHOR]

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