research notes and comments: Estimating nodal attractions with exogenous spatial interaction and impedance data using the gravity model

Unlike the conventional calibration of a gravity model in which nodal attractions are treated exogenously, this study treats the attraction of a node as an endogenous composite indicator of many contributing factors associated with the node and estimates the nodal attraction based upon exogenous spatial interaction (flow) and impedance data. An algebraic method is developed for the general $N\times N$ O-D matrix and applied to a hypothetical $5\times 5$ O-D flow case. A theoretical discussion of utilizing regression to estimate the contributing factors of nodal attractions is also presented.