Estimating Aggregated Gravitational Attractions by an Algebraic Simplification

Abstract

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Reverse-fitting the gravity model to inter-city airline passenger flows by an algebraic simplification

“…With reference to the gravity model (2), nodal attractions, P i (or P j ), are computed endogenously with exogenous spatial interactions, G ij , and spatial impedance, F ðd ij Þ, hence a reverse-fitting of the gravity model. This paper simplifies the general reverse-fitting algebraic method developed in Shen (1999Shen ( , 2002. The algebraic simplification is novel in that it substantially reduces the size of the spatial interaction matrix required by the algebraic method for estimating good-fit nodal attractions.…”

“…This method assumes that the exogenous spatial interactions, G ij , are generated by strong gravitational propulsion and attraction at nodes and that it is appropriate to estimate nodal attractions that best fit the inter-nodal flow data using the gravity model. Selected literature includes Evans and Kirby (1974) on the well-known iterative Furness procedure; Wilson (1967), Flowerdew and John (1982), and Sen and Smith (1995) on statistics regression estimation; O' Kelly et al (1995) on a linear programming technique; and Shen (1999Shen ( , 2002 on an algebraic approach. Comparable procedures with various examples can also be found in Tobler (1979), Fotheringham and O'Kelly (1989), and Fotheringham et al (2000).…”

“…Outline of the algebraic approach Shen (1999Shen ( , 2002 developed an algebraic method (AM) to estimate n nodal attractions P i (or P j ) such that the exogenous symmetrical spatial interaction matrix, G ij , and distance matrix, Fd ij ), best fit the gravity model (2). By using the notation P i P j ¼ kG ij F ðd ij Þ, where k ¼ r À1 , we can summarize the distribution of equations based on the gravity model (2) in Table 1.…”