A Theoretical Analysis of Aggregation in Spatial Interaction Models

The spatial interaction model expresses the idea that the proportion of all flows leaving origin i that go to the particular destination j depends upon the attractiveness of that destination mf and on some function of its distance from the origin d,.Symbolically, Typically, r q is measured as the "size" of destination j (and a is a parameter reflecting the significance of size as an attractive force).Various forms of the function f have been proposed, including where P and y are parameters to be estimated (p is sometimes called the distance deterrence parameter).Spatial interaction models have a long history in geographic thought, including applications to freight flows, commuting patterns, migration, and shopping behavior [13,20].However, despite Wilson's [22] rigorous derivation of this model, these simple notions are not sufficiently precise to support the empirical analyses that geographers have made of spatial interactions.In particular, the model does not identify the actors whose behavior is to be described-flows are from "origins" to "destinations"-so that empirical studies are confused about what is being estimated and about the methods to employ in estimation.This shortcoming has given rise to some results that are unsatisfactory, especially to geographers who wish to interpret the parameters estimated in an empirical study of spatial interaction.Typically, published data on spatial interactions are aggregated spatially, and the interaction equation purports to describe these data.