Gravity Models: An Overview

Abstract

Given the general class of spatial interaction processes outlined in Chapter 1, we are now ready to develop the specific class of behavioral models which form the central focus of this book — namely gravity models of spatial interaction behavior. To do so, we begin by recalling from the discussion following the Poisson Characterization Theorem in Chapter 1 that each independent interaction process, P = {P_c:c ∈ C}, is completely characterized by its associated mean interaction frequencies, E_c(N _ij ), ij ∈ I x J, for each separation configuration, c ∈ C. Hence each explicit model of mean interaction frequencies yields a complete specification of probabilistic interaction behavior in this context. With this observation in mind, recall from the Introduction that gravity models are precisely of this type. In particular, if the ‘interaction levels’, T _ij , in expressions (2) through (4) in the Introduction are now interpreted as mean interaction frequencies for the separation configuration defined by distances, d _ij then each of these expressions is seen to constitute an explicit (finite parameter) model of mean interaction frequencies. More generally, even for spatial interaction processes in which the axioms of frequency independence and/or locational independence are not appropriate, gravity models may still be interpreted as representations of average interaction behavior within such processes.