Gravity Models of Spatial Interaction Behavior

Abstract

It could easily be argued that spatial interaction, the movement of people, objects and information over space resulting from a decision process, is one of the most important topics, if not the most important topic, within spatial analysis. The term "spatial interaction" encompasses such diverse subjects as retailing and locational analysis, migration, transportation, residential choice, information dissemination, international trade, the spread of diseases, the provision of hospital services, attendance at events, and telecommunications.Not surprisingly, therefore, the study of spatial interaction is found in several disciplines including geography, economics, regional science, civil engineering, planning, and marketing, and there is an extensive and diverse literature on the subject. Underpinning the topic are concepts such as spatial choice and spatial cognition, as well as various statistical, mathematical, and computational issues that are necessary to understand both the theoretical development of spatial interaction models and their empirical application. Several well-known texts on spatial interaction modelling already exist, such as those of Wilson (19741, Batty(19761, Fotheringham and O'Kelly (1989), Erlander and Stewart (19891, and Ortuzar and Williamson (1990).Viewed against this backcloth, one can appreciate the potential importance of this book by Ashish Sen and Tony Smith which, by any criterion, is a serious tome. With 572 densely packed pages containing 1547 equations and over 300 references, the authors clearly intend it to be a standard reference text in spatial interaction modeling. This is not the product of a ~~~ ~~~~~ brief sabbatical-it has taken the better part of a decade to prepare and write and, like a good whisky, it has benefited from its lengthy distillation. The book has two parts: Part 1, "Theoretical Development," and Part 2, "Methods." Part 1 consists of four chapters, the first two of which contain overviews of spatial interaction processes and gravity models, respectively. The well-written first chapter provides discussions on macro and micro approaches to spatial interaction modeling, statics versus dynamics, probabilistic versus deterministic modeling, the measurement of variables, and general spatial interaction processes. The second chapter provides the general probabilistic model form that is used throughout the book and in which each observed flow is seen as the mean of a Poisson process. The chapter also discusses deterrence functions and generalizations of gravity models. The third and fourth chapters extend those themes. The third presents a formal discussion of search processes and mathematical formulations of space and interaction, and the fourth describes, in a series of propositions and proofs, the behavioral axioms embedded in various spatial interaction models. There is no doubt that it takes a great deal of effort and stamina to maintain interest throughout some of these sections (for example pages 21 to 48, pages 50 to 88, and the whole of Chapter 3) which ar...

The suitability of hedonic models for cost-benefit analysis: Evidence from commuting flows

“…There are various ways to accomplish this. In this paper, we use the popular gravity model approach (Sen and Smith, 1995). Other options are of course available (Ortuzar and Willumsen, 2011).…”

The Spatial Transferability of Parameters in a Gravity Model of Commuting Flows

“…Both models belong to the gravity modelling tradition. For a general discussion of this modelling tradition see Erlander and Stewart (1990) or Sen and Smith (1995). The chosen model, represented by Equations (1), (2), and (3), is somewhat extended compared to a standard gravity model specification.…”

“…A variety of models have been developed with the aim of modelling such flows. One popular class of models, and the focus of this paper, is the gravity modelling tradition (Sen and Smith, 1995). These models can be derived from a variety of different angles; from classical physics to random utility theory.…”

Allee Effect and Control of Lake System Invasion

“…However, it appears that in many economical and geographical problems the set of connections between the nodes of a transportation network can be reasonably approximated by the so-called gravity models [27], where it is assumed that…”

“…This can be described by the connectivity matrix, showing the intensity of the boat exchange between the lakes. Often the connection matrix can be approximated by so-called gravity models [27], which have been successfully applied to the problem of lake invasions by a number of authors [3,1,17].…”