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North American Meeting of the Regional Science Association in Santa ... by high-school seniors, but it applies to many other choice situations (for example,.

Environment and Planning A, 1991, volume 23, pages 1233-1235

Commentary

Spatial interaction and choice The concern with spatial interaction and choice is central to geography and regional science. In recent years significant progress has been made in the formal analysis of these issues from a diversity of perspectives, ranging from abstract mathematical frameworks, algorithms, and general systems analytic models, to behavioural approaches and utility theory. This progress was accompanied by parallel developments of a variety of advanced statistical and econometric methods. However, this progress has tended to be achieved in specialized areas, without much emphasis on overarching themes, integrating concepts, and cross-fertilization between competing approaches. Given the importance of the research questions associated with spatial interaction and choice as a central theme in analytical geography and regional science, Luc Anselin (University of California, Santa Barbara) and Manfred M Fischer (Vienna University of Economics and Business Administration) have organized an Advanced Workshop, titled "Movement, Migration and Transportation: Regional Science Perspectives", on behalf of the International Geographical Union (IGU) Commission on Mathematical Models which was held in the framework of the 36th North American Meeting of the Regional Science Association in Santa Barbara, in November 1989. The aims of the workshop were to establish effective crossfertilization between separate areas of specialization, to take stock of the progress to date, to report on recent results, and to outline the most crucial directions for future research. In order to achieve these aims, the workshop was organized around two major themes: first, theoretical and methodological approaches to spatial interaction and choice; second, application of formal methods and models to the analysis of spatial interaction (migration, transportation, etc.) as well as of policy issues. The papers included in this special issue of Environment and Planning A are a selection of papers presented at the above-mentioned workshop of the IGU Commission on Mathematical Models under the first theme which focused on theoretical and methodological approaches (including measurement and estimation issues). The work on spatial choices during the 1960s and early 1970s was dominated by spatial interaction (gravity) models justified by using probability arguments and entropy-maximizing formulations. This lack of behavioural content, which began to be criticized in the early 1970s, gave rise to the study of individual choice behaviour which, in conjunction with the parallel development of discrete choice models, made it possible to propose new alternatives (for more details, see Fischer et al, 1990). Thus, it is not surprising that much recent progress in the field of spatial interaction and choice relates to (random-utility based) discrete choice models, and In conventional models, such as the multinomial logit model, it is assumed that the decisionmaker's choice is known and fixed (that is, exogenous). Thus, they are misspecified if the choice set is endogenous rather than exogenous, for example, as a consequence of the cost of acquiring information about choice alternatives. This issue is addressed in the first paper, by Horowitz, included in this special issue. Horowitz presents models for choice-set generation in this context and for choice conditional on endogenous choice sets. These models are more complex both

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analytically and computationally than are conventional choice models with exogenous choice sets. The context is motivated by the problem of modelling college choice by high-school seniors, but it applies to many other choice situations (for example, housing choice, job choice) as well. In the second contribution, Smith suggests a decision theory of spatial interaction in which interaction decisions are postulated to involve a number of distinct factors, relating to properties both of actors and of opportunities, as well as to the spatial separation between them. Especially, it is postulated that favourable conditions for such factors arise as independent random events over space, and that interactions are taken when an appropriate conjunction of such events occurs. The central result in the paper is that the asymptotically most probable interaction frequencies predicted by the theory correspond precisely to the solutions of the general spatial interaction model proposed by Alonso (1973) which formally extends the family of spatial interaction models developed by Wilson (1971). This result thus provides a behavioural foundation for the Alonso model, and, especially, leads to an explicit behavioural interpretation of its parameters. In the paper by Getis special attention is paid to the relationships between spatial interaction and autocorrelation models. The author shows that the crossproduct statistic developed by Hubert et al (1981) allows for a unification of the two types of models. This is accomplished by means of the development of a spatial autocorrelation statistic which serves as a measure of spatial interaction as well. The relationship between these two types of spatial models is especially strong when the focus is on measurements from a single point. As a consequence, the way is now paved for the development of statistical tests on spatial interaction theory. Lo analyses parameter variation and model performance of conventional spatial interaction models by using different sets of interaction data to simulate intraurban shopping trips according to a translog preference structure in various spatial settings. Three major sources of variation are considered in detail: spatial configuration, spatial size (size of origins and destinations), and spatial substitutability. The results of the simulation experiments show that the gravity model tends to predict less well in situations when spatial configuration is more dispersed, where spatial size is marked by a higher degree of dissimilarity, and where the destinations are more interdependent (that is, more substitutable or more complementary). The author stresses in particular the important role of spatial substitution effects in shaping the size of the distance parameter which conventional models are unable to capture. The results achieved confirm that, first, conventional spatial interaction models perform better when spatial structure is more homogenous; second, the distance parameters are spatially transferable only in systems with similar spatial structures; and, third, the distance parameter reflects the compounding influence of these spatial elements which affect travel behaviour, and, thus, a perception of distance rather than a true friction of space. Pumain and Haag suggest the master-equation approach should be taken to model urban and regional dynamics where special emphasis is laid on interurban and intraurban interactions of individual agents (households, landlords, firms, etc). The master-equation approach which has been brought to the attention of the regional science community in the 1980s (for example, see, Haag and Weidlich, 1984) opens a large field of applications in the social and economic sciences in general and in analytical geography and regional science in particular. The masterequation approach shows some very attractive features in the modelling of nonlinear dynamic behaviour of spatial choice and interaction systems, and has in particular the characteristic of linking the microlevel decisions of individuals with the macrolevel

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behaviour of collective variables in a spatial system. Feedback elements, heterogeneity, and nonstationarity can be taken care of. The authors suggest a stochastic theory of urban and regional dynamics, specify the individual transition rates (decision rates) of the different individual agents associated with the main subsystems (housing market, land market, services, labour market, transportation) of the urban system, formulate the dynamic equations of motion for the probability distribution to find a certain population distribution to be realized, and derive quasideterministic equations for the population numbers from the stochastic system. Moreover, the authors outline how the trend parameters of the system can be estimated by using empirical data. The papers included in this special issue illustrate the diversity of perspectives in the field of spatial interactions and choice, on the one hand, and point to increasing efforts to unify and integrate different concepts and approaches on the other. This certainly can be taken as an indicator that compared with the 1970s the field has reached a significantly much more mature state now. M M Fischer References Alonso W, 1973, "National interregional demographic account: a prototype", monograph number 10, Institute of Urban and Regional Development, University of California, Berkeley, CA Fischer M M, Nijkamp P, Papageorgiou Y Y (Eds), 1990 Spatial Choices and Processes (North-Holland, Amsterdam) Haag G, Weidlich W, 1984, "A stochastic theory of interregional migration" Geographical Analysis 16 331-357 Hubert L J, Golledge R G, Constanzo C M, 1981, "Generalized procedures for evaluating spatial autocorrelation" Geographical Analysis 17224-233 Wilson A G, 1971, "A family of spatial interaction models, and associated developments" Environment and Planning 3 1-32