Spatial representation and spatial interaction PDF
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-------~- Studies in applied regional science This series in applied regional, urban and environmental analysis aims to provide regional scientists with a set of adequate tools for empirical regional analysis and for prac tical regional planning problems. The major emphasis in this series will be upon the applicability of theories and methods in the field of regional science; these will be pre sented in a form which can be readily used by practitioners. Both new applications of existing knowledge and newly developed ideas will be published in the series. Studies in. applied regional science Vol. 10 Editor-in-Chief P. Nijkamp Free University, Amsterdam Editorial Board A.E Andersson University of Gothenburg, Gothenburg W.Isard Regional Science Institute, Philadelphia L.H. Klaassen Netherlands Economic Institute, Rotterdam I. Masser State University, Utrecht N. Sakashita Osaka University, Osaka Spatial representation and spatial interaction Edited by Ian Masser Professor of Urban and Regional Planning, University of Utrecht, the Netherlands Peter J. B. Brown Lecturer in Transport Studies, University of Liverpool, England Contributors Peter W. J. Batey, Michael Batty, Howard R. Kirby, Stan Openshaw, Roger Sammons, Jan Scheurwater cfJJartinus c!:Nijhoff Social Sciences Division CLeiden ClJoston 1978 I ISBN-13: 978-90-207-0717-5 e-ISBN-I3: 978-1-4613-4067-6 DOl: 10.1007/978-1-4613-4067-6 Copyright © 1978 by H.E. Stenfert Kroese B.V., Leiden No part of this book may be reproduced in any form by print, photoprint, microfilm or any other means, without written permission from the publisher Preface In recent years the development of spatial referencing techniques in com puter-based information systems has enormously increased the opportuni ties that exist for the treatment and presentation of both point and interaction data. The extent of this increase has drawn attention to the need for special aggregation and clustering procedures to be developed which enable data to be grouped in an efficient way for analytical pur poses with a minimum loss of detail. In the case of interaction data, economy of representation is particularly important as the analysis is further complicated by the two-way directionality that is inherent in each data set. Procedural rules of this kind are needed not only for descriptive analy sis and spatial accounting but also for hypothesis testing and the develop ment of operational models of spatial interaction. Yet the importance of spatial representation in this kind of research has only recently been fully understood. The first generation of urban development models that were developed in Europe and North America during the 1960's often treated matters of zoning system specification very casually, even though in some cases this imposed severe limits on the interpretation of their findings and it was not until the Centre for Environmental Studies/Cheshire project (Barras et al., 1971) that a serious attempt was made to put forward general principles which could be used as guidelines in future work. Since that time a number of studies have been undertaken which en able the main problems needing attention to be identified. These have been largely carried out in the framework of spatial interaction research, but this findings are applicable to the field as a whole. Most of them have been undertaken in Britain and reflect the continuing interest that has been shown by planners and geographers in that country in the develop ment of operational tools for empirical research (see, for example, Batty, 1976a; Baxter, 1976; and Wilson, 1974). An important feature of these studies of spatial representation is the extent to which approaches have been developed which are larg1y complementary to each -other despite marked differences in both starting points and basic objectives. VI PREFACE The localisation of interests prompted the British section of the Regional Science Association to set up a special workshop group on spatial re presentation in August 1975 with a view to stimulating collective dis cussion and encouraging collaborative research in this field. Financial support for this project was obtained from the Social Science Research Council. In May 1976 a meeting was organised by the workshop in con junction with the Quantitative Methods study group of the Institute of British Geographers on the subject of 'Dynamic models and spatial re presentation in geography and regional science'. The papers presented at this meeting drew attention to the extent that methods had already been developed for the systematic treatment of spatial representation in em pirical studies, even though the findings of this research were available in published form for only a few cases. As a result of this meeting the present editors carried out a comprehensive review of recent develop ments in this field with a view to establishing a basic framework for dis cussion purposes (Masser and Brown, 1977). The findings of this review are largely responsible for the present volume in that they emphasised the importance of making the results of this research available in a much more integrated manner than is normally possible through the medium of journal articles. This book contains edited and revised versions of both published and unpublished material from British sources. The editors have exercised their discretion in the selection of this material and also made a number of revisions to the original manuscripts to avoid unnecessary duplication, but, nevertheless, the views that are expressed are solely those of the authors themselves. The introductory chapter is a revised version of the review paper that was mentioned above which also incorporates new material. It discusses recent developments in the field in general terms and provides a general framework for the more detailed discussion that is contained in subsequent chapters. Chapter 2 is based on part of a paper prepared for the British section of the Regional Science Association meeting in August 1973 (Masser, Batey and Brown, 1975). In its present form this chapter also includes new material regarding the practical ap plication of a number of methods to the design of a zoning system for the Wirral district of Merseyside. Chapters 3, 4 and 8 are revised versions of papers that were given at the May 1976 conference that was referred to above. A considerably extended version of chapter 4 appeared in the Geographical Paper series that is published by the University of Reading (Sammons, 1976). Chapters 5, 6 and 7 have been specially prepared for this volume with the common objective of integrating and extending the authors' previous papers on these topics. Consequently, chapter 5 incor porates the main findings of two other papers by this author (Openshaw, 1977a, 1977b), chapter 6, four earlier papers by the author (Batty, 1972, PREFACE Vll 1974a, 1974b, 1976b) and chapter 7, three earlier papers (Masser and Brown, 1975; Masser, 1976; Masser and Scheurwater, 1977). A number of general themes emerge from these studies which are likely to affect the choice of topics for future research on spatial representation. These are summarised in chapter 9 for discussion purposes in the hope that the next phase of spatial representation research will take place in a more organised manner than that reported on in this book. Ian Masser Peter J. B. Brown Contents Preface v List of contributors xii IAN MASSER AND PETER J. B. BROWN 1. Spatial representation and spatial interaction: an overview 1.1. Introduction I 1.2. The multi-criteria aggregation problem 2 1.3. The multi-level specification problem 12 PART I: MULTI-CRITERIA AGGREGATION PROBLEMS IAN MASSER, PETER W. J. BATEY AND PETER J. B. BROWN 2. Sequential treatment of the multi-criteria aggregation problem: a case study of zoning system design 27 2.1. Introduction 27 2.2. The Wirral case study 30 2.3. Conclusions 47 PETER J. B. BROWN AND IAN MASSER 3. An empirical investigation of the use of Broadbent's rule in spatial system design 51 3.1. Introduction 51 3.2. Broadbent's rule 51 3.3. The Merseyside study 55 3.4. Conclusions 65 ROGER SAMMONS 4. A simplistic approach to the redistricting problem 71 4.1. Introduction 71 IX x CONTENTS 4.2. Electoral redistricting methods 71 4.3. The development of the simplistic algorithm 75 4.4. The redistricting algorithm 79 4.5. Application of the procedure to the West Midlands 82 4.6. Conclusions 93 STAN OPENSHAW 5. An optimal zoning approach to the study of spatially aggregated data 95 5.1. Introduction 95 5.2. Alternative approaches to the design of zoning systems for spatial study 96 5.3. Solving the automatic zoning problem 100 5.4. Applications 105 5.5. Zone design and spatial study 110 MICHAEL BATTY 6. Speculations on an information theoretic approach to spatial representation 115 6.1. Introduction 115 6.2. Spatial entropy functions 118 6.3. Measures of relative spatial information 121 6.4. The aggregation of information 124 6.5. Theoretical aggregation problems: in a population density model 127 6.6. Hierarchical aggregation 134 6.7. Information measures of spatial efficiency 138 6.8. Spatial probability models incorporating zone size 140 6.9. An empirical algorithm based on spatial information theory 143 6.10. Conclusions 146 PART II: MULTI-LEVEL SPECIFICATION PROBLEMS IAN MASSER AND JAN SCHEURWATER 7. The specification of multi-level systems for spatial analysis 151 7.1. Introduction 151 7.2. Slater's method 152 7.3. The Intramax procedure 156 7.4. An analytical framework for the specification of multi-level spatial systems 164
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