Table Of Content-------~-
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
