Table Of ContentExploratory and explanatory statistical analysis
of spatial data
Exploratory and explanatory
statistical analysis of spatial data
CORNELIS P. A. BARTELS and RONALD H. KETELLAPPER, editors
University of Groningen
GMartinus GJVijhoff Publishing
Boston/TheHague/London 1979
Distributors for North America:
Martinus Nijhoff Publishing
Kluwer Boston, Inc.
160 Old Derby Street
Hingham, Massachusetts 02043
Distributors outside North America:
K1uwer Academic Publishers Group
Distribution Centre
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Library of Congress Cataloging in Publication Data
Regional Science Symposium, University of Groningen, 1977.
Exploratory and explanatory statistical analysis
of spatial data.
Contains, for the most part, papers presented at a
Regional Science Symposium, held at the Faculty of
Economics of the University of Groningen in the
Netherlands.
Includes bibliographies.
I. Regional economics-Statistical methods-Con
gresses. 2. Regional planning-Statistical methods
Congresses. I. Bartels, Comelis, P.A.
II. Ketellapper, Ronald H. III. Title.
HT391.R3374 1977 330'.01'82 79-13142
ISBN-13: 978-94-009-9235-1 e-ISBN-13: 978-94-009-9233-7
001: 10.10071978-94-009-9233-7
Copyright ©1979 by Martinus Nijhoff Publishing.
Softcover reprint of the hardcover 15t edition 1979
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 September 1977 a "Regional Science Symposium" was held at
the Faculty of Economics of the University of Goningen in the
Netherlands.
The impetus in organizing this symposium was the recent estab
lishmen t at the F acuIty of Economics of a group engaged in teaching
and research within the field of regional science. The aim of the
symposium was to familiarize university members with regional
science and to introduce the new group to both the national and
international scene. Two separate topics of potential interest to
both researchers and policy-makers were selected.
The first theme, spatial inequalities and regional development,
was chosen because of its central place in regional science. Authors
from several disciplines were asked to approach this theme from a
general, policy-oriented point of view. This ensured the spotlighting
of the various dimensions of spatial inequality and its implications
for regional policy. The results of their efforts have been collected
in a volume entitled Spatial Inequalities and Regional Development.
The second theme focussed on spatial statistical analysis. This
branch of statistics is a relatively new one. It is receiving growing
attention from researchers in the field of applied regional science.
The conference dealing with this topic concentrated on recent
research results related to the use of appropriate statistical and
econometric methods for analyzing spatial data. The papers con
cerned have been collected in another volume, entitled Exploratory
and Explanatory Statistical Analysis of Spatial Data.
Both volumes contain, for the most part, papers presented at the
symposium. Some additional papers have been included to improve
the consistency of the volumes. All contributions have been revised
prior to final publication. In this process critical comments made by
participants at the symposium have proven to be very helpful. We
believe that these efforts have helped considerably to improve the
quality of both volumes.
Groningen, April 1978 The editors
Contents
PREFACE v
CONTENTS VII
LIST OF CONTRIBUTORS XI
Part 1: Introduction 1
1. GENERAL INTRODUCTION 3
CORNELIS P.A. BARTELS AND
RONALD H. KETELLAPPER
2. OPERATIONAL STATISTICAL METHODS FOR
ANALYSING SPATIAL DATA 5
CORNELIS P. A. BARTELS
2.1. Introduction 5
2.2. The structure of spatial data 6
2.3. Methods based on simple correlations between
cross-regional data 7
2.4. Time-series analysis applied to spatial data 13
2.5. Adaptations of time-series analysis to the spatial
context 20
2.6. Single equation explanatory models 28
2.7. Simultaneous equation models with spatial data 40
2.8. Some remaining topics 42
2.9. Final remarks 45
References 45
VIII CONTENTS
Part 2: Exploratory statistical analysis 51
3. THE ANALYSIS OF GEOGRAPHICAL MAPS 53
BRIAN D. RIPLEY
3.1. Introduction 53
3.2. Methods of analysis 54
3.3. Models 55
3.4. Tests for randomness 60
3.5. Examples 65
3.6. Conclusions 67
References 71
4. CONSTRUCTION OF INTERREGIONAL INPUT- 73
OUTPUT TABLES BY EFFICIENT INFORMATION
ADDING
FOLKE SNICKARS
4.1. Introduction 73
4.2. Regional and national accounts 75
4.3. Generation of survey-based transaction tables 79
4.4. Results of the statistical estimations 91
4.5. Results of the minimum information estimations 105
4.6. Some conclusions 110
References III
5. FURTHER EVIDENCE ON ALTERNATIVE PRO
CEDURES FOR TESTING OF SPATIAL AUTO-
CORRELATION AMONG REGRESSION DIS- 113
TURBANCES
ANDRIES S. BRANDSMA AND RONALD H. KETELLAPPER
5.1. Introduction 113
5.2. Formulation of the statistical decision problem 115
5.3. Moran's test statistic 116
5.4. Moments of the Moran statistic using OLS and
LUS estimators 118
5.5. The likelihood ratio test 122
5.6. Simulation study of the Moran and likelihood
ratio tests 125
5.7. Results 126
CONTENTS IX
5.8. Conclusions 132
Appendix 134
References 135
Part 3: Explanatory statistical analysis 137
6. MULTIVARIATE MODELS OF DEPENDENT SPATIAL
DATA 139
BERND STREITBERG
6.1. Introduction 139
6.2. Decomposable covariance structures 141
6.3. Linear models 157
6.4. Principal components 172
6.5. Conclusion 173
References 176
7. BAYESIAN ANALYSIS OF THE LINEAR MODEL
WITH SPATIAL DEPENDENCE 179
LESLIE W. HEPPLE
7.1. Introduction 179
7.2. The nature of Bayesian inference 180
7.3. Linear regression model with spatially auto-
correlated disturbances 185
7.4. An empirical application 193
7.5. Concluding remarks 197
References 198
8. ALTERNATIVE METHODS OF ESTIMATING SPATIAL
INTERACTION MODELS AND THEIR PERFORMANCE
IN SHORT-TERM FORECASTING 201
STAN OPENSHAW
8.1. Introduction 201
8.2. Description of data and models 203
8.3. Parameter estimation and model calibration in
terms of 1966 and 1971 data 206
8.4. On the accuracy of short-term forecasts made by
spatial interaction models 212
X CONTENTS
8.5. An evaluation of some alternatives designed to
improve model performance 216
8.6. Conclusions 223
References 224
9. TWO ESTIMATION METHODS FOR SINGLY CON-
STRAINED SPATIAL DISTRIBUTION MODELS 227
JAN VAN EST AND JAN VAN SETTEN
9.1. Introduction 227
9.2. The calibration of a model 228
9.3. The maximum likelihood method 230
9.4. The least-squares method for the singly con-
strained model 234
9.5. Numerical results 237
9.6. Conclusions 240
References 241
Part 4: The introduction of stochastics in regional
control 243
10. STOCHASTIC CONTROL OF REGIONAL
ECONOMIES 245
ROBERT J. BENNETT AND K.C. TAN
10.1. Introduction 245
10.2. Mathematical representation of regional systems 246
10.3. Optimal control models of regional systems 250
10.4 Interaction of optimal control of regional
economies with national governments 255
10.5. Problems in applying optimal control to
regional systems 264
10.6. Conclusion 266
References 267
List of contributors
Cornelis P.A. Bartels is assistant professor in regional economics at the University
of Groningen (Netherlands). His publications include a book on economic aspects
of regional welfare and several articles on development economics, income distribu
tion, regional unemployment and econometric techniques applied to spatial data.
Robert J. Bennett is affiliated with the Department of Geography of the University
of Cambridge. His various publications include books on spatial time series and en
vironmental systems, and articles on the identification, representation and estimation
of dynamic spatial models, optimal control models of regional economies, and tech
niques for non-stationary parameter estimation.
Andries S. Brandsma was student in the Faculty of Econometrics at the University
of Groningen, Netherlands. His master thesis focused on methods to account for
spatial autocorrelation in the estimation of regional economic models.
Leslie W. Hepple is at the Department of Geography of the University of Bristol,
England. He published studies on several aspects of econometric estimation with
spatial data, e.g., the use of stochastic process theory in spatial analYSiS, spectral
analysis, maximum likelihood estimation and Bayesian analysis of regional models.
Ronald H. Ketellapper is assistant professor in econometrics at the University of
Groningen (Netherlands). His research is mainly in the field of the estimation of eco
nometric models, the analysis of errors-in-variables models, and the study of tech
niques to test for spatial autocorrelation.
Stan Openshaw is lecturer at the Department of Town and Country Planning of the
University of Newcastle upon Tyne, England. His research concentrated on several
aspects of the use of spatial interaction models in planning, especially the specification
of deterrence functions, the determination of optimal zonings, and properties of
alternative specifications of such interaction models.
Brian D. Ripley is associated with the Department of Mathematics of the Imperial
College in London. He has published articles on the theoretical and empirical analysis
of stationary point process in space.
Folke Snickars is member of the research group for Urban and Regional Planning at
XII LIST OF CONTRIBUTORS
the Royal Institute of Technology in Stockholm. His research includes studies on the
application of information theory in regional science, and the analysis of regional
migration.
Bernd Streitberg works in the field of econometrics and statistics at the Freie Univer
sitat, Berlin. His research concentrated on the estimation oflinear multivariate models
with dependent data.
K.C. Tan worked at the Department of Geography of the University College, London.
He published on optimal control theory for linear econometric systems with linear
equality and inequality constraints on the control variables.
Jan van Est is research fellow at TNO, Delft, Netherlands. He works on the estimation
and application of large scale spatial distribution models.
Jan van Setten is research fellow at TNO, Delft, Netherlands. His research includes the
estimation of spatial interaction models; and the specification of mathematical models
of spatial patterns in the service system.
