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Daniel A. Griffith
Larry j. Layne
A CASEBOOK
FOR SPATIAL
STATISTICAL
DATA ANALYSIS
A COMPILATION OF ANALYSES
OF DIFFERENT THEMATIC DATA SETS
SPATIAL INFORMATION SYSTEMS
A CASEBOOK FOR SPATIAL STATISTICAL DATA ANALYSIS
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A CASEBOOK FOR
SPATIAL STATISTICAL DATA ANALYSIS
A Compilation of Analyses of Different Thematic Data Sets
DANIEL A. GRIFFITH
LARRY J. LAYNE
with contributions by J. K. Orel and Akio Sone
New York Oxford
Oxford University Press
1999
Oxford University Press
Oxford New York
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Copyright © 1999 by Oxford University Press
Published by Oxford University Press, Inc.
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Oxford is a registered trademark of Oxford University Press
All rights reserved. No part of this publication may be reproduced,
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without the prior permission of Oxford University Press.
Library of Congress Cataloging-in-Publication Data
Griffith, Daniel A.
A casebook for spatial statistical data analysis; a compilation of analyses
of different thematic data sets / Daniel A. Griffith and Larry J. Layne
with contributions by J. K. Ord and Akio Sone.
p. cm.
Includes bibliographical references and index.
ISBN 0-19-510958-9
1. Geography—Statistical methods. 2, Spatial analysis (Statistics).
1. Layne, Larry J. 11. Ord, J. K. III. Sone, Akio, IV. Title.
G70.3.G744 1999
910,.72—dc21 9853829
987654321
Printed in the United States of America
on acid-free paper
This book is dedicated to R. Dale and Mary E. Swartz.
Daniel A, Griffith
o
This book is dedicated to Dr. Francesco Lagona and Ludmiia Coromoto Ortegano
Sanchez.
Larry J. Layne
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PREFACE
If a lunatic scribbles a jumble of mathematical symbols it does
not follow that the writing means anything merely because to the
inexpert eye it is indistinguishable from higher mathematics.
Eric Temple Bell (Newman 1956, 308)
If a naive researcher completes a standard statistical analysis of georeferenced data,
it does not follow that the data analytic results have turned data into meaningful
information merely because to the inexpert eye they are indistinguishable from
conventional statistics results! Empirical work in many scientific fields is based on
data for which the location of observations is an important feature. These type of
data, especially when they are accompanied by a iocational tag (e.g., latitude and
longitude, Cartesian or Universal Transverse Mercator [UTM] coordinates), can
be referred to as georeferenced or spatial data. The observations often consist of
a single cross-section of spatial units or sometimes of a time series of cross-
sections. The distinctive characteristic of the statistical analysis of spatial data is
that the spatial pattern of locations (point patterns), the spatial association between
attribute values observed at different locations (spatial dependence), and the
systematic variation of phenomena by location (spatial heterogeneity) become the
major foci of inquiry. In addition to being of interest in and of itself (from a
geographer's perspective), any spatial pattern embedded in data causes a number
of measurement problems, referred to as spatial effects (spatial autocorrelation,
spatial heterogeneity), that affect the validity and robustness of traditional
statistical description and inference methods when applied to this category of data.
Recognition of this complication has given rise to an increasingly sophisticated
body of specialized techniques developed in the fields of geostatistics, spatial
statistics, and spatial econometrics. These techniques are not just relevant in
geography but are applicable to a wide range of scientific areas, such as
agriculture, archaeology, criminology, demography, ecology, environmental
studies, epidemiology, forestry, geology, international relations, natural resources,
vm Preface
regional science, remote sensing, sociology, statistics, urban planning, and urban
and regional economics.
With the increasing availability of geographic information systems (GIS),
which has helped to pique interest in spatial data analysis in a wide range of fields
(Wilson, 1996), the need has arisen to furnish many more empirical applications
of good spatial analysis. This very goal is echoed by contributors to both Spatial
Statistics: Past, Present, and Future (Griffith 1990) and Geostatistical Case
Studies (Matheron and Armstrong 1987), and with the aim of helping to avoid
spatial statistical malpractice, it was a principal motivation for compiling the CRC
Practical Handbook of Spatial Statistics (Arlinghaus 1996). In a cross-disciplinary
context this goal also is promoted as a fruitful direction for research by the editorial
panel of and contributors to the National Research Council's Spatial Statistics and
Digital Image Analysis (1991).
As one response to this literature gap and this clamor for more empirical
applications, we
• discuss, in summary format, the theoretical basis of prominent spatial
statistical techniques, in an applications format with implementation
guidelines;
• provide additional numerical evidence establishing links between geo- and
spatial statistics; and
• present a wide variety of data examples taken from a disparate set of
disciplines.
Principal templates for this type of volume are provided by Hand et al. (1994),
Handbook of Small Data Sets, and Andrews and Herzberg (1985), Data: A
Collection of Problems from Many Fields for the Student and Research Worker.
The data sets analyzed in this book comprise readily available ones (35), some of
our own (3), and some unpublished ones from colleagues (4). But published
georeferenced data sets are not always complete, frequently lacking locational tags.
In some cases, we have secured locational tags from other (especially Internet)
sources, or we have performed the digitizing task ourselves. Additional valuable
georeferenced data sets are noted throughout, too, especially from such popular
sources as Hamilton (1992), Rasmussen (1992), Carr (1995), and Chatterjee et al.
(1995); and, government data sets are everywhere online, with many linked to the
National Spatial Data Clearinghouse Web site being well worth retrieving.
Analyzing such a broad collection of data sets, covering a wide range of situations,
illustrates many types of spatial statistical analyses and helps point out gaps in
current spatial statistical methodology.
Georeferenced data sets increasingly are massive; historically, one major
source of such very large data sets has been remote sensing. Special concerns
affiliated with this size of data set resulted in the National Research Council
publishing Massive Data Sets (1996). To date, sampling often has been used to
reduce such data sets to a manageable form, but sampling may well obscure latent
spatial dependency. In §5.7, we illustrate the ability to analyze such voluminous
data using implementations outlined in this text.
Preface (x
Software for implementation purposes discussed in this book includes SAS
and SPSS routines (which, together with Dr. Akio Sone of Tsukuba University, we
have developed), GEO-EAS, Heuvelink's semivariogram model fitting module, and
VARIOWIN. Accordingly, the recent release of PROC GIS in SAS makes this
book a timely addition to the literature. Many other dedicated software packages
are available, too, and sometimes are mentioned in this book, including Deutsch
and Joumel's GISLIB, specially developed MINITAB macro code, and Anselin's
GAUSS-based package for the analysis of spatial data (SpaceStat).
In addition to Advanced Spatial Statistics (Griffith, 1988), a number of
books have appeared during the past decade that deal with spatial statistics, such
as Anselin's Spatial Econometrics (1988), Arbia's Spatial Data Configuration in
Statistical Analysis of Regional Economics and Related Problems (1989),
Christakos's Random Field Models in Earth Sciences (1992), Christensen's Linear
Models for Multivariate, Time Series, and Spatial Data (1991), Cressie's Statistics
for Spatial Data (1991), Gregoire et al.'s Modelling Longitudinal and Spatially
Correlated Data (1997), Isaaks and Srivastava's An Introduction to Applied
Geostatistics (1989), Ripley's Statistical Inference for Spatial Processes (1988),
Guyon's Random Fields on a Network {1995), Haining's Spatial Data Analysis in
the Social and Environmental Sciences (1990), and Upton and Fingleton's Spatial
Data Analysis by Example (1985, 1989). None of these publications, however,
specifically addresses the goals that we have outlined. Furthermore, this volume
differs from these others in that we deal with spatial statistics by
• pursuing unification of the perspectives advanced in geostatistics, spatial
statistics, and spatial econometrics (although Cressie's treatise verges on
being an exception), and
• combining a rigorous methodological treatment with a comparative
applications focus, while including numerous new or freshly analyzed,
illustrative data sets and worked examples.
In achieving these goals and pursuits in this volume, we hope to have furnished
invaluable insights to professional researchers, academics, graduate students, and
analysts in a range of disciplines that deal with spatial data and who are increas-
ingly using the tool of GIS in their work.
Acknowledgments
The assistance of many people made this book possible. Both of us enjoyed the
complete support of the Department of Geography, Syracuse University, with
funding from the National Science Foundation (#SBR-9507855), over two years,
enabling us to complete the research upon which this book is based. Parts of this
volume were presented to the Spring 1997 students of GEO 686: Advanced Spatial
Statistics; their feedback is most appreciated. We especially appreciate the efforts
of Mr. Peter L. Fellows, a student in this class, who completed the task of double-
checking much of the SAS code. Dr. J. Keith Ord, of the Pennsylvania State
University, contributed a commentary on our paper appearing in the 1996
