Table Of Contentspatial data
analysis
AN INTRODUCTION FOR GIS USERS
Christopher D. Lloyd
School of Geography, Archaeology, and Palaeoecology
Queen’s University, Belfast
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Lloyd, Christopher D.
Spatial data analysis : an introduction for GIS users / Christopher D. Lloyd.
p. cm.
ISBN 978-0-19-955432-4
1. Geography—Statistical methods. 2. Geographic information systems. I. Title.
G70.3.l56 2010
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2009039593
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Preface
Th ere is a plethora of books available that introduce, at a variety of levels, approaches
for the analysis of spatial data. Why write yet another one? Th e most obvious reason is
that, while many of the existing books provide excellent accounts of a wide range of
methods, none of the existing texts started and concluded at a level that I felt was
appropriate for the students (mostly at an undergraduate level) whom I have had the
responsibility to teach. Many existing introductory texts on geographical information
systems (GIS) include material at an appropriate level about data models, databases,
visualization, and elements of spatial analysis, amongst other themes. However,
in my experience, a combination of texts was required to address fully the key issues
in spatial data analysis in suffi cient depth. While some texts covered many approaches
to spatial data analysis, the prior expectations, in terms of existing knowledge, made
such texts inaccessible to many undergraduate students in geography and others with
a burgeoning interest in spatial data analysis. Th is book is intended as a bridge between
texts that introduce some key principles of GIS and those that go into a great deal of
depth about a wide body of methods for spatial analysis.
Another concern is to introduce in a reasonably small amount of text a set of key
ideas so that the book could be used to support part of a course concerned with, for
example, GIS and GIScience in general. Although there is a focus on how the methods
work, the aim is also to develop an understanding of when and how it is appropriate to
apply particular methods. One key reason for writing this book follows from my belief
that academic courses in GIScience should focus on education and not simply on
training—that is, while it is important for students to learn how to use soft ware, with-
out some understanding of what is being done and of the implications of particular
decisions, the process is reduced to training.
Th is book is also a logical progression from previous work: another book (Lloyd,
2006) published before this book was started had a rather diff erent focus and intended
audience with some introductory material provided but a fair amount of background
knowledge assumed. On fi nishing that book, writing a more general text that started
from fi rst principles was tempting and the present book is the result. I hope that this
book builds knowledge and fosters interest. If it provokes readers to fi nd out more
then it will have succeeded in its aims.
Contents
Chapter 1 Introduction 1
1.1 Spatial data analysis 1
1.2 Purpose of the book 2
1.3 Key concepts 3
1.4 Structure of the book 4
Further reading 5
Chapter 2 Key concepts 1: GIS 6
2.1 Introduction 6
2.2 Data and data models 7
2.2.1 Raster data 7
2.2.2 Vector data 8
2.2.3 Topology 9
2.2.4 Rasters and vectors in GIS soft ware 11
2.3 Databases 11
2.3.1 Database management 12
2.3.2 Th e Geodatabase 12
2.4 Referencing systems and projections 12
2.5 Georeferencing 13
2.6 Geocoding 13
2.7 Spatial scale 14
2.8 Spatial data collection 15
2.8.1 Spatial sampling 15
2.8.2 Secondary data sources 16
2.8.3 Remote sensing 16
2.8.4 Ground survey 17
2.9 Sources of data error 18
2.9.1 Uncertainty in spatial data analysis 19
2 .10 Visualizing spatial data 19
2 .11 Querying data 21
2.11.1 Boolean logic 21
Summary 23
Further reading 23
viii
CONTENTS
Chapter 3 Key concepts 2: statistics 24
3.1 Introduction 24
3.2 Univariate statistics 25
3.3 Multivariate statistics 31
3.4 Inferential statistics 39
3.5 Statistics and spatial data 41
Summary 42
Further reading 42
Chapter 4 Key concepts 3: spatial data analysis 43
4.1 Introduction 43
4.2 Distances 44
4.3 Measuring lengths and perimeters 45
4.3.1 Length of vector features 45
4.4 Measuring areas 45
4.4.1 Areas of polygons 45
4.5 Distances from objects: buffers 47
4.5.1 Vector buff ers 47
4.5.2 Raster proximity 47
4.6 Moving windows: basic statistics in subregions 48
4.7 Geographical weights 50
4.8 Spatial dependence and spatial autocorrelation 55
4.9 The ecological fallacy and the modifi able areal unit problem 60
4 .10 Merging polygons 63
Summary 63
Further reading 64
Chapter 5 Combining data layers 65
5.1 Introduction 65
5.2 Multiple features: overlays 65
5.2.1 Point in polygon 66
5.2.2 Overlay operators 67
5.2.3 ‘Cookie cutter’ operations: erase and clip 69
5.2.4 Applications and problems 70
5.3 Multicriteria decision analysis 71
5.4 Case study 72
Summary 74
Further reading 74
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CONTENTS
Chapter 6 Network analysis 75
6.1 Introduction 75
6.2 Networks 75
6.3 Network connectivity 76
6.4 Summaries of network characteristics 79
6.5 Identifying shortest paths 80
6.6 The travelling salesperson problem 83
6.7 Location–allocation problems 83
6.8 Case study 84
Summary 85
Further reading 85
Chapter 7 Exploring spatial point patterns 86
7.1 Introduction 86
7.2 Basic measures 88
7.3 Exploring spatial variations in point intensity 89
7.3.1 Quadrats 89
7.3.2 Kernel estimation 93
7.4 Measures based on distances between events 97
7.4.1 Nearest-neighbour methods 97
7.4.2 K function 99
7.5 Applications and other issues 102
7.6 Case study 102
Summary 105
Further reading 105
Chapter 8 Exploring spatial patterning in data values 106
8.1 Introduction 106
8.2 Spatial autocorrelation 106
8.3 Local statistics 107
8.4 Local univariate measures 107
8.4.1 Local spatial autocorrelation 110
8.5 Regression and correlation 113
8.5.1 Spatial regression 113
8.5.2 Moving window regression 114
8.5.3 Geographically weighted regression 115
8.6 Other approaches 123
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CONTENTS
8.7 Case studies 124
8.7.1 Spatial autocorrelation analysis 124
8.7.2 Geographically weighted regression 125
Summary 127
Further reading 128
Chapter 9 Spatial interpolation 129
9.1 Introduction 129
9.2 Interpolation 129
9.3 Triangulated irregular networks 130
9.4 Regression for prediction 132
9.4.1 Trend surface analysis 133
9.5 Inverse distance weighting 134
9.6 Thin plate splines 136
9.7 Ordinary kriging 140
9.7.1 Variogram 141
9.7.2 Kriging 146
9.7.3 Cokriging 150
9.8 Other approaches and issues 150
9.9 Areal interpolation 150
9 .10 Case studies 152
9.10.1 Variogram estimation 152
9.10.2 Interpolation 153
Summary 154
Further reading 154
Chapter 10 Analysis of grids and surfaces 155
1 0.1 Introduction 155
1 0.2 Map algebra 155
1 0.3 Image processing 157
1 0.4 Spatial fi lters 158
1 0.5 Derivatives of altitude 160
1 0.6 Other products derived from surfaces 162
1 0.7 Case study 168
Summary 170
Further reading 170
xi
CONTENTS
Chapter 11 Summary 171
1 1.1 Review of key concepts 171
1 1.2 Other issues 172
1 1.3 Problems 172
1 1.4 Where next? 173
Summary and conclusions 174
References 175
Appendix A Matrix multiplication 180
Appendix B Th e exponential function 181
Appendix C Th e inverse tangent 182
Appendix D Line intersection 183
Appendix E Ordinary least squares 188
Appendix F Ordinary kriging system 191
Appendix G Common problems in spatial data analysis 202
Index 203
1
Introduction
1.1 Spatial data analysis
Geographical or spatial data play a vital role in many parts of daily life. Either directly,
as in the use of a map for navigating around a city, or indirectly, where we use resources
like water or gas, we are dependent on information about where things are located
and about the attributes of those things. Making use of spatial data requires a whole
set of approaches to extract information from those data and make them useful.
Geographical information systems (GIS) play a key role in this context. GIS provide a
means of generating, modifying, managing, analysing, and visualizing spatial data.
Th e key contribution of GIS, above and beyond functions provided by other forms of
soft ware such as cartographic mapping or computer-aided design packages, is in the
analysis of spatial data. Broadly, analysis is concerned with breaking apart a problem
with the aim of fi nding a solution to this problem. In terms of this book, the aim is to
introduce some ideas and methods that may be useful in the analysis of spatial data.
For example, approaches are presented for:
• summarizing a set of values (e.g. what is the mean average of all values?)
• identifying overlaps between diff erent features (e.g. what areas with pollution
above some critical threshold are located in areas that have a population of
greater than a particular size?)
• fi nding the shortest route between one place and another through a network
(e.g. a road network)
• identifying clustering in point events such as cases of some disease (e.g. where
are disease incidence rates highest?)
• exploring spatial patterning in variables (a variable being a quantity that may
vary across samples; precipitation amount or elevation, for example, can be
considered variables) (e.g. does the concentration of some pollutant vary
spatially and where are values largest?)
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INTRODUCTION
• exploring how two or more variables are related at diff erent places (e.g. does the
relationship between altitude and snowfall vary from place to place?)
• estimating the values of some property (e.g. precipitation amount) at locations
where there are no samples available (necessary as a prior stage to many other
procedures)
• assessing the construction costs of alternative routes for a new road.
Th ere are many other kinds of approaches covered in this book, but many are based on
common concepts such as measurement of distances or diff erences in properties in
diff erent areas. Th ese fundamental concepts are described along with some particu-
larly widely used approaches and the selected approaches are illustrated with example
applications. Th e emphasis throughout is on education rather than simply training,
based on the conviction that users of spatial data analysis tools should know something
about how the approaches work rather than simply how to apply them. Appendix G
details some spatial analysis tasks and the sections of the book that contain relevant
material. Th e remainder of this chapter sets out the purpose of the book and its
contents.
1.2 Purpose of the book
Th e aim of this book is to introduce a set of key ideas or frameworks that will give the
reader knowledge of the kinds of problems that can be tackled using widely available
tools for the analysis of spatial data. Another key concern is that readers understand
how the methods work, therefore a large majority of methods introduced are demon-
strated through small case studies. Th e book includes detailed coverage of a relatively
limited number of basic key methods for the analysis of spatial data. Th ese are intended
to illustrate the workings of particular methods as well as to demonstrate key concepts
that will support understanding of other approaches.
Th is is not an introduction to GIS. Readers who wish to know about, for example,
data models, databases, or visualization will fi nd brief introductions in this book,
although they should consult one of a range of textbooks such as those by Heywood
et al. (2006) or Longley et al. (2005a) for more in-depth accounts. A full description of
some key GIS algorithms (put simply, sets of instructions that are worked through to
achieve some particular objective) is provided by Wise (2002). In this book, little prior
knowledge is assumed of readers. However, it is expected that readers will have some
basic knowledge of GIS principles. Th e book is also not an introduction to statistics,
although some key ideas are discussed. Th e book by Rogerson (2006) provides a good
introduction to statistics for geographers. Only a very limited prior knowledge of sta-
tistics is required to make full use of the present book and it is an aim in this book that
no terms likely to cause confusion will be dropped in without explanation. While it is
assumed that most readers will work through the book systematically, it is designed so
