Quantitative Geography

Perspectives on Spatial Data Analysis

A Stewart Fotheringham, Chris Brunsdon, Martin Charlton

Integrating a discussion of the application of quantitative methods with practical examples, this book explains the philosophy of the new quantitative methodologies and contrasts them with the methods associated with geography?s `Quantitative Revolution? of the 1960s. Key issues discussed include: the nature of modern quantitative geography; spatial data; geographical information systems; visualization; local analysis; point pattern analysis; spatial regression; and statistical inference. Concluding with a review of models used in spatial theory, the authors discuss the current challenges to spatial data analysis.

Written to be accessible, to communicate the diversity and excitement of recent thinking, Quantitative Geography will be required reading for students and researchers in any discipline where quantitative methods are used to analyse spatial data.

`This is a veritable tour de force of everything that is exciting about quantitative geography and GIS. It is a timely, thorough and exciting account of the state of the art and science of spatial analysis? - Paul Longley, University of Bristol

`A highly innovative and up-to-date text. It is unique in its coverage of the many developments that have taken place in the field over the past few years. The book is one that is highly readable and stimulating for those with some background in the field, and its expositional style and many examples will make it stimulating to newcomers as well? - Peter Rogerson, State University of New York at Buffalo

`Brings the field thoroughly up to date, integrating modern methods of GIS with a comprehensive and easy-to-read overview of the most recent and powerful techniques of spatial analysis. The book will be valuable to students and researchers in any discipline that seeks to explore or explain phenomena in geographical context, and will make excellent reading for geographers, political scientists, criminologists, anthropologists, geologists, epidemiologists, ecologists, and many others. It offers a spirited challenge to critics of a scientific approach to social science, and demonstrates the value of its subject matter through abundant examples? - Michael Goodchild, National Center for Geographic Information and Analysis, University of California, Santa Barbara

`There is a view within some parts of academic geography that what used to be called "quantitative geography" is dead, having been subsumed within "geographical information systems" or else of no continuing interest. This book should correct this view. First, it shows that quantitative methods have remained an exciting area of development and, second, it shows that, if anything, they have more relevance to substantive problems of interest than they have ever had. Although not specifically about GIS, it is a book that should be read by everyone concerned with the analysis of geographical information? - David Unwin, Birkbeck College, University of London

Establishing the Boundaries

1.1 Setting the scene

For many reasons, it is often difficult to write anything definitive about academic trends. Some trends are so short lived that they have relatively little impact; some are cyclical so that their impact at the time of writing is different from that at the time of reading; and some trends exhibit marked variations across countries in both their intensity and their timing so that any comments have limited spatial application. These caveats aside, it is fair to say that quantitative geography generally experienced a ‘downturn’ in its popularity between the early 1980s and the mid-1990s (Johnston, 1997; Graham, 1997). The reasons for this are difficult to separate and probably include a mix of the following:

1	A disillusionment with the positivist philosophical underpinnings of much of the original research in quantitative geography and the concomitant growth of many new paradigms in human geography, such as Marxism, post-modernism, structuralism and humanism, which have attracted adherents united often in their anti-quantitative sentiments. This disillusionment is very much a phenomenon of human geography: there appears to be no equivalent in physical geography where quantitative methods are generally viewed as an essential component of research. The demise of quantitative human geography has therefore inevitably led to an unfortunate widening of the gap between human and physical geographers because of the lack of any common language or philosophy. As Graf (1998, p. 2) notes:
	While their human geographer colleagues have been engaged in an ongoing debate driven first by Marxism, and then more recently by post-structuralism, post-modernism, and a host of other isms, physical geographers are perplexed, and not sure what all the fuss is about. . . . They do not perceive a need to develop a post-modern climatology, for example, and they suspect . . . that some isms are fundamentally anti-scientific.
2	The seemingly never-ending desire for some new paradigm or, in less polite terms, ‘bandwagon’ to act as a cornerstone of geographical research. The methodology of quantitative geography, had, for some, run its course by 1980 and it was time to try something new. While it is a strength of geography that the discipline quickly absorbs new trends and research paradigms, it is also a considerable weakness. The observations of de Leeuw (1994) on social sciences in general are apposite here. In adding to Newton’s famous phrase concerning the cumulative nature of research that we stand ‘on the shoulders of giants’, de Leeuw (p. 13) comments:
	It also means . . . that we stand on top of a lot of miscellaneous stuff put together by thousands of midgets. . . . This is one of the peculiar things about the social sciences. They do not seem to accumulate knowledge, there are very few giants, and every once in a while the midgets destroy the heaps.
3	A line of research that appears to be better accepted in human geography than in some related disciplines is one that is critical of existing paradigms. As quantitative geography was a well-established paradigm, it became, inevitably, a focal point for criticism. Unfortunately, much of this criticism originated from individuals who had little or no understanding of quantitative geography. As Gould (1984, p. 26) notes:
	few of those who reacted against the later mathematical methodologies knew what they were really dealing with, if for no other reason than they had little or no mathematics as a linguistic key to gain entry to a different framework, and no thoughtful experience into the actual employment of such techniques to judge in an informed and reasoned way. Furthermore, by associating mathematics with the devil incarnate, they evinced little desire to comprehend. As a result, they constantly appeared to be against something, but could seldom articulate their reasons except in distressingly emotional terms.
4	As part of the broader ‘information revolution’ which has taken place in society, the growth of geographical information systems (GIS), or what is becoming known as geographical information science (GISc), from the mid-1980s onwards has had some negative impacts on quantitative studies within geography. Interestingly, these negative impacts appear to have resulted from two quite different perceptions of GISc. To some, GISc is seen either as the equivalent of quantitative geography, which it most certainly is not, or as the academic equivalent of a Trojan horse with which quantitative geographers are attempting to reimpose their ideas into the geography curriculum (Johnston, 1997; Taylor and Johnston, 1995). To others, particularly in the USA where geography has long been under threat as an academic discipline, GISc has tended to displace quantitative geography as the paramount area in which students are provided with all-important job-related skills (Miyares and McGlade, 1994; Gober et al., 1995).^1
5	Quantitative geography is relatively ‘difficult’ or, perhaps more importantly, is perceived to be relatively difficult both by many academic geographers, who typically have limited quantitative and scientific backgrounds, and by many students. This affects the popularity of quantitative geography in several ways. It is perceived by many students to be easier to study other types of geography and their exposure to quantitative methodology often extends little beyond a mandatory introductory course. It deters established non-quantitative researchers from understanding the nature of the debates that have emerged and which will continue to emerge within quantitative geography. It also makes it tempting to dismiss the whole field of quantitative geography summarily through criticisms that have limited validity rather than trying to understand it. As Robinson (1998, p. 9) states:
	It can be argued that much of the antipathy towards quantitative methods still rests upon criticisms based on consideration of quantitative work carried out in the 1950s and 1960s rather than upon attempts to examine the more complete range of quantitative work performed during the last two decades.
	The relative difficulty of the subject matter might also have encouraged some researchers to ‘jump ship’ from quantitative geography (for some interesting anecdotes along these lines, see Billinge et al., 1984) as they struggled to keep up with the development of an increasingly wide array of techniques and methods. As Hepple (1998) notes:
	I am inclined to the view that some geographers lost interest in quantitative work when it became too mathematically demanding, and the ‘hunter-gatherer’ phase of locating the latest option in SPSS or some other package dried up.

This book is written in response to several of the issues raised in the above discussion. Despite being perceived from the outside as a relatively static research area, quantitative geography has witnessed a number of profound changes in the way it is approached. One purpose of this book is to describe not only some of these developments but also the debates surrounding them. In this way, we hope to present a view of quantitative geography as a vibrant, intellectually exciting, area in which many new developments are taking place, and in which many more await discovery.

A second reason for writing the book is that we hope to demonstrate that because of the changes taking place and that have taken place within the subject, several of the well-oiled criticisms traditionally levelled at quantitative geography no longer apply. For instance, the overly simplistic depictions of many that quantitative geographers search for global laws, and that individuals’ actions can be modelled without understanding their cognitive and behavioural processes, have rather limited applicability. For those who insist on ‘pigeon-holing’ everything, modern quantitative geography, with its emphasis on issues such as local relationships, exploratory analysis and individuals’ spatial cognitive processes, must be a difficult area to classify.

A third reason is the hope that some of the changes taking place in quantitative geography might make it more appealing to students and by advertising the existence of these developments, we might foster a greater interest in and appreciation for what modern quantitative geography has to offer. This is particularly the case, for example, in the subsequent discussions on topics such as visualization, exploratory data analysis, local forms of analysis, experimental significance testing and GIS-based forms of spatial analysis.

Ultimately, we hope that this book finds readership not just amongst established quantitative geographers who wish to keep abreast of the rapid developments in the field. It should also be useful to quantitative researchers in related disciplines who are increasingly recognizing the need for specialized techniques for handling spatial data. We hope it might also be of some use to non-quantitative geographers who would like to understand some of the current issues and debates in quantitative geography. Finally, it may be of assistance to students who would like to have a better understanding of what quantitative geography can offer, prior to making informed, rather than prejudicial, decisions related to career paths. Given the diversity of our intended audience, we recognize that it will be impossible to satisfy every level of readership on every page. Those who are not quantitatively trained are advised to skim some of the more mathematical sections whilst those who are quantitatively trained are asked to be tolerant through some of the more descriptive sections.

1.2 What is quantitative geography?

Quantitative geography consists of one or more of the following activities: the analysis of numerical spatial data; the development of spatial theory; and the construction and testing of mathematical models of spatial processes. The goal of all these activities is to add to our understanding of spatial processes. This can be done directly, as in the case of spatial choice modelling (Chapter 9) where mathematical models are derived based on theories of how individuals make choices from a set of spatial alternatives. Or, it can be done indirectly, as in the analysis of spatial point patterns (Chapter 6), from which a spatial process might be inferred.

It would perhaps be difficult to claim that the field of quantitative geography is sustained by any deep-rooted philosophical stance or any political agenda. For most of its practitioners, the use of quantitative techniques stems from a simple belief that in many situations, numerical data analysis or quantitative theoretical reasoning provides an efficient and generally reliable means of obtaining knowledge about spatial processes. Whilst it is recognized that various criticisms can be levelled at this approach (and quantitative researchers are often their own sternest critics), it is also recognized that no alternative approach is free of criticism and none comes close to providing the level of information on spatial processes obtained from the quantitative analysis of spatial data. The objective of most studies in quantitative geography is therefore not to produce a flawless piece of research (since in most cases, especially when dealing with social science data, this is impossible), but rather it is to maximize knowledge on spatial processes with the minimum of error. The appropriate question to ask of quantitative research therefore is ‘How useful is it?’ and not ‘Is it completely free of error?’. This does not mean that error is to be ignored. Indeed, the ability to assess error is an important part of many quantitative studies and is obviously a necessary component in determining the utility of an analysis. It does imply, however, that studies can be useful even though they might be subject to criticism.

It might be tempting to label all quantitative geographers as positivists or naturalists (Graham, 1997) but this disguises some important differences in philosophy across the protagonists of quantitative geography. For example, just as some quantitative geographers believe in a ‘geography is physics’ approach (naturalism) which involves a search for global ‘laws’ and global relationships, others recognize that there are possibly no such entities. They concentrate on examining variations in relationships over space through what are known as ‘local’ forms of analysis (Fotheringham, 1998; Fotheringham and Brunsdon, 1999; see also Chapters 5 and 6). This division of belief is perhaps quite strongly correlated with subject matter. Quantitative physical geographers, because their investigations are more likely to involve predictable processes, tend to adopt a naturalist viewpoint more frequently than their human geography counterparts. In human geography, where the subject matter is typically clouded by human idiosyncrasies, measurement problems and uncertainty, the search is not generally for hard evidence that global ‘laws’ of human behaviour exist. Rather, the emphasis of quantitative analysis in human geography is to accrue sufficient evidence which makes the adoption of a particular line of thought compelling. As Bradley and Schaefer (1998, p. 71) note in discussing differences between social and natural scientists:

the social scientist is more like Sherlock Holmes, carefully gathering data to investigate unique events over which he had no control. Visions of a positive social science and a ‘social physics’ are unattainable, because so many social phenomena do not satisfy the assumptions of empirical science. This does not mean that scientific techniques, such as careful observation, measurement, and inference ought to be rejected in the social sciences. Rather, the social scientist must be constantly vigilant about whether the situation being studied can be modeled to fit the assumptions of science without grossly misrepresenting it. . . . Thus, the standard of persuasiveness in the social sciences is different from that of the natural sciences. The standard is the compelling explanation that takes all of the data into account and explicitly involves interpretation rather than controlled experiment. The goals of investigation are also different – the creation of such compelling explanations rather than the formation of nomothetic laws.

As well as being less concerned with the search for global laws than some might imagine, quantitative geography is not as sterile as some would argue in terms of understanding and modelling human feelings and psychological processes (Graham, 1997). Current research, for example, in spatial interaction modelling emphasizes the psychological and cognitive processes underlying spatial choice and how we think about space (see Chapter 9). Other research provides information on issues such as the effects of race on shopping patterns (Fotheringham and Trew, 1993) and gender on migration (Atkins and Fotheringham, 1999). There appears to be a strong undercurrent of thought amongst those who are not fully aware of the nuances of current quantitative geography that it is deficient in its treatment of human influences on spatial behaviour and spatial processes. While there is some validity in this view, quantitative geographers increasingly recognize that spatial patterns resulting from human decisions need to account for aspects of human decision-making processes. This is exemplified by the current interest in spatial information processing strategies and the linking of spatial cognition with spatial choice (see Chapter 9). It should also be borne in mind that the actions of humans in aggregate often result from two types of determinants which mitigate against the need to consider every aspect of human behaviour. There are those, such as the deterrence of distance in spatial movement, which can be quantified and applied to groups of similar individuals; and those, such as shopping at a store because of knowing someone who works there, which are highly idiosyncratic and very difficult to quantify. One of the strengths of a quantitative approach is that it enables the measurement of the determinants that can be measured (and in many cases these provide very useful and very practical information for real-world decision making) whilst recognizing that for various reasons, these measurements might be subject to some uncertainty. This recognition of the role of uncertainty is often more important in the applications of quantitative techniques to human geography than to physical geography and makes the former in some ways more challenging and at the same time more receptive to innovative ideas about how to handle this uncertainty.

To some extent the above comments ca...

Table of contents

• Cover Page
• Title Page
• Copyright Page
• Contents
• Preface
• 1 Establishing the Boundaries
• 2 Spatial Data
• 3 The Role of Geographical Information Systems
• 4 Exploring Spatial Data Visually
• 5 Local Analysis
• 6 Point Pattern Analysis
• 7 Spatial Regression and Geostatistical Models
• 8 Statistical Inference for Spatial Data
• 9 Spatial Modelling and the Evolution of Spatial Theory
• 10 Challenges in Spatial Data Analysis
• Bibliography
• Index