# Spatial Science - an overview (2022)

## Geography

R.J. Johnston, in , 2001

### 3.1 Spatial Science

Spatial science remains a substantial component of contemporary human geography. It is strongly quantitative, but the formal (geometrical) location theories based on a single causal variable (space) have largely been abandoned: the search for spatial order neither anticipates the discovery of regular structures nor seeks universal laws of spatial behavior. Sayer (1984) drew an important distinction between extensive and intensive research: the former seeks empirical regularities whereas the latter explores the causal chains responsible for particular outcomes. Much spatial science is extensive research, a necessary precursor to many detailed investigations; by not eschewing empirical generalisations, it identifies significant features and trends in the mass of numerical data which characterize modern societies.

In the 1950s–1970s geographers assumed that standard statistical procedures could be applied unproblematically to analyses of point, line, flow, and area patterns. This was challenged by work on spatial autocorrelation, which identified a range of problems and proposed new methods of spatial data analysis (e.g. Haining 1990). Other issues identified included the modifiable areal unit problem. Some geographical analyses study the characteristics of populations aggregated by areas (such as census administrative units), but there is an extremely large number of ways in which such places can be defined, involving both scale (how large are the areas?) and aggregation (how many different ways can areas of the same size be created?) effects. Openshaw (1983) showed that different aggregations can produce divergent statistical results, creating problems in deciding which to employ. There are also related geographical examples of ecological fallacies—assumptions that results for a particular dataset can be generalized to others at different scales and/or aggregations (including individuals). Various procedures for attacking these problems and providing robust solutions are exemplified by essays in Longley and Batty (1996), many significantly assisted by developments in computing power (including applications of artificial intelligence) and stimulating the conception of geocomputation to describe such work in both physical and human geography (Longley et al. 1998).

The most significant technological developments have been in geographical information systems (GIS: Longley et al. 1999), combined hardware and software for the organization, integration, analysis, and display of spatially-referenced data, with the powerful display media underpinning the growth of visualization strategies. These systems have revolutionized spatial analysis and led to the identification of a geographical information science: traditional studies can be undertaken much more readily and quickly; exploratory studies are increasingly feasible, and large-scale modeling strategies integrating datasets collected on different spatial templates made possible.

Much contemporary spatial science, including GIS, is applied in a wide range of public and private sector contexts—as in spatially-targeted niche marketing strategies based on small-area classifications (geodemographics). This has partly been in response to changes in the economic context for universities: the pressure to increase nonstate income has stimulated ‘applied research’ and has seen the development of such skills as a major selling point in the attraction of students to read for geography degrees (see NRC 1997).

View chapterPurchase book

URL:

https://www.sciencedirect.com/science/article/pii/B0080430767024700

## Postmodernism in Geography

E.W. Soja, in , 2001

### 1 The Postmodern Turn in Geography

Postmodernism entered geography as an offshoot and extension of critical responses to the positivist ‘spatial science’ paradigm that began to dominate the discipline in the 1960s. These critical responses took two major forms. A radical or Marxist Geography consolidated in the 1970s as a critique of prevailing modes of explanation in spatial science and as a means of making geography more socially and political relevant. Rather than focusing primarily on statistically measurable surface appearances and searching for empirical regularities based on the frictions of distance and spatial covariation, how one geographical pattern or distribution correlates with another, Marxist geographers analyzed and explained what they called specific geographies as socially constructed outcomes of underlying processes such as class formation and capitalist accumulation. This carried with it a strong emphasis on structural explanation of geographical phenomena (see Structuralism) and gave rise to a specifically geographical (urban, regional, international, ecological) political economy perspective that would influence the discipline significantly in subsequent years.

The second stream of critical response, developing initially as Humanistic Geography, also concentrated on alternative modes of explanation, but emphasized the role of human agency and subjectivity much more than the effects of powerful structuring forces emanating either from society or the environment (Ley and Samuels 1978). Drawing on phenomenology, existentialism, and hermeneutics as well as traditional forms of cultural geography and landscape analysis, these geographical humanists were less concerned with space and political economy than with place, nature–society relations, and the interpretation of cultural landscapes. Continuing long-established links with anthropology, this reinvigorated form of Cultural Geography would also influence the development of postpositivist critical human geography over the next several decades as an important countercurrent to the Marxist critique.

By the early 1980s, the spatial science paradigm had passed its peak of influence and many new approaches were entering geography, each competing to define the leading edge of postpositivist research. At the same time, significant critiques were developing both within and between Marxist and humanistic geography (and within spatial science as well), adding further to the proliferation of new perspectives. Perhaps the most challenging critiques came from feminist geographers, who saw an exploitative and demeaning masculinism inherent in every branch of what would be labeled modern geography. This patriarchal order was not only expressed in the workplace (e.g., in university privileges, hiring, salaries) but also in the very practice of geography, whether theoretical or empirical, positivist, Marxist, or Humanist. The feminist critique echoed on a broader platform many other concerns over what was perceived as an excessive narrowing of perspectives affecting and constraining the development of (modern) critical human geography. It was in this atmosphere of increasing epistemological fragmentation and escalating internal critique of modern geographical practices that postmodernism first entered the disciplinary discourse.

(Video) Week 1a: What is spatial analysis? (Introduction to Spatial Data Science)

The deepest divisions within postpositivist geography revolved around traditional philosophical dichotomies or binary oppositions: Subject–Object, Idealism–Materialism, Agency–Structure. Their particular expression, however, took the form of an opposition between approaches that emphasized spatial political economy vs. those that stressed place-based culture. In the late 1970s, there had been some efforts to bring these opposing positions together, most notably in the writings of Derek Gregory. Influenced by the social theorist Anthony Giddens, also then at Cambridge University, Gregory (1978) argued for a critical synthesis of ‘structural’ and ‘reflexive’ approaches to geographical explanation that would go beyond their traditional antagonism to create a new, socially and politically ‘committed’ critical human geography. Gregory was one of the first geographers to recognize the potential relevance of postmodern and closely associated poststructuralist debates to achieving this goal, and for the next two decades would be a leading voice in adding a postmodern, poststructuralist, and, later, postcolonial perspective to geographical research, theory, and teaching (Gregory and Walford 1989, Gregory 1994).

In addition to the influence of Gregory's work and the growing impact on geography of Giddens's structuration theory, there were other developments in the early 1980s that attempted to overcome the divisions and fragmentation of postpositivist geography by at least in part introducing some aspects of the postmodern and poststructuralist critiques (Olsson 1980). In retrospect, however, the key turning point in the postmodernization of geography came from outside the discipline, with the publication (in 1984) of Fredric Jameson's Postmodernism, or the Cultural Logic of Late Capitalism. Jameson, a widely recognized Marxist literary critic and cultural studies scholar, had recently become interested in continental European theories of space, place, and architecture, and especially in the work of the French philosopher and urbanist Henri Lefebvre. Then teaching in the History of Consciousness program at the University of California-Santa Cruz, Jameson had organized a lecture tour by Lefebvre in the previous year and hosted his stay as visiting professor at Santa Cruz in 1984.

While he saw architecture as the ‘privileged’ language of postmodernism, Jameson was aware of the new developments in critical human geography and gathered a group of geographers, urbanists, and architects, mainly from California, at a conference to celebrate Lefebvre's creative spatial theories. When the article appeared, presenting a postmodern and explicitly spatial critique that effectively bridged Marxist political economy and critical cultural studies, innovatively interpreting emerging forms of contemporary urban geography, and calling for a new ‘political esthetic’ based on what Jameson termed a ‘cognitive mapping’ of ‘postmodern hyperspace,’ its effect on geography was particularly powerful.

The impact was especially intense among geographers working in California and, in particular, in Los Angeles, from whose geography Jameson drew some of his most imaginative examples and where there already existed one of the largest clusters of critical human geographers in the US. In the ensuing years, the geography and the geographers of Los Angeles would play a leading role in defining postmodernism and extending its impact on the discipline.

View chapterPurchase book

URL:

https://www.sciencedirect.com/science/article/pii/B0080430767025055

## Time–Space in Geography

D.G. Janelle, in , 2001

Debates about the nature of time and space in geography are closely allied with the discipline's changing philosophical perspectives. The operational viewpoint of descriptive regional geography, a dominant theme prior to the 1960s, separated space from time. The more staunch advocates of geography's spatial-science paradigm in the 1960s accorded special significance to space over time. However, analytical geography's growing emphasis on predictive models resulted in a more deliberate focus on the importance of the time dimension. Thus, the integration of time with space, as time–space, was recognized explicitly in attempts to forecast landscape changes through models of time–space diffusion and through simulation of complex human processes, including land use succession and migration behavior, and the development of settlement and transportation systems. The deliberate focus on time–space as a single construct of reality gained acceptance in the 1960s with the advent of concepts such as time–space convergence and divergence, and time geography. Later constructs regarding human extensibility in time–space, time–space distanciation, and time–space compression provided a more firm grounding for time–space perspectives in theories of structuration, critical science, and capitalism. More recently, advances in graphical visualization and dynamic cartography are opening new possibilities for an expanded role for time–space analysis in geographical discourse.

URL:

https://www.sciencedirect.com/science/article/pii/B0080430767024803

## Region: Geographical

M.B. Pudup, in , 2001

(Video) Spatial Science

### 2.2 The Region is Dead! Long Live the Region!

By the 1960s, many geographers openly questioned whether the region could any longer provide an integrative framework of study. The criticism leveled at regional geography was often upsparing, as when Peter Gould characterized it as ‘shabby, parochial, and unintelligent’ (cited in Johnston 1991, p. 40) and easily caricatured. Gould's comments contributed to a wider assault on regional geography by a new generation of geographers seeking to redefine the discipline as a spatial science. Through the very real weaknesses of the traditional regional approach, and the sheer hubris of geography's so-called young turks (such as Gould), spatial analysis decisively eclipsed regional synthesis as the discipline's heart and soul. Suddenly the strenuous disagreements about particularism and areal classification sounded oddly antiquarian compared with the clarion and oh-so-modern call of the quantitative revolution.

Amidst this upheaval, regional geography did not vanish. Quantitative methods lent the Hartshornian region something of a new lease on life. Those working in the Sauerian tradition simply ignored the spatial science gold rush and continued advocating their cultural landscape approach in what became something of a lively, though curious, intellectual backwater. But the region generated little in the way of theoretical or methodological debate until the late 1970s. By that time, the euphoria surrounding spatial science had run its course and quantification was finally understood as a tool, albeit a powerful one, rather than geography's raison d'être. A new methodological pluralism overtook geography and the region once again began inspiring fierce discussion and debate—the news of its death having been vastly overstated.

The 1980s witnessed a resurgence of interest in regional geography emanating from two disparate sources (Pudup 1988). The first was practitioners of traditional regional geography who shared an unwavering belief that geography's modus vivendi remained regional synthesis. Emblematic of the revivified tradition was the election of two of its chief contemporary practitioners, John Fraser Hart and Peirce Lewis, to the Presidency of the Association of American Geographers (AAG) during the 1980s. Both used their AAG presidential addresses to celebrate traditional regional approaches. Hart called regional geography ‘the highest form of the geographer's art’ and the discipline's long neglected unifying theme: ‘I know of no other theme that is even remotely so satisfying as the idea of the region. All of the different strands of geography converge when we try to understand regions, and we need the concept of the region in order to understand why we need the diverse and variegated systematic sub-fields of geography.’ (Hart 1982, p. 18). Three years later, Peirce Lewis echoed Hart's sentiment in another spirited defense of synthetic description which he considered ‘a kind of rough and ready definition of geography: describing the earth's surface and trying to make sense of it.’ (Lewis 1985, p. 47).

Such ‘back to basics’ calls could be dismissed as pure nostalgia were it not for the equally spirited discussions about regions arising from a very different quarter—geographers who sought to rehabilitate the concept and create a ‘reconstructed regional geography.’ The new regional scholarship was pioneered, perhaps unsurprisingly, by a generational changing of the guard. Skeptical about both spatial science and regional synthesis, geographers coming of age in the 1980s brought to the study of regions a deep engagement with theoretical debates and philosophical discussions ranging across the social sciences (Thrift 1983). They also brought to the study of regions a consciousness borne from being living witnesses to dramatic changes wrought by globalization (Massey 1995, Allen et al. 1998, Storper 1997).

The study of regions underwent a profound transformation. Regions ceased to be a topic interesting chiefly to geographers and historians and became an object of fascination in mainstream social sciences. Economists, political scientists, sociologists and, of course, geographers began asserting ‘that the region might be a fundamental basis of economic and social life “after mass production.”’ That is, since new successful forms of production—different from the canonical mass production systems of the postwar period—were emerging in some regions and not others, and since they seemed to involve both localization and regional differences and specificities (institutional, technological), it followed that there might be something fundamental that linked late 20th century capitalism to regionalism and regionalization’ (Storper 1997, p. 3). The apparent fin de siècle tendency toward regionalization of economic and social life, in places like ‘the third Italy,’ Baden-Wurttemburg, and Silicon Valley, was wildly at odds with post-World War II era expectations of global integration and homogeneity. The global village seemed to be giving way to a world of regions.

View chapterPurchase book

URL:

https://www.sciencedirect.com/science/article/pii/B008043076702475X

## Western European Studies: Geography

R. Hudson, in , 2001

### 1 The Changing Discipline of Human Geography

This section presents a brief history of geographical thought in order to situate the approaches that human geographers have developed in studying Western Europe (for a fuller history, see Johnston 1991). During the nineteenth century, geography in Western Europe sought to describe and explain the spatial distributions of the natural world and of people and their activities. However, association between strong strands of environmental determinism that sought to explain human characteristics in terms of natural environmental conditions, exemplified by the work of Ellen Semple, and the politically discredited doctrine of Lebensraum in Nazi Germany, produced a shift from explanatory concerns to regional description. While there were variations between national ‘schools,’ with the French under the influence of Paul Vidal de la Blache most powerfully exemplifying the regional descriptive approach, there was also a degree of commonality of approach to geographical scholarship across Western Europe.

Then, in the 1960s, influenced by earlier developments in North America summarized as the ‘quantitative’ and ‘conceptual’ revolutions, human geography in Western Europe began to be redefined. The emphasis switched to spatial science and explanation of generalized spatial patterns, drawing on ideas from neoclassical economics, and from qualitative regional description to quantitative—especially statistical—analysis of spatial patterns. Initially ‘revolution’ was concentrated in a few Departments in the UK and Sweden. From there, it diffused to other parts of Western Europe. These changes were contested, however. Much Western European geography retained a strong interest in the uniqueness of places, a focus that later re-emerged, albeit in a modified way. It soon became clear that spatial science had major limitations. Initially, behavioral geographers in Western Europe, as in North America, responded to these by seeking more realistic assumptions about the knowledge and motives that underlay peoples' spatial behaviors (Pred 1967). This did little to remedy the explanatory weaknesses, however. Consequently, human geographers sought stronger explanations grounded in more powerful abstractions of the processes that generated spatial patterns. As a result, Marxian and neoMarxian political economy soon became the focal point of ‘critical’ geography within Western Europe (Carney et al. 1980) and more generally (Harvey 1982). However, there were again strong counter-pressures, with humanistic geography (Ley and Samuels 1978) emphasizing human agency, meaning, intentionality, and individual life-worlds, rather than the unfolding structural logic of capital in explaining spatial variations in human activity.

Around the late 1970s, however, some important changes emerged in the social sciences, with implications for theory and practice in human geography and the ways in which Europe was studied. As a result, human geography in Western Europe became a pluralist discipline, encompassing many epistemological positions and substantive focuses, with strong links to cognate social sciences. Most importantly, there was an elaboration of seminal ideas about the centrality of space to social and economic life and growing recognition of the significance of spatiality in many of the social sciences. This generated a constructive dialogue within Western Europe across national and disciplinary boundaries. It involved social scientists seeking to infuse their theories with spatial sensitivity, and geographers (such as Massey 1984) exploring relations between social process and spatial form. ‘The difference space makes’ to the constitution of societies, and the ways in which economic, social, and political processes operate within the structural limits that define capitalist economies, became cross-disciplinary research frontiers.

There was growing recognition that relationships between social processes and spatial forms are reciprocal, contingent, and indeterminate. This led to exploration of the ways in which such relationships actually do evolve and the spatiotemporally variable forms that they take, directing attention to the institutions through which societies and their geographies are constituted and reproduced. The prime focus of concern became middle-level theories and concepts as human geography underwent an ‘institutional turn.’ Linked to this, poststructural approaches resulted in greater sensitivity to the limitations of, and absences from, metanarratives. This was associated with a broader ‘cultural turn’ in human geography and the social sciences, and heightened awareness of cultural variation in the ways in which capitalist societies are constituted and of the variable meanings that people, places, and events can assume because of this (Hudson 2001).

Paralleling developments of the 1980s in terms of sociospatial relationships, in the 1990s the social sciences in Western Europe increasingly acknowledged the significance of connections between the social and natural worlds in understanding societies and their geographies. As such, another ‘traditional’ geographical concern was given a new twist and became central to broader social science debates. One consequence of this was growing interest in Actor–Network theories, which seek to bridge the divide between social and natural worlds and explore how human subjects and nonhuman objects become contingently linked in networks in particular time/space contexts (Thrift 1996).

These growing concerns with relationships between society, space, and nature coalesced in debates about processes of globalization, links between ‘the global and the local’ and their impacts on and in Europe (Amin and Thrift 1994). This led to recognition that changes at ‘global’ and ‘local’ levels are reciprocal and complex rather than simply one-way and one-directional. While processes of globalization influence ‘local’ change in Europe, those processes are affected by ‘local’ place-specific effects in Europe (from the formation of the European Union to local social movements protesting about environmental pollution or cultural destruction). Some see ‘globalization’ as homogenizing, eliminating differences between places under the relentless pressures of capital accumulation and technological advances in transport, information technology, and telecommunications as the world of places dissolves into a world of flows (Castells 1996). In contrast, human geographers in Europe have conceptualized it as a complex interplay of processes that both link and help define varying spatial scales in a complex mosaic. Globalization is seen as the latest phase of combined and uneven development, enhancing the distinctiveness of places and their importance in the contemporary world.

View chapterPurchase book

URL:

https://www.sciencedirect.com/science/article/pii/B0080430767032526

(Video) Spatial Data Science Overview

## GIS Methods and Techniques

Xinyue Ye, in Comprehensive Geographic Information Systems, 2018

### 1.05.3 Open Source GIS

The Free and Open Source Software for Geospatial Conference has been playing a pivotal role in promoting the open science in software development. Open source GIS is gaining growing market shares in academia, business, and public administration. This recognition came at a time when many open source programming and scripting languages such as Python and R are starting to make major inroads in geospatial data production, analysis, and mapping (Ye and Rey, 2013). As a consequence, open source software development has been a crucial element in the GIS community’s engagement with open GIS and the most well-developed aspect of open GIS (Rey, 2009). The availability and widespread use of codes and tools to support more robust data analysis will play a critical role in the adoption of new perspectives and ideas across the spatial sciences. The openness to scrutiny and challenge underlies the open source GIS movement through the release of the source code, which has subsequently influenced software functionality and support (Neteler and Mitasova, 2008). Users have the freedom to access, modify, and distribute the source code based on licensing agreements such as MPL, MIT, Apache, GPL, and BSD. Making source code both legally and technically open is the very first step of being promoted as a public good (Rey and Ye, 2010). In particular, scientists could benefit from the open source code, which would reduce code duplication and free up additional developer time to enhance the respective applications (Rey, 2009). Bonaccorsi and Rossi (2003) argued that “when programmers are allowed to work freely on the source code of a program, this will inevitably be improved because collaboration helps to correct errors and enables adaptation to different needs and hardware platforms”. The credibility of research findings tends to be higher for papers with the available code. Third-party researchers might be more likely to adopt such papers as the foundation of additional research. In addition, coding repository platforms such as GitHub and BitBucket are making this open source tide stronger. Links from code to a paper might enhance the search frequencies of the paper because of accelerated awareness of the methods and findings.

The dramatic improvement in computer technology and the availability of large-volume geographically referenced data have enabled the spatial analytical tools to move from the fringes to central positions of methodological domains. By and large, however, many existing advanced spatial analysis methods are not in the open source context. The open source and free approach offer unprecedented opportunities and the most effective solution for developing software packages through attracting both users and developers. Instead of reinventing the wheel, we can study how the program works, to adapt it, and to redistribute copies including modifications from a number of popular alternatives. Anselin (2010) emphasized the role of the open source software movement in stimulating new development, transcending disciplinary boundaries, and broadening the community of developers and adopters. With accelerated development cycle, open source tools can give GIS users more flexibility to meet the user community needs that are only bound by our imaginations, which are aligned with more efficient and effective scientific progress. New theories and novel practices can thus be developed beyond narrowly defined disciplinary boundaries (Sui, 2014). Regarding open source efforts on spatial analysis, Arribas-Bel (2014) argued, “the traditional creativity that applied researchers (geographers, economists, etc.) have developed to measure and quantify urban phenomena in contexts where data were scarce is being given a whole new field of action”. Sui (2014) also noted that a hybrid model integrating both open/free paradigm and proprietary practices (copyright and patent, IP stuff) would be the most realistic option and promising route to move GIS forward. Open source GIS can facilitate the interdisciplinary research due to “the collaborative norms involving positive spillover effects in building a community of scholars” (Rey, 2009; Ye etal., 2014).

During the past several decades, burgeoning efforts have been witnessed on the development and implementation of spatial statistical analysis packages, which continue to be an active area of research (Rey and Anselin, 2006; Anselin, 2010). The history of open source movement is much younger, but its impact on GIS world is impressive (Rey, 2009). As Rey (2009) commented, “a tenet of the free software (open source) movement is that because source code is fundamental to the development of the field of computer science, having freely available source code is a necessity for the innovation and progress of the field”. The development of open source packages has been boosted. However, many duplicates and gaps in the methodological development have also been witnessed. The open source toolkit development is community-based with developers as well as casual and expert users located everywhere. Through the use of an online source code repository and mailing lists, users and developers can virtually communicate to review the existing code and develop new methods. However, Tsou and Smith (2011, p. 2) argued that “open source software is not well adopted in GIS education due to the lack of user-friendly guidance and the full integration of GIS learning resources”. Some representative open source desktop GIS software packages include KOSMO, gvSIG, uDig, Quantum GIS (QGIS), Geographic Resource Analysis Support System (GRASS), and so on. KOSMO was implemented using the Java programming language based on the OpenJUMP platform and free code libraries. Developed by the European GIS community offering multiple language user interfaces, gvSIG is known for having a user-friendly interface, being able to access a wide range of vector and raster formats. Built upon IBM’s Eclipse platform, uDig (user-friendly desktop Internet GIS) is an open source (EPL and BSD) desktop application framework. QGIS integrates with other open source GIS packages such as PostGIS, GRASS GIS, and MapServer, along with plugins being written in Python or C++. As a founding member of the Open Source Geospatial Foundation (OSGeo), GRASS offers comprehensive GIS functions for data management, image processing, cartography, spatial modeling, and visualization.

View chapterPurchase book

URL:

https://www.sciencedirect.com/science/article/pii/B9780124095489095920

## GIS Applications for Socio-Economics and Humanity

Daniel A. Griffith, Yongwan Chun, in Comprehensive Geographic Information Systems, 2018

### 3.01.4.2 Spatially Varying Coefficient Models

Spatial heterogeneity, along with spatial dependency, is a common characteristic of spatial data. It generally refers to a diversified mixture of spatial process outcomes or events, which relates to intensity of a spatial phenomenon. In spatial data modeling, heterogeneity often relates to structural instability in space in the form of varying coefficients or different functional descriptions (Anselin and Griffith, 1988). The spatial expansion model (Cassetti, 1972, 1997) furnishes a method to model spatial heterogeneity by introducing spatially explicit variables in a regression model: for example, x, y coordinates of spatial units (often centroids of areal units). Although the spatial expansion method furnishes a classical technique to capture spatial heterogeneity, more recent approaches focus on spatially varying coefficient models, which allow a specification of different relationships between a dependent variable and covariates in space. GWR (Fotheringham etal., 2003) provides one method to investigate spatially varying coefficients by extending local regression to a geographical context. ESFs furnished another method for specifying spatially varying coefficients (Griffith, 2008; Hughes and Haran, 2013; Helbich and Griffith, 2016), whereas Bayesian approaches have been developed in statistics (Gelfand etal., 2003; Wheeler and Waller, 2009) to achieve this end. This section presents a discussion of spatially varying coefficients in terms of GWR and ESF specifications.

GWR is a local regression method that specifies weights with local kernels; its linear regression equation can be written as

${y}_{i}=\sum _{j=1}^{p}{x}_{ij}{\beta }_{ij}+{\varepsilon }_{i}\text{,}$

where yi denotes the value of the dependent variable at location i, xij denotes the value of the jth independent variable for location i, βij denotes a location-specific coefficient corresponding to xij, and ɛi denotes a random error at location i. The coefficient estimators of GWR can be expressed as

${\stackrel{ˆ}{\beta }}_{i}={\left({\mathbf{X}}^{\mathrm{T}}{\mathbf{G}}_{i}\mathbf{X}\right)}^{-1}{\mathbf{X}}^{\mathrm{T}}{\mathbf{G}}_{i}\mathbf{Y}\text{,}$

where Gi is a matrix of location-specific weights. This weights matrix is a diagonal matrix whose diagonal elements, (gi1, gi2, gi3, …, gin), represent weights for each observation used to estimate a local parameter at its location i. These weights commonly are specified with a kernel function that yields greater weights for observations nearby location i, with these weights declining for observations at increasing distances from i. A bi-square kernel function produces a weight that is defined as

(Video) Spatial regression overview

${g}_{ik}=\left\{\begin{array}{c}\hfill {\left[1-{\left({d}_{ik}/h\right)}^{2}\right]}^{2}\phantom{\rule{0ex}{0ex}}\mathrm{if}\phantom{\rule{0ex}{0ex}}{d}_{ik}

where h is a bandwidth. When dik is larger than the bandwidth h, the weight becomes zero: observations with zero weights effectively are excluded from the estimation of coefficients (Brunsdon etal., 1998). These weights also can be assigned employing a fixed distance or an adaptive bandwidth. The bandwidth of a kernel can be estimated with two different methods. One is cross-validation, which iteratively finds a bandwidth by minimizing cross-validation errors. The other is minimization of the AIC for GWR.

Although GWR is widely used in spatial science research, a number of its potential weaknesses are reported in the literature. One issue is correlation between GWR estimates (Wheeler and Tiefelsdorf, 2005). Specifically, strong correlation or dependency makes the separation of effects of individual variables from the other variables difficult. Páez etal. (2011) discuss that GWR can be sensitive to multicollinearity, especially when a sample size is small. To remedy the multicollinearity issue, two extended approaches are proposed: ridge regression (Wheeler, 2007) and lasso regression (Wheeler, 2009). Fotheringham and Oshan (2016) claim, based on a simulation study with 2500 spatial units, that GWR is robust to the multicollinearity issue when the sample size is large enough. Their claim is consistent with some about multicollinearity in conventional linear regression analysis (Dormann etal., 2013).

Fig.5 portrays the estimated linear regression coefficients for the GRW model with the same variables as the linear regression summarized in Table2, using ArcGIS version 10.1 and an AIC-based bandwidth selection criterion. That is, the dependent variable is the density of out-relocation people, and the two independent variables are ROR and ALV. The estimated ROR coefficients are high for the spatial units in the eastern, and low for those in the western, parts of the metropolitan area. The estimated ALV coefficients are low for the spatial units at the center of the metropolitan area. Most of these low values are within the boundaries of Seoul. In contrast, the estimated AVL coefficients are high around the edge of the Seoul metropolitan area. This nonconstant relationship for AVL may be explained by the ALVs being higher within rather than outside of the city. These two maps show that the relationship between each individual variable and the dependent variable is not constant across the study area. The R2 of the GWR model is 0.5274, which is larger than that of its global linear regression counterpart, but smaller than that for a spatial regression model accounting for spatial autocorrelation in the data.

In its original conceptualization, ESF furnishes a specification that includes a spatially varying intercept term coupled with global regression coefficients for covariates. Griffith (2008) extends ESF to a complete spatially varying coefficients model specification. In its original form, ESF is a method to account for spatial autocorrelation in regression models by isolating spatial components from the nonspatial random error term (Griffith, 2003). This method utilizes eigenvectors extracted from the following transformed spatial weights matrix:

$\left(\mathbf{I}-\frac{\mathbf{1}{\mathbf{1}}^{\mathrm{T}}}{n}\right)\mathbf{C}\left(\mathbf{I}-\frac{\mathbf{1}{\mathbf{1}}^{\mathrm{T}}}{n}\right)$

where 1 is a vector of ones. These eigenvectors are mutually orthogonal and uncorrelated, and, furthermore, represent latent spatially autocorrelated patterns when they are mapped with the spatial tessellations from which the spatial weights matrix is generated (Tiefelsdorf and Boots, 1995; Griffith, 1996b; Tiefelsdorf and Griffith, 2007). ESF introduces a set of these eigenvectors as independent variables in a regression model, with these eigenvectors capturing unexplained spatial components. Hence, ESF allows the estimation of a linear regression model with standard estimation methods (i.e., OLS for linear regression), in the presence of spatial autocorrelation, but without suffering from spatial autocorrelation’s ill effects. A small set of eigenvectors can be selected with a stepwise regression technique from a candidate eigenvector set, which is a reduced subset from the full set of n eigenvectors.

The ESF-based spatially varying coefficients model specification contains statistical interaction terms between the selected eigenvectors and the independent variables (Griffith, 2008) included in a spatial analysis. It may be written as

$\mathbf{Y}=\left({\beta }_{0}1+\sum _{{k}_{0}=1}^{{K}_{0}}{\mathbf{E}}_{{k}_{0}}{\beta }_{{k}_{0}}\right)+\sum _{p=1}^{P}\left({\beta }_{p}1+\sum _{{k}_{p}=1}^{{K}_{0}}{\mathbf{E}}_{{k}_{p}}{\beta }_{{k}_{p}}\right)\circ {\mathbf{X}}_{p}+\mathbf{\epsilon }$

where Xp is a n-by-1 vector of the pth independent variable, ${\mathbf{E}}_{{k}_{p}}$ is the kp eigenvector, and $\circ$ denotes element-wise matrix multiplication (i.e., a Hadamard product). Here, β0 and βp are the global parameters for the intercept and the pth independent variable. The linear combination of the selected eigenvectors with estimated parameters, ${\sum }_{{k}_{0}=1}^{{K}_{0}}{\mathbf{E}}_{{k}_{0}}{\beta }_{{k}_{0}}$, constructs a spatially varying intercept around the global intercept parameter, and, similarly, ${\sum }_{{k}_{p}=1}^{{K}_{0}}{\mathbf{E}}_{{k}_{p}}\circ {\mathbf{X}}_{p}{\beta }_{{k}_{p}}$ constructs a spatially varying regression coefficient around the global regression coefficient for the pth independent variable. This model specification can be estimated with OLS. Helbich and Griffith (2016) emphasize that this ESF-based spatially varying coefficients model specification has two advantages. First, the coefficients vary around their respective global coefficient values. Second, multicollinearity among coefficients can be examined in terms of common eigenvectors.

Fig.6 portrays ESF-based spatially varying coefficients for the ROR and ALV variables. The map pattern of these coefficients has a local concentration compared with the GWR coefficients that show a metropolitan region-wide pattern (Fig.5). Because these maps are classified with the natural break option in ArcGIS, a direct comparison of patterns may not be meaningful. For the ROR coefficients (Fig.6A), two clusters (one comprising relatively high values, and the other comprising relatively low values) are conspicuous and positioned at the center of the Seoul metropolitan area. Other clusters are visible in the southwestern (high coefficients) and in the northern (low coefficients) parts of this metropolitan area. The global coefficient for ROR is 0.7008. The ALV map pattern exhibits two noticeable clusters (Fig.6B). A low values cluster appears at the center of the metropolitan area, and contains most of the spatial units within the boundaries of Seoul. The other cluster, containing high values, is located in the western part of the metropolitan area. Many spatial units have a coefficient essentially the same as (or close to) the global coefficient of 1.1655.

View chapterPurchase book

URL:

(Video) 01 Spatial Technology: Introduction

https://www.sciencedirect.com/science/article/pii/B9780124095489096809

## FAQs

### What is meant by spatial science? ›

Spatial Sciences can be roughly understood as any discipline dealing with the analysis and visualization of our lived environment. They encompass specific "spatial" disciplines such as geography, GIS (geographic information systems), cartography, urban planning, and architecture.

### Why is spatial science important? ›

The application of spatial research and data collection has a major influence on transport planning, construction, town planning, agriculture, aquaculture, property management, land management, the distribution of utilities and the extraction, processing and production of energy and raw materials.

### How geography is spatial science? ›

Geography is described as a spatial science because it focuses is on "where" things are and why they occur there. Geographers seek to answer all or more than one of four basic questions when studying our environment. These relate to location, place, spatial pattern, and spatial interaction.

### Is geography a science or an art what makes it a spatial science? ›

Above all else, geography is considered a spatial science. It is concerned with the spatial behavior of people, with the spatial relationships that are observed between places on the earth's surface, and with the spatial processes that create or maintain those behaviors and relationships.

### When did geography become a spatial science? ›

Spatial Science is an approach in the human geography, starting in the 1950's. Geographers in North America and Britain were convinced that geography could be treated as any other science.

### Who established geography as a spatial science? ›

The alteration towards modern geography as a “spatial science” set in some selected centres in the United States around mid 1950s. From there it chronologically stretched out in other parts of the world. John Weaver, Harold McCarty, Edward Ullman, William Bunge, and many others made notable contributions in this field.

### How is spatial data beneficial to studying environmental issues? ›

Historically, spatial analysis has contributed to addressing environmental problems in a myriad of ways, such as monitoring sea-level rise, identifying biodiversity loss, understanding vegetation changes, and spotting at-risk ecosystems.

### How is space related to science? ›

Scientific research in space can be divided into five general areas: (1) solar and space physics, including study of the magnetic and electromagnetic fields in space and the various energetic particles also present, with particular attention to their interactions with Earth, (2) exploration of the planets, moons, ...

### What does spatial mean in geography? ›

Spatial data is any type of data that directly or indirectly references a specific geographical area or location. Sometimes called geospatial data or geographic information, spatial data can also numerically represent a physical object in a geographic coordinate system.

### Why is hecataeus known as the father of geography? ›

Hecateaus gave a detailed account of the Mediterranean Sea, islands, straits, and described the general outline of all the countries of the world. It is the first systemic description of the world and because of this fact Hecataeus is known as the 'father of geography'.

### Why geography is called the mother of all sciences? ›

Answer: Geography is often times called the “mother of all sciences” because geography is one of the earliest known scientific disciplines that date back to the original Homo-sapiens who migrated out of eastern Africa, into Europe, Asia, and beyond.

### Is geography a hard subject? ›

No, geography is so simple to study. In geography, we studied day to day activities happen on the earth, those are interlinked to each other in practically as well as theoretically.

### Why geography is not a science? ›

Geographic Data Science is currently a community of practice of (data‐driven) Geography or Geoscience, and therefore not (yet) a distinct scientific discipline. GIScience, in contrast, is a distinct meta‐scientific discipline, that is, a discipline about (geographic information) methods.

### Why is geography called a science? ›

Geography is the science that studies the relationships among areas, natural systems, cultural activities and the interdependence of all these over space. Why is Geography unique among all disciplines? Its primary concern with how things are distributed on the earth's surface.

### What is the relationship between geography and natural science? ›

Geography stresses integration and interdependence between these spheres. In this sense it serves as a bridge between natural science and social science disciplines, with particular emphasis on studying the conditions required to support human life.

### What are the 3 types of geography? ›

There are three main strands of geography:
• Physical geography: nature and the effects it has on people and/or the environment.
• Human geography: concerned with people.
• Environmental geography: how people can harm or protect the environment.

### What are the two main types of geography? ›

Geography is often defined in terms of two branches: human geography and physical geography.

### What are the types of geography? ›

Geography is divided into two main branches: human geography and physical geography. There are additional branches in geography such as regional geography, cartography, and integrated geography (also known as environmental geography).

### What does spatial mean in geography? ›

Spatial data is any type of data that directly or indirectly references a specific geographical area or location. Sometimes called geospatial data or geographic information, spatial data can also numerically represent a physical object in a geographic coordinate system.

### How is space related to science? ›

Scientific research in space can be divided into five general areas: (1) solar and space physics, including study of the magnetic and electromagnetic fields in space and the various energetic particles also present, with particular attention to their interactions with Earth, (2) exploration of the planets, moons, ...

### Why geography is a science? ›

Geography is the science that studies the relationships among areas, natural systems, cultural activities and the interdependence of all these over space. Why is Geography unique among all disciplines? Its primary concern with how things are distributed on the earth's surface.

### What are examples of spatial? ›

Spatial skills are used in many areas of life. Some examples of spatial skills include packing a suitcase, interpreting graphs, creating a sculpture from a block of marble, landing a flip, navigating using a physical or mental map, merging into traffic, or brushing your hair.

### What are the 3 types of spatial distribution? ›

Spatial distribution can be measured as the density of the population in a given area. The three main types of population spatial distribution are uniform, clumped, and random. Examples of the types of spatial distribution: uniform, random, and clumped.

### What are spatial features? ›

The spatial attribute of a spatial feature is the geometric representation of its shape in some coordinate space. This is referred to as its geometry.

### What is the study of space science called? ›

Astronomy - The general field of natural science concerned with celestial objects including Solar System, Galactic and Extragalactic objects. Most of the enrolled students in the field work in this overarching area.

### How many branches of space science are there? ›

Space scientists can specialize in many different fields that relate to the study of space, planets and life in the universe, including astrophysics, biology, chemistry, geology, meteorology and physics.

### What is a space scientist called? ›

An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, moons, comets and galaxies – in either observational (by analyzing the data) or theoretical astronomy.

### What are the 3 types geography? ›

There are three main strands of geography:
• Physical geography: nature and the effects it has on people and/or the environment.
• Human geography: concerned with people.
• Environmental geography: how people can harm or protect the environment.

### Why geography is called the mother of all sciences? ›

Answer: Geography is often times called the “mother of all sciences” because geography is one of the earliest known scientific disciplines that date back to the original Homo-sapiens who migrated out of eastern Africa, into Europe, Asia, and beyond.

## Videos

1. Introduction to Spatial Information (2011)
(DOCskillable)
2. A Practical Introduction to GIS (Spatial Data Visualization and Analytics)
(Spatial Thoughts)
3. Spatial Sciences: Increasingly Important to Everyday Lives
(USC Dornsife College of Letters, Arts and Sciences)
4. Week 1b: Spatial data analysis (Introduction to Spatial Data Science)
(GeoDa Software)
5. What is Spatial Data Science?
(CARTO)
6. Study Spatial Science at Curtin
(Student Edge)

## Latest Posts

Article information

Author: Ray Christiansen

Last Updated: 08/27/2022

Views: 6323

Rating: 4.9 / 5 (69 voted)

Author information

Name: Ray Christiansen

Birthday: 1998-05-04

Address: Apt. 814 34339 Sauer Islands, Hirtheville, GA 02446-8771

Phone: +337636892828