Modelling spatial processes in quantitative human geography
TL;DR: In this paper, the authors discuss the nature of processes relating to human behaviour and how to model such processes when they vary over space, and describe the role of local modelling and how the bandwidth bandwidth is used.
Abstract: We discuss the nature of processes relating to human behaviour and how to model such processes when they vary over space. In so doing, we describe the role of local modelling and how the bandwidth ...
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TL;DR: This work argues that identification problems bedevil most applied spatial research and advocates an alternative approach based on the ‘experimental paradigm’ which puts issues of identification and causality at centre stage.
Abstract: We argue that identification problems bedevil most applied spatial research Spatial econometrics solves these problems by deriving estimators assuming that functional forms are known and by using model comparison techniques to let the data choose between competing specifications We argue that in most situations of interest this, at best, achieves only very weak identification Worse, in most cases, such an approach will simply be uninformative about the economic processes at work rendering much applied spatial econometric research ‘pointless’, unless the main aim is simply description of the data We advocate an alternative approach based on the ‘experimental paradigm’ which puts issues of identification and causality at centre stage
100 citations
TL;DR: In this paper , the authors examine the implications of thinking locally not only for modeling spatial processes but also more broadly in terms of our understanding of behavior in space, commenting on replicability and how local models can be used to measure previously unmeasurable place-based 'contextual' effects.
Abstract: Over the past two decades increasing focus has been given to local forms of spatial analysis, both in terms of descriptive statistics and spatial modeling. We term this “thinking locally” Fundamental to thinking locally is that a global approach to spatial analysis may not be suitable and that there may be situations where the conditioned relationships we want to measure vary over space. This paper examines the implications of thinking locally not only for modeling spatial processes but also more broadly in terms of our understanding of behavior in space. We begin with a brief survey of local statistical modeling and what might cause relationships to vary spatially and then describe the operation of one type of local modeling framework – that of (Multiscale) Geographically Weighted Regression – to demonstrate the basic concepts inherent in local models and the type of output that is generated by such models. We then examine the implications of a local approach to statistical analysis focussing on the role of local models compared to spatial regression models, diagnostics for local models, and how a local approach relates to issues of spatial scale which have plagued spatial analysis for decades. Attention is then turned to the implications of a local modeling approach to society, commenting on replicability and how local models can be used to measure previously unmeasurable place-based ‘contextual’ effects. We demonstrate the issues raised throughout the paper with an empirical example of house price determinants.
5 citations
TL;DR: In this paper , the authors examined bandwidth at a conceptual, operational and empirical level within the framework of geographically weighted regression, one of the more frequently employed local spatial models, and outlined how bandwidth relates to three characteristics of spatial processes: variation, dependence and strength.
Abstract: Abstract Models designed to capture spatially varying processes are now employed extensively in the social and environmental sciences. The main strength of such models is their ability to represent relationships that vary across locations through locally varying parameter estimates. However, local models of spatial processes also provide information on the nature of these spatially varying relationships through the estimation of a ‘bandwidth’ parameter. This paper examines bandwidth at a conceptual, operational and empirical level within the framework of geographically weighted regression, one of the more frequently employed local spatial models. We outline how bandwidth relates to three characteristics of spatial processes: variation, dependence and strength.
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TL;DR: In this paper, a new general class of local indicators of spatial association (LISA) is proposed, which allow for the decomposition of global indicators, such as Moran's I, into the contribution of each observation.
Abstract: The capabilities for visualization, rapid data retrieval, and manipulation in geographic information systems (GIS) have created the need for new techniques of exploratory data analysis that focus on the “spatial” aspects of the data. The identification of local patterns of spatial association is an important concern in this respect. In this paper, I outline a new general class of local indicators of spatial association (LISA) and show how they allow for the decomposition of global indicators, such as Moran's I, into the contribution of each observation. The LISA statistics serve two purposes. On one hand, they may be interpreted as indicators of local pockets of nonstationarity, or hot spots, similar to the Gi and G*i statistics of Getis and Ord (1992). On the other hand, they may be used to assess the influence of individual locations on the magnitude of the global statistic and to identify “outliers,” as in Anselin's Moran scatterplot (1993a). An initial evaluation of the properties of a LISA statistic is carried out for the local Moran, which is applied in a study of the spatial pattern of conflict for African countries and in a number of Monte Carlo simulations.
8,933 citations
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31 Aug 1988TL;DR: In this article, a typology of Spatial Econometric Models is presented, and the maximum likelihood approach to estimate and test Spatial Process Models is proposed, as well as alternative approaches to Inference in Spatial process models.
Abstract: 1: Introduction.- 2: The Scope of Spatial Econometrics.- 3: The Formal Expression of Spatial Effects.- 4: A Typology of Spatial Econometric Models.- 5: Spatial Stochastic Processes: Terminology and General Properties.- 6: The Maximum Likelihood Approach to Spatial Process Models.- 7: Alternative Approaches to Inference in Spatial Process Models.- 8: Spatial Dependence in Regression Error Terms.- 9: Spatial Heterogeneity.- 10: Models in Space and Time.- 11: Problem Areas in Estimation and Testing for Spatial Process Models.- 12: Operational Issues and Empirical Applications.- 13: Model Validation and Specification Tests in Spatial Econometric Models.- 14: Model Selection in Spatial Econometric Models.- 15: Conclusions.- References.
8,282 citations
"Modelling spatial processes in quan..." refers background in this paper
...…development of various forms of what became known as spatial regression models exemplified by that of a spatial error model shown in equation (2) (Anselin, 1988; Gibbons & Overman, 2012; Kelejian & Prucha, 1998, 1999; Lesage, 2016; LeSage & Pace, 2010). y ¼ β0 þ β1x1 þ β2x2 þ . . .þ βnxn þ λ Wð…...
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...…in process rather than form, came a focus on the development of models, particularly explicitly spatial models, such as spatial regression models (Anselin, 1988, 2002, 2009; Griffith & Csillag, 1993; Haining, 1993; Tiefelsdorf, 2000; Gelfand et al., 2003; Haining, 2003; Waller & Gotway, 2004;…...
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...…data values clustered was appealing and spurned a huge literature (Moran 1948, 1950; Whittle 1954; Matheron 1963; Paelinck and Klaassen 1979; Cliff and Ord 1981; Hubert, Golledge, and Costanzo 1981; Anselin 1988, 1995; Getis 1991; Getis and Ord 1992; Ord and Getis 1995, 2001; Griffith 2003)....
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TL;DR: A Computer Movie Simulating Urban Growth in the Detroit Region as discussed by the authors was made to simulate urban growth in the city of Detroit, Michigan, United States of America, 1970, 1970.
Abstract: (1970). A Computer Movie Simulating Urban Growth in the Detroit Region. Economic Geography: Vol. 46, PROCEEDINGS International Geographical Union Commission on Quantitative Methods, pp. 234-240.
7,533 citations
"Modelling spatial processes in quan..." refers background in this paper
...Around this time, human geography developed its first, and possibly only, ‘law’ which again focused on data – ‘everything is related to everything else, but near things are more related than distant things’ Tobler 1970....
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TL;DR: Two problems arising in the two and three-dimensional cases of stochastic phenomena which are distributed in space of two or more dimensions are considered.
Abstract: The study of stochastic processes has naturally led to the consideration of stochastic phenomena which are distributed in space of two or more dimensions. Such investigations are, for instance, of practical interest in connexion with problems concerning the distribution of soil fertility over a field or the relations between the velocities at different points in a turbulent fluid. A review of such work with many references has recently been given by Ghosh (1949) (see also Matern, 1947). In the present note I consider two problems arising in the twoand three-dimensional cases.
5,771 citations
TL;DR: In this article, a family of statistics, G, is introduced to evaluate the spatial association of a variable within a specified distance of a single point, and a comparison is made between a general G statistic and Moran's I for similar hypothetical and empirical conditions.
Abstract: Introduced in this paper is a family of statistics, G, that can be used as a measure of spatial association in a number of circumstances. The basic statistic is derived, its properties are identified, and its advantages explained. Several of the G statistics make it possible to evaluate the spatial association of a variable within a specified distance of a single point. A comparison is made between a general G statistic and Moran’s I for similar hypothetical and empirical conditions. The empirical work includes studies of sudden infant death syndrome by county in North Carolina and dwelling unit prices in metropolitan San Diego by zip-code districts. Results indicate that G statistics should be used in conjunction with I in order to identify characteristics of patterns not revealed by the I statistic alone and, specifically, the G i and G i ∗ statistics enable us to detect local “pockets” of dependence that may not show up when using global statistics.
4,532 citations