A. Stewart Fotheringham

Spatial Analysis and GIS

Keywords: integration of GIS Reference Record created on 2005-06-20, modified on 2016-08-08

GIS and spatial analytical problems

Abstract Increasingly, methods of spatial analysis are being integrated within geographical information systems. As this integration occurs, it is important to ensure that, (i) users of GIS recognize the limitations of spatial analysis, (ii) researchers continue to work on removing the existing impediments to accurate spatial analysis, and (iii) developers of GIS consider these limitations. In this article we discuss eight general impediments that arise in spatial analyses that span a diverse range of substantive applications. Geographical information systems offer not only the opportunity to integrate various methods of spatial analysis, but also the chance to learn more about the underlying impediments.

Matrix Comparison, Goodness-of-Fit, and Spatial Interaction Modeling

The usefulness of various statistics for comparing observed and predicted spatial interaction matrices is examined. Results indicate that some statistics may yield misleading information about error levels in predicted matrices. Other statistics are found to be unsuitable for significance testing. The concept of experimental distributions is discussed for several of the statistics. Although framed in the context of spatial interaction modeling, the discussion is relevant to most matrix comparison problems.

Principal Component Analysis on Spatial Data: An Overview

This article considers critically how one of the oldest and most widely applied statistical methods, principal components analysis (PCA), is employed with spatial data. We first provide a brief guide to how PCA works: This includes robust and compositional PCA variants, links to factor analysis, latent variable modeling, and multilevel PCA. We then present two different approaches to using PCA with spatial data. First we look at the nonspatial approach, which avoids challenges posed by spatial data by using a standard PCA on attribute space only. Within this approach we identify four main methodologies, which we define as (1) PCA applied to spatial objects, (2) PCA applied to raster data, (3) atmospheric science PCA, and (4) PCA on flows. In the second approach, we look at PCA adapted for effects in geographical space by looking at PCA methods adapted for first-order nonstationary effects (spatial heterogeneity) and second-order stationary effects (spatial autocorrelation). We also describe how PCA can be used to investigate multiple scales of spatial autocorrelation. Furthermore, we attempt to disambiguate a terminology confusion by clarifying which methods are specifically termed “spatial PCA” in the literature and how this term has different meanings in different areas. Finally, we look at a further three variations of PCA that have not been used in a spatial context but show considerable potential in this respect: simple PCA, sparse PCA, and multilinear PCA.

Modelling spatial choice: a review and synthesis in a migration context

This paper reviews various approaches to the modelling of spatial choice. Spatial choice modelling is viewed as a distinct area of research, within the larger field of discrete choice modelling, with a sound methodological basis and computationally tractable modelling framework. This review draws upon empirical application of spatial choice models to interregional migration and identifies the main research issues, summarizes the progress of research thus far, and suggests some paths for future research. It is argued that some of the widely used models suffer from problems derived from their development in aspatial choice contexts. Acknowledging the increased complexity and, possibly, the different choice process that spatial choice situations present over their aspatial counterparts leads to the development of the socalled competing destinations model and its variants. Evidence from empirical tests of these spatial choice models suggests that analysts engaged in interregional migration modelling risk model misspecification if they ignore the peculiarities of spatial choice.

The integration of spatial analysis and gis

Abstract It is widely expected that future GISs will have increased analytical capabilities that will take them beyond being efficient display and database management devices. Several attempts have already been made to link existing analytical software to various GISs. However, a problem with all of these attempts is that the user is forced to switch back and forth between the GIS operating environment and the analytical software. In this paper we present a Statistical Analysis Module, SAM, that runs totally within the operating environment of a GIS and utilizes a command structure that makes running the package transparent to the user of the GIS. We believe that the development of this module is an important step in linking spatial analysis with GIS technology.

Geographically weighted regression with a non-Euclidean distance metric: a case study using hedonic house price data

Geographically weighted regression (GWR) is an important local technique for exploring spatial heterogeneity in data relationships. In fitting with Tobler’s first law of geography, each local regression of GWR is estimated with data whose influence decays with distance, distances that are commonly defined as straight line or Euclidean. However, the complexity of our real world ensures that the scope of possible distance metrics is far larger than the traditional Euclidean choice. Thus in this article, the GWR model is investigated by applying it with alternative, non-Euclidean distance (non-ED) metrics. Here we use as a case study, a London house price data set coupled with hedonic independent variables, where GWR models are calibrated with Euclidean distance (ED), road network distance and travel time metrics. The results indicate that GWR calibrated with a non-Euclidean metric can not only improve model fit, but also provide additional and useful insights into the nature of varying relationships within the house price data set.

The Development of a Migration Model for England and Wales: Overview and Modelling Out-Migration

This paper reports the results of an extensive project to model interregional migration within England and Wales. The project took place over a two-year period and was sponsored by the UK Office of the Deputy Prime Minister (formerly the Department of Transport, Local Government and the Regions). The results of the study are reported in three separate papers. In this paper we present an overview of the project and then describe in detail both the process of modelling out-migration rates from origins across England and Wales and the calibration results from this modelling stage. The results yield important information on the determinants of out-migration and population re-distribution within England and Wales. In paper 2 we describe the modelling of the destination choices of migrants and the calibration results from such models. In paper 3 we tie both the out-migration and the destination choice results together into a mapping and visualisation system (MIGMOD) which can be used to assess the impacts of various policies on population movements in England and Wales. The simple policy scenarios reported in this third paper are illustrative and indicative of the models potential, rather than necessarily being a true reflection of the effects of policy changes. The three papers contribute substantially to the existing migration literature because they present the most exhaustive analysis of the determinants of both out-migration and destination choice that has ever been undertaken. The number of variables in both modelling processes is far larger than has ever been assembled before and the results therefore provide much greater insight into the role of various attributes in determining out-migration rates and in-migration rates than has previously been possible. The papers also provide an interesting lesson in a problem rarely encountered—that of having too much data.

DIFFUSION-LIMITED AGGREGATION AND THE FRACTAL NATURE OF URBAN-GROWTH

This paper introduces the mechanism of diffusion-limited aggregation (DLA) as a new basis for understanding urban growth. Through DLA, urban form is related to the processes of rural-to-urban migration and contiguous growth. However, despite being based on very simple principles, DLA simulations are shown to have properties found in most urban areas such as negative density gradients and ordered chaotic structures. The paper examines variations in the simulated urban structures produced by different assumptions regarding the rural-to-urban migration mechanism. An important finding is that urban density gradients can occur independently of the generally accepted reasons for their presence. We also comment on boundary effects in the measurement of urban density gradients.

Measuring destination attractivity: a migration example

The power of places to draw migrants is a topic of fundamental interest in geographical and related social studies and also in policy circles. This paper describes and demonstrates the utility of a measure of migration attractivity which is considered superior to those most widely used previously. Following a review of the importance now attached to measuring place attractiveness the paper documents the deficiencies of the most commonly used methods involving numbers and rates of in-migration and net migration. It goes on to argue for a measure of the relative intrinsic attractivity (RIA) of places which takes account of the spatial context of each place in terms of its accessibility from all the other places that are ‘at risk’ of supplying residents to it. It applies this approach to migration that took place in 1990-91 between all the local authority districts of mainland Britain as recorded by the 1991 Census. The resultant ranking of these 451 places on the basis of their migration attractivity for all persons is compared with the patterns indicated by more traditional measures. The paper then explores the characteristics of places to see what features are most closely associated with high and low levels of migration attractivity. Finally RIA scores are calculated separately for two age groups thought to have different views about what makes for an attractive place to live namely young adults and people at the peak of the family-building stage of their lives. (authors)