Determining the size of spatial clusters in focused tests: Comparing two methods by means of simulation in a GIS

 Based on a four-point evaluation system consisting of accuracy, consistency, power, and chance to commit type I errors, this study compares Tango's minimum p (MinP) and Stone's maximum relative risk (MaxRR) methods for detecting focused cluster size through simulations in GIS. It reveals that the MinP method is more effective than the MaxRR method. The MinP method exhibits higher levels of accuracy and consistency; and its power and chance to commit type I errors are similar to the MinP method. The MaxRR method has a tendency to underestimate the cluster size, while the MinP method tends to overestimate the cluster size, particularly when the clusters are relatively big and have high relative risk levels. In addition, the MinP method seems to be most effective in revealing the size of clusters when clusters are neither too strong nor too weak. The lowest detection rates for clustering occur when the clustering signal is relatively weak, which is easily understandable. In practice, it might be useful to use both the methods to estimate a range of possible cluster sizes, where the MaxRR method indicates the lower estimate, while the MinP method gives the higher estimate of the cluster size. Received: 24 August 2002 / Accepted: 20 December 2002     

Developing a bivariate spatial association measure: An integration of Pearson's r and Moran's I

 This research is concerned with developing a bivariate spatial association measure or spatial correlation coefficient, which is intended to capture spatial association among observations in terms of their point-to-point relationships across two spatial patterns. The need for parameterization of the bivariate spatial dependence is precipitated by the realization that aspatial bivariate association measures, such as Pearson's correlation coefficient, do not recognize spatial distributional aspects of data sets. This study devises an L statistic by integrating Pearson's r as an aspatial bivariate association measure and Moran's I as a univariate spatial association measure. The concept of a spatial smoothing scalar (SSS) plays a pivotal role in this task. Received: 07 November 2000 / Accepted: 02 August 2001     

Geostatistical incorporation of spatial coordinates into supervised classification of hyperspectral data

 This paper presents a methodology to incorporate both hyperspectral properties and spatial coordinates of pixels in maximum likelihood classification. Indicator kriging of ground data is used to estimate, for each pixel, the prior probabilities of occurrence of classes which are then combined with spectral-based probabilities within a Bayesian framework. In the case study (mapping of in-stream habitats), accounting for spatial coordinates increases the overall producer's accuracy from 85.8% to 93.8%, while the Kappa statistic rises from 0.74 to 0.88. Best results are obtained using only indicator kriging-based probabilities, with a stunning overall accuracy of 97.2%. Significant improvements are observed for environmentally important units, such as pools (Kappa: 0.17 to 0.74) and eddy drop zones (Kappa: 0.65 to 0.87). The lack of benefit of using hyperspectral information in the present study can be explained by the dense network of ground observations and the high spatial continuity of field classification which might be spurious. Received: 12 April 2001 / Accepted: 7 September 2001     

Modeling spatial dependence in high spatial resolution hyperspectral data sets

 As either the spatial resolution or the spatial scale for a geographic landscape increases, both latent spatial dependence and spatial heterogeneity also will tend to increase. In addition, the amount of georeferenced data that results becomes massively large. These features of high spatial resolution hyperspectral data present several impediments to conducting a spatial statistical analysis of such data. Foremost is the requirement of popular spatial autoregressive models to compute eigenvalues for a row-standardized geographic weights matrix that depicts the geographic configuration of an image's pixels. A second drawback arises from a need to account for increased spatial heterogeneity. And a third concern stems from the usefulness of marrying geostatistical and spatial autoregressive models in order to employ their combined power in a spatial analysis. Research reported in this paper addresses all three of these topics, proposing successful ways to prevent them from hindering a spatial statistical analysis. For illustrative purposes, the proposed techniques are employed in a spatial analysis of a high spatial resolution hyperspectral image collected during research on riparian habitats in the Yellowstone ecosystem. Received: 25 February 2001 / Accepted: 2 August 2001     

Spatial statistical techniques for aggregating point objects extracted from high spatial resolution remotely sensed imagery

 Using a local maximum filter, individual trees were extracted from a 1 m spatial resolution IKONOS image and represented as points. The spatial pattern of individual trees was determined to represent forest age (a surrogate for forest structure). Point attributes, based on the spatial pattern of trees, were generated via nearest neighbour statistics and used as the basis for aggregating points into forest structure units. The forest structure units allowed for the mapping of a forested area into one of three age categories: young (1–20 years), intermediate (21–120 years), and mature (>120 years). This research indicates a new approach to image processing, where objects generated from the processing of image data (rather than pixels or spectral values) are subjected to spatial statistical analysis to estimate an attribute relating an aspect of forest structure. Received: 22 April 2002 / Accepted: 23 November 2002     

Testing spatial patterns and growth spillover effects in clusters of cities

 This paper analyzes the spatial patterns of households' distribution in clusters of cities and the effects on regional growth using spatial exploratory techniques and a model of growth that incorporates spatial location. Our empirical analysis shows that, over the 1980–1990 period, in Southern New England, patterns of spatial clustering of households did create heterogeneous growth rates in the region. Also, there is evidence that clusters of cities and isolated cities created spillover growth effects in bordering towns. Received: 5 September 2001 / Accepted: 2 August 2002     

An integrated representation of spatial and temporal relationships between evolving regions

 The study of relationships between evolving regions within GIS still needs the development of operators that integrate the spatial and temporal dimensions. This paper introduces a new approach that combines topological relationships between regions in 2-dimensional space with temporal relationships between convex intervals in time. Resulting relationships are defined and visually presented within a 3-dimensional space that integrates the geographical space as a 2-dimensional space and the time line as the third dimension. Conceptual neighbourhoods are identified and extended by the concept of semi-transitions and transitions. Such a flexible framework presents the advantage of being derived from accepted relationships in both space and time. Its computational implementation is therefore compatible with current spatial and temporal GIS models. Received: May 2000 / Accepted: June 2001     

Toward micro-scale spatial modeling of gentrification

 A simple preliminary model of gentrification is presented. The model is based on an irregular cellular automaton architecture drawing on the concept of proximal space, which is well suited to the spatial externalities present in housing markets at the local scale. The rent gap hypothesis on which the model's cell transition rules are based is discussed. The model's transition rules are described in detail. Practical difficulties in configuring and initializing the model are described and its typical behavior reported. Prospects for further development of the model are discussed. The current model structure, while inadequate, is well suited to further elaboration and the incorporation of other interesting and relevant effects. Received: 1 November 2001 / Accepted: 12 April 2002 Town centres data were made available by kind permission of the UK Department of the Environment, Transport and the Regions.     

The role of spatial effects in the empirical analysis of regional concentration

 Economists have recently devoted an increasing attention to the issue of spatial concentration of economic activities. However, surprisingly enough, most of the empirical work is still based on the computation of very basic statistical measures in which the geographical characteristics of data play no role. By making use of a series of empirical examples we show that spatial concentration consists of two different features that are rarely kept as separate in the statistical analysis: an a-spatial concept of variability which is invariant to permutations, and the concept of polarization that refers to the geographical position of observations. Received: 8 August 2000 / Accepted: 20 June 2001     

Spatial econometrics functions in R: Classes and methods

 Placing spatial econometrics and more generally spatial statistics in the context of an extensible data analysis environment such as R exposes similarities and differences between traditions of analysis. This can be fruitful, and is explored here in relation to prediction and other methods usually applied to fitted models in R. Objects in R may be assigned a class attribute, including fitted model objects. Such fitted model objects may be provided with methods allowing them to be displayed, compared, and used for prediction, and it is of interest to see whether fitted spatial models can be treated in the same way. Received: 26 August 2002 / Revised version: 15 January 2003     

Developing local measures of spatial association for categorical data

This paper describes a procedure for extending local statistics to categorical spatial data. The approach is based on the notion that there are two fundamental characteristics of categorical spatial data; composition and configuration. Further, it is argued that, when considered locally, the latter should be measured conditionally with respect to the former. These ideas are developed for binary, gridded data. Local composition is measured by counting the numbers of cells of a particular type, while local configuration is measured by join counts. The approach is illustrated using a small, empirical data set and an ad hoc procedure is developed to deal with the impact of global spatial autocorrelation on the local statistics.The author gratefully acknowledges financial support from the GEOIDE Network of Centres of Excellence (ENV #4) and the helpful comments of three anonymous reviewers.     

Solution and econometric estimation of spatial dynamic models in continuous space and continuous time

 This paper presents and demonstrates a general approach to solving spatial dynamic models in continuous space and continuous time that characterize the behaviour of intertemporally and interspatially optimizing agents and estimating from discrete data the parameters of such models. The approach involves the use of a projection method to solve the models and a quasi-Newton algorithm to update quasi-FIML parameter estimates. Received: 26 July 2000 / Accepted: 31 January 2001     

Change detection thresholds for remotely sensed images

 The detection of change in remotely sensed images is often carried out by designating a threshold to distinguish between areas of change and areas of no change. The choice of threshold is often arbitrary however. The purpose of this paper is to offer a statistical framework for the selection of thresholds. The framework accounts for the facts that one carries out multiple tests of the null hypothesis of no change, when searching for regions of change over an image with a large number of pixels. Special attention is given to global spatial autocorrelation, which can affect the selection of appropriate threshold values. Received: 8 March 2001 / Accepted: 12 October 2001     

Simultaneous modelling of multi-purpose/multi-stop activity patterns and quantities consumed

 Whereas for commuting travel there is a one-to-one correspondence between commuters and jobs, and for commodity flows a one-to-one correspondence between the size of orders and the shipping cost of the commodities, the situation is much more complex for retail/service travel. A typical shopper may make a single trip or multi-stop tour to buy/consume a quite diverse set of commodities/services at different locations in quite variable quantities. At the same time, the general pattern of the tour is clearly dependent on the activities and goods available at potential stops. These interdependencies have been alluded to in the literature, especially by spatial economists. However, until some preliminary work by the first author, there has been no attempt to formally include these interdependencies in a general model. This paper presents a framework for achieving this goal by developing an evolutionary set of models starting from the simplest forms available. From the above, it is clear that such interdependency models will inevitably have high dimensionality and combinatorial complexity. This rules out a simultaneous treatment of all the events using an individual choice approach. If an individual choice approach is to be applied in a tractable manner, the set of interdependent events needs to be segmented into several subsets, with simultaneity recognised within each subset, but a mere sequential progression occurring between subsets. In this paper, full event interdependencies are retained at the expense of modelling market segments of consumers rather than a sample of representative individuals. We couple the travel and consumption events in the only feasible way, by modelling the tours as discrete entities, in conjunction with the amount of each commodity consumed per stop on each such tour in terms of the continuous quantities of microeconomics. This is performed both under a budget/income constraint from microeconomics and a time budget constraint from time geography. The model considers both physical trips and tele-orders. Received: 14 August 2000 / Accepted: 6 October 2001     

Mapping of stream microhabitats with high spatial resolution hyperspectral imagery

 Maximum likelihood supervised classifications with 1-m 128 band hyperspectral data accurately map in-stream habitats in the Lamar River, Wyoming with producer's accuracies of 91% for pools, 87% for glides, 76% for riffles, and 85% for eddy drop zones. Coarser resolution 5-m hyperspectral data and 1-m simulated multiband imagery yield lower accuracies that are unacceptable for inventory and analysis. Both high spatial resolution and hyperspectral coverage are therefore necessary to map microhabitats in the study area. In many instances, the high spatial resolution hyperspectral (HSRH) imagery appears to map the stream habitats with greater accuracy than our ground-based surveys, thus challenging classical approaches used for accuracy assessment in remote sensing. Received: 9 April 2001 / Accepted: 8 October 2001     

Web-enabled spatial decision analysis using Ordered Weighted Averaging (OWA)

 This paper presents a spatial decision support tool that implements the Ordered Weighted Averaging (OWA) method. OWA is a family of multicriteria evaluation operators characterised by two sets of weights: criterion importance weights and order weights. We propose a highly interactive way of choosing, modifying, and fine-tuning the decision strategy defined by the order weights. This exploratory approach to OWA is supported by a graphical representation of the operator's behaviour in terms of decision risk and tradeoff/dispersion between criteria. Our prototype implementation is based on the CommonGIS software, and thus, Web-enabled and working with vector data. We successfully demonstrate online, exploratory support of spatial decision strategies using a data set of skiing resorts in Wallis, Switzerland. Received: 24 September 2002 / Accepted: 10 January 2003     

Adjacency selection in Markov Random Fields for high spatial resolution hyperspectral data

 Markov Random Fields, implemented for the analysis of remote sensing images, capture the natural spatial dependence between band wavelengths taken at each pixel, through a suitable adjacency relationship between pixels, to be defined a priori. In most cases several adjacency definitions seem viable and a model selection problem arises. A BIC-penalized Pseudo-Likelihood criterion is suggested which combines good distributional properties and computational feasibility for analysis of high spatial resolution hyperspectral images. Its performance is compared with that of the BIC-penalized Likelihood criterion for detecting spatial structures in a high spatial resolution hyperspectral image for the Lamar area in Yellowstone National Park. Received: 9 March 2001 / Accepted: 2 August 2001     

Spatial decision support system for home-delivered services

 We present a spatial decision support system for the non-profit sector, designed to assist planning in the area of home-delivered services such as meals on wheels. Using data collected from existing programs, current and forecasted demographic data, and a set of algorithmic tools, we provide a system for evaluating current meals on wheels facilities, and for making incremental facility location decisions that satisfy coverage and equity requirements. Received: 27 September 2000 / Accepted: 22 March 2001