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     

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     

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     

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     

Area-based tests for association between spatial patterns

 Edge effects pervade natural systems, and the processes that determine spatial heterogeneity (e.g. physical, geochemical, biological, ecological factors) occur on diverse spatial scales. Hence, tests for association between spatial patterns should be unbiased by edge effects and be based on null spatial models that incorporate the spatial heterogeneity characteristic of real-world systems. This paper develops probabilistic pattern association tests that are appropriate when edge effects are present, polygon size is heterogeneous, and the number of polygons varies from one classification to another. The tests are based on the amount of overlap between polygons in each of two partitions. Unweighted and area-weighted versions of the statistics are developed and verified using scenarios representing both polygon overlap and avoidance at different spatial scales and for different distributions of polygon sizes. These statistics were applied to Soda Butte Creek, Wyoming, to determine whether stream microhabitats, such as riffles, pools and glides, can be identified remotely using high spatial resolution hyperspectral imagery. These new “spatially explicit” techniques provide information and insights that cannot be obtained from the spectral information alone. Received 1 June 2001 / Accepted 25 October 2001     

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     

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     

Assessing representation error in point-based coverage modeling

 Accurately representing geographic space in a digital environment continues to confound and challenge researchers. Carrying out spatial analysis in a setting where geographic representation is subject to change poses problems to be addressed. In this paper we examine spatial representation in the context of coverage-based location modeling. A geographic region can be represented in a variety of ways. We present an evaluation of spatial representation in the location of facilities that provide coverage oriented services. The analysis shows that the modeling results are sensitive to how spatial demand for service is represented in a digital environment. We develop an approach for evaluating representational appropriateness. This research contributes to spatial analysis integrated in geographic information system environment. Received: 10 January 2001 / Accepted: 8 April 2002     

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     

Emerging and vector-borne diseases: Role of high spatial resolution and hyperspectral images in analyses and forecasts

 Many infectious diseases that are emerging or transmitted by arthropod vectors have a strong link to landscape features. Depending on the source of infection or ecology of the transmitting vector, micro-habitat characteristics at the spatial scale of square meters or less may be important. Recently, satellite images have been used to classify habitats in an attempt to understand associations with infectious diseases. Whether high spatial resolution and hyperspectral (HSRH) images can be useful in studies of such infectious diseases is addressed. The nature of questions that such studies address and the desired accuracy and precision of answers will determine the utility of HSRH data. Need for such data should be based on the goals of the effort. Examples of kinds of questions and applications are discussed. The research implications and public health applications may depend on available analytic tools as well as epidemiological observations. Received: 30 July 2001 / Accepted: 14 October 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.     

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     

Alonso's Theory of Movements: Developments in Spatial Interaction Modeling

 The Spatial Interaction Model proposed by Alonso as “Theory of Movements” offers an innovative specification of spatial origin-destination flow models. Equations for flows between regions, total outflow from and total inflow to a region are linked by balancing factors. This paper presents a consistent formulation of Spatial Interaction Models in the Wilson tradition and Alonso's Theory of Movements. The paper is intended as an introduction to the model and a review of␣the state of the art. Besides it is argued that simultaneous equation techniques are required to estimate the so-called systemic parameters. Received: 21 May 2000 / Accepted: 18 January 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     

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     

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     

Misspecifications in interaction model distance decay relations: A spatial structure effect

 An exclusively statistical approach is proposed to address the spatial structure effects of general interaction models. It is shown that the spatial heterogeneity in the estimated region-specific distance decay parameters may in part be due to the combination of two factors: (a) a functional mis-specification of the global distance decay relationship; and (b) the heterogeneity in the region-specific conditional distance distributions. A properly specified global distance decay function allows controlling for these spatially induced biases in the local distance decay parameters. However, inherent multicollinearities between the set of region specific distance decay parameters and other estimated model parameters prevent an unambiguous interpretation. A key conclusion is that a proper model specification, in particular, the specification of the global distance decay relationship, is of paramount importance in interaction modeling and for accessibility studies. Received: September 2002 / Accepted: January 2003     

Volume-preserving interpolation of a smooth surface from polygon-related data

 The interpolation of continuous surfaces from discrete points is supported by most GIS software packages. Some packages provide additional options for the interpolation from 3D line objects, for example surface-specific lines, or contour lines digitized from topographic maps. Demographic, social and economic data can also be used to construct and display smooth surfaces. The variables are usually published as sums for polygonal units, such as the number of inhabitants in communities or counties. In the case of point and line objects the geometric properties have to be maintained in the interpolated surface. For polygon-based data the geometric properties of the polygon boundary and the volume should be preserved, avoiding redistribution of parts of the volume to neighboring units during interpolation. The pycnophylactic interpolation method computes a continuous surface from polygon-based data and simultaneously enforces volume preservation in the polygons. The original procedure using a regular grid is extended to surface representations based on an irregular triangular network (TIN). Received: 5 October 2000 / Accepted: 20 December 2000