Showing papers on "Spatial analysis published in 2002"

Geographically Weighted Regression: The Analysis of Spatially Varying Relationships

Abstract: Acknowledgements.Local Statistics and Local Models for Spatial Data. Geographically Weighted Regression: The Basics. Extensions to the Basic GWR Model. Statistical Inference and Geographically Weighted Regression. GWR and Spatial Autocorrelation. Scale Issues and Geographically Weighted Regression. Geographically Weighted Local Statistics. Extensions of Geographically Weighting. Software for Geographically Weighted Regression. Epilogue. Bibliography.Index.

Geographic Information Analysis

Abstract: Preface to the Second Edition. Acknowledgments. Preface to the First Edition. 1 Geographic Information Analysis and Spatial Data. Chapter Objectives. 1.1 Introduction. 1.2 Spatial Data Types. 1.3 Some Complications. 1.4 Scales for Attribute Description. 1.5 GIS and Spatial Data Manipulation. 1.6 The Road Ahead. Chapter Review. References. 2 The Pitfalls and Potential of Spatial Data. Chapter Objectives. 2.1 Introduction. 2.2 The Bad News: The Pitfalls of Spatial Data. 2.3 The Good News: The Potential of Spatial Data. Chapter Review. References. 3 Fundamentals-Mapping It Out. Chapter Objectives. 3.1 Introduction: The Cartographic Tradition. 3.2 Geovisualization and Analysis. 3.3 The Graphic Variables of Jacques Bertin. 3.4 New Graphic Variables. 3.5 Issues in Geovisualization. 3.6 Mapping and Exploring Points. 3.7 Mapping and Exploring Areas. 3.8 Mapping and Exploring Fields. 3.9 The Spatialization of Nonspatial Data. 3.10 Conclusion. Chapter Review. References. 4 Fundamentals-Maps as Outcomes of Processes. Chapter Objectives. 4.1 Introduction: Maps and Processes. 4.2 Processes and the Patterns They Make. 4.3 Predicting the Pattern Generated by a Process. 4.4 More Definitions. 4.5 Stochastic Processes in Lines, Areas, and Fields. 4.6 Conclusions. Chapter Review. References. 5 Point Pattern Analysis. Chapter Objectives. 5.1 Introduction. 5.2 Describing a Point Pattern. 5.3 Assessing Point Patterns Statistically. 5.4 Monte Carlo Testing. 5.5 Conclusions. Chapter Review. References. 6 Practical Point Pattern Analysis. Chapter Objectives. 6.1 Introduction: Problems of Spatial Statistical Analysis. 6.2 Alternatives to Classical Statistical Inference. 6.3 Alternatives to IRP/CSR. 6.4 Point Pattern Analysis in the Real World. 6.5 Dealing with Inhomogeneity. 6.6 Focused Approaches. 6.7 Cluster Detection: Scan Statistics. 6.8 Using Density and Distance: Proximity Polygons. 6.9 A Note on Distance Matrices and Point Pattern Analysis. Chapter Review. References. 7 Area Objects and Spatial Autocorrelation. Chapter Objectives. 7.1 Introduction: Area Objects Revisited. 7.2 Types of Area Objects. 7.3 Geometric Properties of Areas. 7.4 Measuring Spatial Autocorrelation. 7.5 An Example: Tuberculosis in Auckland, 2001-2006. 7.6 Other Approaches. Chapter Review. References. 8 Local Statistics. Chapter Objectives. 8.1 Introduction: Think Geographically, Measure Locally. 8.2 Defining the Local: Spatial Structure (Again). 8.3 An Example: The Getis-Ord Gi and Gi Statistics. 8.4 Inference with Local Statistics. 8.5 Other Local Statistics. 8.6 Conclusions: Seeing the World Locally. Chapter Review. References. 9 Describing and Analyzing Fields. Chapter Objectives. 9.1 Introduction: Scalar and Vector Fields Revisited. 9.2 Modeling and Storing Field Data. 9.3 Spatial Interpolation. 9.4 Derived Measures on Surfaces. 9.5 Map Algebra. 9.6 Conclusions. Chapter Review. References. 10 Knowing the Unknowable: The Statistics of Fields. Chapter Objectives. 10.1 Introduction. 10.2 Regression on Spatial Coordinates: Trend Surface Analysis. 10.3 The Square Root Differences Cloud and the (Semi-) Variogram. 10.4 A Statistical Approach to Interpolation: Kriging. 10.5 Conclusions. Chapter Review. References. 11 Putting Maps Together Map Overlay. Chapter Objectives. 11.1 Introduction. 11.2 Boolean Map Overlay and Sieve Mapping. 11.3 A General Model for Alternatives to Boolean Overlay. 11.4 Indexed Overlay and Weighted Linear Combination. 11.5 Weights of Evidence. 11.6 Model-Driven Overlay Using Regression. 11.7 Conclusions. Chapter Review. References. 12 New Approaches to Spatial Analysis. Chapter Objectives. 12.1 The Changing Technological Environment. 12.2 The Changing Scientific Environment. 12.3 Geocomputation. 12.4 Spatial Models. 12.5 The Grid and the Cloud: Supercomputing for Dummies. 12.6 Conclusions: Neogeographic Information Analysis? Chapter Review. References. Appendix A: Notation, Matrices, and Matrix Mathematics. A.1 Introduction. A.2 Some Preliminary Notes on Notation. A.3 Matrix Basics and Notation. A.4 Simple Matrix Mathematics. A.5 Solving Simultaneous Equations Using Matrices. A.6 Matrices, Vectors, and Geometry. A.7 Eigenvectors and Eigenvalues. Reference. Index.

Spatial autocorrelation and autoregressive models in ecology

Abstract: Recognition and analysis of spatial autocorrelation has defined a new par- adigm in ecology. Attention to spatial pattern can lead to insights that would have been otherwise overlooked, while ignoring space may lead to false conclusions about ecological relationships. We used Gaussian spatial autoregressive models, fit with widely available software, to examine breeding habitat relationships for three common Neotropical migrant songbirds in the southern Appalachian Mountains of North Carolina and Tennessee, USA. In preliminary models that ignored space, the abundance of all three species was cor- related with both local- and landscape-scale habitat variables. These models were then modified to account for broadscale spatial trend (via trend surface analysis) and fine-scale autocorrelation (via an autoregressive spatial covariance matrix). Residuals from ordinary least squares regression models were autocorrelated, indicating that the assumption of independent errors was violated. In contrast, residuals from autoregressive models showed little spatial pattern, suggesting that these models were appropriate. The magnitude of habitat effects tended to decrease, and the relative importance of different habitat variables shifted when we incorporated broadscale and then fine-scale space into the analysis. The degree to which habitat effects changed when space was added to the models was roughly correlated with the amount of spatial structure in the habitat variables. Spatial pattern in the residuals from ordinary least squares models may result from failure to include or adequately measure autocorrelated habitat variables. In addition, con- tagious processes, such as conspecific attraction, may generate spatial patterns in species abundance that cannot be explained by habitat models. For our study species, spatial patterns in the ordinary least squares residuals suggest that a scale of 500-1000 m would be ap- propriate for investigating possible contagious processes.

The consequences of spatial structure for the design and analysis of ecological field surveys

Abstract: In ecological field surveys, observations are gathered at different spatial locations. The purpose may be to relate biological response variables (e.g., species abundances) to explanatory environmental variables (e.g., soil characteristics). In the absence of prior knowledge, ecologists have been taught to rely on systematic or random sampling designs. If there is prior knowledge about the spatial patterning of the explanatory variables, obtained from either previous surveys or a pilot study, can we use this information to optimize the sampling design in order to maximize our ability to detect the relationships between the response and explanatory variables? The specific questions addressed in this paper are: a) What is the effect (type I error) of spatial autocorrelation on the statistical tests commonly used by ecologists to analyse field survey data? b) Can we eliminate, or at least minimize, the effect of spatial autocorrelation by the design of the survey? Are there designs that provide greater power for surveys, at least under certain circumstances? c) Can we eliminate or control for the effect of spatial autocorrelation during the analysis? To answer the last question, we compared regular regression analysis to a modified t-test developed by Dutilleul for correlation coefficients in the presence of spatial autocorrelation. Replicated surfaces (typically, 1000 of them) were simulated using different spatial parameters, and these surfaces were subjected to different sampling designs and methods of statistical analysis. The simulated surfaces may represent, for example, vegetation response to underlying environmental variation. This allowed us 1) to measure the frequency of type I error (the failure to reject the null hypothesis when in fact there is no effect of the environment on the response variable) and 2) to estimate the power of the different combinations of sampling designs and methods of statistical analysis (power is measured by the rate of rejection of the null hypothesis when an effect of the environment on the response variable has been created). Our results indicate that: 1) Spatial autocorrelation in both the response and environmental variables affects the classical tests of significance of correlation or regression coefficients. Spatial autocorrelation in only one of the two variables does not affect the test of significance. 2) A broad-scale spatial structure present in data has the same effect on the tests as spatial autocorrelation. When such a structure is present in one of the variables and autocorrelation is found in the other, or in both, the tests of significance have inflated rates of type I error. 3) Dutilleul's modified t-test for the correlation coefficient, corrected for spatial autocorrelation, effectively corrects for spatial autocorrelation in the data. It also effectively corrects for the presence of deterministic structures, with or without spatial autocorrelation. The presence of a broad-scale deterministic structure may, in some cases, reduce the power of the modified t-test.

A balanced view of scale in spatial statistical analysis

Abstract: Concepts of spatial scale, such as extent, grain, resolution, range, footprint, support and cartographic ratio are not interchangeable. Because of the potential confusion among the definitions of these terms, we suggest that authors avoid the term "scale" and instead refer to specific concepts. In particular, we are careful to discriminate between observation scales, scales of ecological phenomena and scales used in spatial statistical analysis. When scales of observation or analysis change, that is, when the unit size, shape, spacing or extent are altered, statistical results are expected to change. The kinds of results that may change include estimates of the population mean and variance, the strength and character of spatial autocorrelation and spatial anisotropy, patch and gap sizes and multivariate relationships, The First three of these results (precision of the mean, variance and spatial autocorrelation) can sometimes be estimated using geostatistical support-effect models. We present four case studies of organism abundance and cover illustrating some of these changes and how conclusions about ecological phenomena (process and structure) may be affected. We identify the influence of observational scale on statistical results as a subset of what geographers call the Modifiable Area Unit Problem (MAUP). The way to avoid the MAUP is by careful construction of sampling design and analysis. We recommend a set of considerations for sampling design to allow useful tests for specific scales of a phenomenon under study. We further recommend that ecological studies completely report all components of observation and analysis scales to increase the possibility of cross-study comparisons.

Combining Incompatible Spatial Data

Abstract: Global positioning systems (GPSs) and geographical information systems (GISs) have been widely used to collect and synthesize spatial data from a variety of sources. New advances in satellite imagery and remote sensing now permit scientists to access spatial data at several different resolutions. The Internet facilitates fast and easy data acquisition. In any one study, several different types of data may be collected at differing scales and resolutions, at different spatial locations, and in different dimensions. Many statistical issues are associated with combining such data for modeling and inference. This article gives an overview of these issues and the approaches for integrating such disparate data, drawing on work from geography, ecology, agriculture, geology, and statistics. Emphasis is on state-of-the-art statistical solutions to this complex and important problem.

Spatial/spectral endmember extraction by multidimensional morphological operations

Abstract: Spectral mixture analysis provides an efficient mechanism for the interpretation and classification of remotely sensed multidimensional imagery. It aims to identify a set of reference signatures (also known as endmembers) that can be used to model the reflectance spectrum at each pixel of the original image. Thus, the modeling is carried out as a linear combination of a finite number of ground components. Although spectral mixture models have proved to be appropriate for the purpose of large hyperspectral dataset subpixel analysis, few methods are available in the literature for the extraction of appropriate endmembers in spectral unmixing. Most approaches have been designed from a spectroscopic viewpoint and, thus, tend to neglect the existing spatial correlation between pixels. This paper presents a new automated method that performs unsupervised pixel purity determination and endmember extraction from multidimensional datasets; this is achieved by using both spatial and spectral information in a combined manner. The method is based on mathematical morphology, a classic image processing technique that can be applied to the spectral domain while being able to keep its spatial characteristics. The proposed methodology is evaluated through a specifically designed framework that uses both simulated and real hyperspectral data.

Spatial Technology and Archaeology: The Archaeological Applications of GIS

Abstract: Archaeology, Space and GIS. The Spatial database. Acquiring and Integrating Data. Manipulating Spatial Data. Digital Elevation Models. Beginning to Quantify Spatial Patterns. Sites, Territories and Distance. Location Models and Prediction. Trend Surface and Interpolation. Visibility Analysis and Archaeology. Cultural Resource Management. Future Directions. References. Index.

Extended statistical approaches to modelling spatial pattern in biodiversity in northeast New South Wales. II. Community-level modelling.

Abstract: Statistical modelling of biological survey data in relation to remotely mapped environmental variables is a powerful technique for making more effective use of sparse data in regional conservation planning. Application of such modelling to planning in the northeast New South Wales (NSW) region of Australia represents one of the most extensive and longest running case studies of this approach anywhere in the world. Since the early 1980s, statistical modelling has been used to extrapolate distributions of over 2300 species of plants and animals, and a wide variety of higher-level communities and assemblages. These modelled distributions have played a pivotal role in a series of major land-use planning processes, culminating in extensive additions to the region's protected area system. This paper provides an overview of the analytical methodology used to model distributions of individual species in northeast NSW, including approaches to: (1) developing a basic integrated statistical and geographical information system (GIS) framework to facilitate automated fitting and extrapolation of species models; (2) extending this basic approach to incorporate consideration of spatial autocorrelation, land-cover mapping and expert knowledge; and (3) evaluating the performance of species modelling, both in terms of predictive accuracy and in terms of the effectiveness with which such models function as general surrogates for biodiversity.

Illustrations and guidelines for selecting statistical methods for quantifying spatial pattern in ecological data

Abstract: This paper aims to provide guidance to ecologists with limited experience in spatial analysis to help in their choice of techniques. It uses examples to compare methods of spatial analysis for ecological field data. A taxonomy of different data types is presented, including point- and area-referenced data, with and without attributes. Spatially and non-spatially explicit data are distinguished. The effects of sampling and other transformations that convert one data type to another are discussed; the possible loss of spatial information is considered. Techniques for analyzing spatial pattern, developed in plant ecology, animal ecology, landscape ecology, geostatistics and applied statistics are reviewed briefly and their overlap in methodology and philosophy noted. The techniques are categorized according to their output and the inferences that may be drawn from them, in a discursive style without formulae. Methods are compared for four case studies with field data covering a range of types. These are: 1) percentage cover of three shrubs along a line transect; 2) locations and volume of a desert plant in a 1 ha area; 3) a remotely-sensed spectral index and elevation from 105 km2 of a mountainous region; and 4) land cover from three rangeland types within 800 km2 of a coastal region. Initial approaches utilize mapping, frequency distributions and variance-mean indices. Analysis techniques we compare include: local quadrat variance, block quadrat variance, correlograms, variograms, angular correlation, directional variograms, wavelets, SADIE, nearest neighbour methods, Ripley's (t), and various landscape ecology metrics. Our advice to ecologists is to use simple visualization techniques for initial analysis, and subsequently to select methods that are appropriate for the data type and that answer their specific questions of interest. It is usually prudent to employ several different techniques.

Socio-economic distance and spatial patterns in unemployment

Abstract: This paper examines the spatial patterns of unemployment in Chicago between 1980 and 1990. We study unemployment clustering with respect to different social and economic distance metrics that reflect the structure of agents' social networks. Specifically, we use physical distance, travel time, and differences in ethnic and occupational distribution between locations. Our goal is to determine whether our estimates of spatial dependence are consistent with models in which agents' employment status is affected by information exchanged locally within their social networks. We present non-parametric estimates of correlation across Census tracts as a function of each distance metric as well as pairs of metrics, both for unemployment rate itself and after conditioning on a set of tract characteristics. Our results indicate that there is a strong positive and statistically significant degree of spatial dependence in the distribution of raw unemployment rates, for all our metrics. However, once we condition on a set of covariates, most of the spatial autocorrelation is eliminated, with the exception of physical and occupational distance. Racial and ethnic composition variables are the single most important factor in explaining the observed correlation patterns. Copyright © 2002 John Wiley & Sons, Ltd.

Accounting for spatial pattern when modeling organism- environment interactions

Abstract: Statistical models of environment-abundance relationships may be influenced by spatial autocorrelation in abundance, environmental variables, or both. Failure to account for spatial autocorrelation can lead to incorrect conclusions regarding both the absolute and relative importance of environmental variables as determinants of abundance. We consider several classes of statistical models that are appropriate for modeling environment-abundance relationships in the presence of spatial autocorrelation, and apply these to three case studies: 1) abundance of voles in relation to habitat characteristics; 2) a plant competition experiment; and 3) abundance of Orbatid mites along environmental gradients. We find that when spatial pattern is accounted for in the modeling process, conclusions about environmental control over abundance can change dramatically. We conclude with five lessons: 1) spatial models are easy to calculate with several of the most common statistical packages; 2) results from spatially-structured models may point to conclusions radically different from those suggested by a spatially independent model; 3) not all spatial autocorrelation in abundances results from spatial population dynamics; it may also result from abundance associations with environmental variables not included in the model; 4) the different spatial models do have different mechanistic interpretations in terms of ecological processes – thus ecological model selection should take primacy over statistical model selection; 5) the conclusions of the different spatial models are typically fairly similar – making any correction is more important than quibbling about which correction to make.

Development of coarse-scale spatial data for wildland fire and fuel management

Abstract: Schmidt, Kirsten M.; Menakis, James P.; Hardy, Colin C.; Hann, Wendel J.; Bunnell, David L. 2002. Development of coarse-scale spatial data for wildland fire and fuel management. Gen. Tech. Rep. RMRS-GTR-87. Fort Collins, CO: U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station. 41 p. + CD. We produced seven coarse-scale, 1-km2 resolution, spatial data layers for the conterminous United States to support national-level fire planning and risk assessments. Four of these layers were developed to evaluate ecological conditions and risk to ecosystem components: Potential Natural Vegetation Groups , a layer of climax vegetation types representing site characteristics such as soils, climate, and topography; Current Cover Type , a layer of current vegetation types; Historical Natural Fire Regimes , a layer of fire frequency and severity; and Fire Regime Current Condition Class , a layer depicting the degree of departure from historical fire regimes, possibly resulting in alterations of key ecosystem components. The remaining three layers were developed to support assessments of potential hazards and risks to public health and safety: National Fire Occurrence, 1986 to 1996 , a layer and database of Federal and non-Federal fire occurrences; Potential Fire Characteristics , a layer of the number of days of high or extreme fire danger calculated from 8 years of historical National Fire Danger Rating System (NFDRS) data; and Wildland Fire Risk to Flammable Structures , a layer of the potential risk of wildland fire burning flammable structures based on an integration of population density, fuel, and weather spatial data. This paper documents the methodology we used to develop these spatial data layers. In a Geographic Information System (GIS), we integrated biophysical and remote sensing data with disturbance and succession information by assigning characteristics to combinations of biophysical, current vegetation, and historical fire regime spatial datasets. Regional ecologists and fire managers reviewed and refined the data layers, developed succession diagrams, and assigned fire regime current condition classes. “Fire Regime Current Conditions” are qualitative measures describing the degree of departure from historical fire regimes, possibly resulting in alterations of key ecosystem components such as species composition, structural stage, stand age, canopy closure, and fuel loadings. For all Federal and non-Federal lands, excluding agricultural, barren, and urban/developed lands, 48 percent (2.4 million km) of the land area of the conterminous United States is within the historical range (Condition Class 1) in terms of vegetation composition, structure, and fuel loadings; 38 percent (1.9 million km2) is moderately altered from the historical range (Condition Class 2); and 15 percent (736,000 km2) is significantly altered from the historical range (Condition Class 3). Managers can use these spatial data to describe regional trends in current conditions and to support fire and fuel management program development and resource allocation.

Conceptual and mathematical relationships among methods for spatial analysis

Abstract: A large number of methods for the analysis of the spatial structure of natural phenomena (for example, the clumping or overdispersion of tree stems, the positions of veins of ore in a rock formation, the arrangement of habitat patches in a landscape, and so on) have been developed in a wide range of scientific fields. This paper reviews many of the methods and describes the relationships among them, both mathematically, using the cross-product as a unifying principle, and conceptually, based on the form of a moving window or template used in calculation. The relationships among these methods suggest that while no single method can reveal all the important characteristics of spatial data, the results of different analyses are not expected to be completely independent of each other.

Advances in mathematical morphology applied to geoscience and remote sensing

Abstract: By concentrating on the analysis of the spatial relationships between groups of pixels, mathematical morphology provides us with an image processing strategy complementary to those based on the analysis of the spectral signature of single pixels. A wide variety of morphological transformations are available for extracting structural information in spatial data. Accordingly, a stream of successful applications in geoscience and remote sensing have been reported since the mid-1980s as highlighted in a brief survey. However, recent advances in the theory of mathematical morphology still remain largely unexplored. We show in this paper that they can enhance methodologies for the processing and analysis of Earth observation data for tasks as diverse as filtering, simplification, directional segmentation and crest line extraction. We also address important issues overlooked in the past and concerning the applicability of a given morphological filter to Earth observation data. In particular, we point out that self-dual or even self-complementary filters are required in many applications to produce results independent of the local contrast of the searched image structures.

Comparative Spatial Filtering in Regression Analysis

Abstract: One approach to dealing with spatial autocorrelation in regression analysis involves the filtering of variables in order to separate spatial effects from the variables' total effects. In this paper we compare two filtering approaches, both of which allow spatial statistical analysts to use conventional linear regression models. Getis' filtering approach is based on the autocorrelation observed with the use of the Gi local statistic. Griffith's approach uses an eigenfunction decomposition based on the geographic connectivity matrix used to compute a Moran's I statistic. Economic data are used to compare the workings of the two approaches. A final comparison with an autoregressive model strengthens the conclusion that both techniques are effective filtering devices, and that they yield similar regression models. We do note, however, that each technique should be used in its appropriate context.

Integrating Geographic Information Systems and Agent-Based Modeling Techniques for Simulating Social and Ecological Processes

Abstract: Preface 1. Integrating Geographic Information Systems and Agent-Based Technologies for Modeling and Simulating Social and Ecological Phenomena 2. Providing a Broad Spectrum of Agents in Spatially Explicit Simulation Models: The Gensim Approach 3. Spatial Units as Agents: Making the Landscape an Equal Player in Agent-Based Simulations 4. Geographic Information Systems and Agent-Based Modeling 5. Management Application of an Agent-Based Model: Control of Cowbirds at the Landscape Scale 6. Integrating Spatial Data into an Agent-Based Modling System: Ideas and Lessons from the Development of the Across-Trophic-Level System Simulation 7. Models of Individual Decision Making in Agent-Based Simulation of Common-Pool-Resource Management Institutions 8. An Agent-Based Approach to Environmental and Urban Systems within Geographic Information Systems 9. Mobile Agents with Spatial Intelligence 10. Simulating Wildland Recreation Use and Conflicting Spatial Interactions using Rule-Driven Intelligent Agents 11. An Intelligent Agent-Based Model for Simulating and Evaluating River Trip Scenarios along the Colorado River in Grand Canyon National Park 12. Agent-Based Simulations of Household Decision Making and Land Use Change near Altamira, Brazil Index

Spatial autocorrelation and statistical tests in ecology

Abstract: The presence of positive spatial autocorrelation in ecological data causes parametric statistical tests to give more apparently significant results than the data justify, which is a serious problem

Multiresolution models for nonstationary spatial covariance functions

Abstract: Many geophysical and environmental problems depend on estimating a spatial process that has nonstationary structure. A nonstationary model is proposed based on the spatial field being a linear combination of multiresolution (wavelet) basis functions and random coefficients. The key is to allow for a limited number of correlations among coefficients and also to use a wavelet basis that is smooth. When approximately 6% nonzero correlations are enforced, this representation gives a good approximation to a family of Matern covariance functions. This sparseness is important not only for model parsimony but also has implications for the efficient analysis of large spatial data sets. The covariance model is successfully applied to ozone model output and results in a nonstationary but smooth estimate.

Cluster Analysis of Spatial Patterns in Malaysian Tree Species

Abstract: Tree species in tropical rain forests exhibit a rich panoply of spatial patterns that beg ecological explanation. The analysis of tropical census data typically relies on spatial statistics, which quantify the average aggregation tendency of a species. In this article we develop a cluster-based approach that complements traditional spa- tial statistics in the exploration and analysis of ecological hypotheses for spatial pattern. We apply this technique to six study species within a fully mapped 50-ha forest census in peninsular Malaysia. For each species we identify the scale(s) of spatial aggregation and the cor- responding tree clusters. We study the correlation between cluster locations and abiotic variables such as topography. We find that the distribution of cluster sizes exhibits equilibrium and nonequilibrium behavior depending on species life history. The distribution of tree diameters within clusters also varies according to species life history. At different spatial scales, we find evidence for both niche-based and dispersal-limited processes producing spatial pattern. Our method- ology for identifying scales of aggregation and clusters is general; we discuss the method's applicability to spatial problems outside of trop- ical plant ecology. Subject heading: tropical forests, spatial statistics, spatial point pro- cesses, continuum percolation, dispersal limitation.

Integrating the statistical analysis of spatial data in ecology

Abstract: In many areas of ecology there is an increasing emphasis on spatial relationships. Often ecologists are interested in new ways of analyzing data with the objective of quantifying spatial patterns, and in designing surveys and experiments in light of the recognition that there may be underlying spatial pattern in biotic responses. In doing so, ecologists have adopted a number of widely different techniques and approaches derived from different schools of thought, and from other scientific disciplines. While the adaptation of a diverse array of statistical approaches and methodologies for the analysis of spatial data has yielded considerable insight into various ecological problems, this diversity of approaches has sometimes impeded communication and retarded more rapid progress in this emergent area. Many of these different statistical methods provide similar information about spatial characteristics, but the differences among these methods make it difficult to compare the results of studies that employ contrasting approaches. The papers in this mini-series explore possible areas of agreement and synthesis between a diversity of approaches to spatial analysis in ecology.

Identifying Spatial Segments in International Markets

Abstract: The identification of geographic target markets is critical to the success of companies that are expanding internationally Country borders have traditionally been used to delineate such target markets, resulting in accessible segments and cost efficient entry strategies However, at present such "countries-as-segments" strategies may no longer be valid In response to the accelerating trend toward global market convergence and within-country fragmentation of consumer needs, cross-national consumer segmentation is increasingly used, in which consumers in different countries are grouped based on the similarities in their needs, ignoring the country borders In this paper, we propose new methodology that helps to improve the identification of spatial segments by using information on the location of consumers Our methodology identifies spatial segments based on consumer needs and at the same time uses spatial information at the subcountry level We suggest that segments of consumers are likely to demonstrate spatial patterns and develop a hierarchical Bayes approach specifying several types of spatial dependence Rather than assigning consumers to segments, we identify spatial segments consisting of predefined regions We develop four models specifying different types of spatial dependence Two models characterize situations of spatial independence and countries-as-segments, which represent existing approaches to international segmentation The other two models accommodate spatial association within and spatial contiguity of segments and are new to the segmentation literature The models account for within-segment heterogeneity in multiattribute-based segmentation, covering numerous applications in response-based market segmentation We show that the models can be estimated using Gibbs sampling, where for the spatial contiguity model, a rejection sampling procedure is proposed We conduct an analysis of synthetic data to assess the performance of the most restrictive spatial segmentation model in situations where spatial patterns do or do not underlie the data-generating process Data for which the true properties are known were analyzed with models of spatial contiguity and spatial independence of segments The results indicate that a substantial improvement in parameter recovery may be realized if a spatial pattern underlies the data-generating process, but that the spatial-independence model may provide a better alternative when this is not the case We empirically illustrate our approach in the setting of international retailing, using survey data collected among consumers in seven countries of the European Union A store image measurement instrument was used This instrument is based on the multiattribute model of store image formation, with overall evaluations of stores as a dependent variable and image perceptions as predictor variables The segmentation basis consists of latent importances of store image attributes, ie, product quality, service quality, assortment, pricing, store atmosphere, and location We argue that store image attribute importances are likely to display spatial variation and expect spatial concentration of segments, or even contiguity, to occur We apply and compare the four spatial segmentation models to the store image data The countries-as-segments model receives lowest support from the data, less than that of the spatially independence model, which is in line with the current notion that consumer preferences cut across national borders However, the spatially contiguity model and spatial-association model demonstrate the best fit Although the differences between the various models are not very large, we find support, consistent across the two fit indices, for the spatial models Substantive results are presented for the spatial contiguity model We identified five spatial segments that cut across borders The segments give rise to different retail positioning strategies, and their importance estimates and location demonstrate face validity

Spatial Models in Real Estate Economics

Abstract: The idea that location is important in real estate economics is not new. However, the spatial dimension of real estate data is not always taken into account in traditional real estate models. Spatial econometrics is a tool that could remedy this problem. The objective of this paper is to review spatial models and apply them to typical hedonic real estate data. By doing so we gain insight into the size of bias that can occur in parameters if we do not take spatial effects into account. The conclusion is that spatial autocorrelation is present, least-square estimates may be biased and inefficient and spatial hedonic models do explain more of the price variation. However, the choice of spatial structure does affect the interpretation of parameters for variables with which it is correlated, i.e. it is a sort of multicollinearity problem. Hence, uncritical use of spatial econometrics may cause problems in the interpretation of individual parameters.

The effect of training strategies on supervised classification at different spatial resolutions

Abstract: Three different training strategies often used for supervised classification-single pixel, seed, and block or polygon training-are compared in this paper. The range parameter of semi-variograms obtained from sample image subsets of each land-uselland-cover class was used to measure the autocorrelation level during training set selection. Eight training sets with different sizes were generated and then applied to image subsets with three multispectral bands and variance texture images in the classification of six land-use classes. The classification results using these training sets were compared at five resolution levels and were based on six Color Infrared Digital Orthophoto Quarter Quadrangle (DOQQ) subsets of different urban land types in urban and rural fringe areas of the San Diego metropolitan area. The performance of different training strategies is shown to be influenced by the training size, the image resolution, and the degree of autocorrelation inherent within each class. Training approaches had more impact on classification results at fine resolution levels than at coarse resolutions. For spectrally homogeneous classes, a spatially independent, single-pixel training approach is preferred. But for spatially heterogeneous classes, small block training has the advantage of readily capturing spectral and spatial information and reduces the amount of interaction time for the analyst.

Spatial statistics for remote sensing

Abstract: Preface. Contributors and editors. Introduction. I. 1. Description of the data B. Gorte. 2. Some basic elements of statistics A. Stein. 3. Physical principles of optical R.S. F. van der Meer. 4. Remote Sensing and GIS S. de Bruin, M. Molenaar. II. 5. Spatial Statistics P.M. Atkinson. 6. Spatial prediction by linear kriging A. Papritz, A. Stein. 7. Issues of scale and optimal pixel size P.J. Curran, P. M. Atkinson. 8. Conditional Simulation J.L. Dungan. 9. Supervised image classification B. Gorte. 10. Unsupervised class detection C.H.M. van Kemenade, et al. 11. Spectral unmixing F. van der Meer. III. 12. Accuracy assessment A.K. Skidmore. 13. Spatial sampling schemes J. de Gruijter. 14. Decision support systems A. Sharifi. Bibliography.

Spatio-temporal predicates

Abstract: Investigates temporal changes of topological relationships and thereby integrates two important research areas: first, 2D topological relationships that have been investigated quite intensively, and second, the change of spatial information over time We investigate spatio-temporal predicates, which describe developments of well-known spatial topological relationships A framework is developed in which spatio-temporal predicates can be obtained by temporal aggregation of elementary spatial predicates and sequential composition We compare our framework with two other possible approaches: one is based on the observation that spatio-temporal objects correspond to 3D spatial objects for which existing topological predicates can be exploited The other approach is to consider possible transitions between spatial configurations These considerations help to identify a canonical set of spatio-temporal predicates

Spatial contextual classification and prediction models for mining geospatial data

Abstract: Modeling spatial context (e.g., autocorrelation) is a key challenge in classification problems that arise in geospatial domains. Markov random fields (MRF) is a popular model for incorporating spatial context into image segmentation and land-use classification problems. The spatial autoregression (SAR) model, which is an extension of the classical regression model for incorporating spatial dependence, is popular for prediction and classification of spatial data in regional economics, natural resources, and ecological studies. There is little literature comparing these alternative approaches to facilitate the exchange of ideas. We argue that the SAR model makes more restrictive assumptions about the distribution of feature values and class boundaries than MRF. The relationship between SAR and MRF is analogous to the relationship between regression and Bayesian classifiers. This paper provides comparisons between the two models using a probabilistic and an experimental framework.