Global and local spatial autocorrelation in bounded regular tessellations

This paper systematically investigates spatially autocorrelated patterns and the behaviour of their associated test statistic Moran's I in three bounded regular tessellations. These regular tessellations consist of triangles, squares, and hexagons, each of increasing size (n=64; 256; 1024). These tesselations can be downloaded at http://geo-www.sbs.ohio-state.edu/faculty/tiefelsdorf/regspastruc/ in several GIS formats. The selection of squares is particularly motivated by their use in raster based GIS and remote sensing. In contrast, because of topological correspondences, the hexagons serve as excellent proxy tessellations for empirical maps in vector based GIS. For all three tessellations, the distributional characteristics and the feasibility of the normal approximation are examined for global Moran's I, Moran's I ^(k) associated with higher order spatial lags, and local Moran's I _i. A set of eigenvectors can be generated for each tessellation and their spatial patterns can be mapped. These eigenvectors can be used as proxy variables to overcome spatial autocorrelation in regression models. The particularities and similarities in the spatial patterns of these eigenvectors are discussed. The results indicate that [i] the normal approximation for Moran's I is not always feasible; [ii] the three tessellations induce different distributional characteristics of Moran's I, and [iii] different spatial patterns of eigenvectors are associated with the three tessellations. Received: 2 July 1999 / Accepted: 9 November 1999     

Urban growth and transport infrastructure interaction in Jeddah between 1980 and 2007

This paper aims to use spatial statistical tools to explore the reciprocal spatial–temporal effects of transport infrastructure and urban growth of Jeddah city, a fast developing polycentric city in Saudi Arabia. Global spatial autocorrelation (Moran's I) and local indicators of spatial association (LISA) are first used to analyze the spatial–temporal clustering of urban growth and transport infrastructure from 1980 to 2007. Then, spatial regression analysis is conducted to investigate the mutual spatial–temporal effects of urban growth and transport infrastructure. Results indicate a significant positive global spatial autocorrelation of all defined variables between 1980 and 2007. LISA results also reveal a constant significant spatial association of transport infrastructure expansion and urban growth variables from 1980 to 2007. The results not only indicate a mutual spatial influence of transport infrastructure and urban growth but also reveal that spatial clustering of transport infrastructure seems to be influenced by other factors. This study shows that transport infrastructure is a constant and strong spatial influencing factor of urban growth in the polycentric urban structure that Jeddah has. Overall, this study demonstrates that exploratory spatial data analysis and spatial regression analysis are able to detect the spatial–temporal mutual effects of transport infrastructure and urban growth. Further studies on the reciprocal relationship between urban growth and transport infrastructure using the study approach for the case of monocentric urban structure cities are necessary and encouraged.     

地球化学的空间自相关异常信息提取方法

针对地球化学数据存在的空间分布相关性特征,该文提出了一种基于空间自相关统计的地球化学异常提取方法。以内蒙古浩布高矿床外围的土壤地球化学数据为例,通过对Sn、Cu元素地球化学数据在不同空间间隔上的全局自相关计算,测算其空间聚集的程度,选取聚集程度最高时的间隔距离作为局部空间自相关的参数,通过局部Moran’s I值研究元素的空间分布特征,分析空间聚类和异常值,从而提取地球化学异常。结果表明,局部空间自相关分析可以揭示Sn、Cu地球化学数据的空间分布特征,能够更好地提取地球化学弱缓异常,说明空间自相关是一种有效的地球化学异常识别方法。     

Decomposing Malaria Mosquito Aquatic Habitat Data into Spatial Autocorrelation Eigenvectors in a SAS/GIS® Module

We present a geostatistical approach that accounts for spatial autocorrelation in malaria mosquito aquatic habitats in two East African urban environments. QuickBird 0.61 m data, encompassing visible bands and the near infra‐red (NIR) bands, were selected to synthesize images of Anopheles gambiae s.l. aquatic habitats in Kisumu and Malindi, Kenya. Field sampled data of An. gambiae s.l. aquatic habitats were used to determine which ecological covariates were associated with An. gambiae s.l. larval habitat development. A SAS/GIS^® spatial database was used to calculate univariate statistics, correlations and perform Poisson regression analyses on the An. gambiae s.l. aquatic habitat datasets. Semivariograms and global autocorrelation statistics were generated in ArcGIS^®. The spatially dependent models indicate the distribution of An. gambiae s.l. aquatic habitats exhibits weak positive autocorrelation in both study sites, with aquatic habitats of similar log‐larval counts tending to cluster in space. Individual anopheline habitats were further evaluated in terms of their covariations with spatial autocorrelation by regressing them on candidate spatial filter eigenvectors. This involved the decomposition of Moran's I statistic into orthogonal and uncorrelated map pattern components using a negative binomial regression. The procedure generated synthetic map patterns of latent spatial correlation representing the geographic configuration of An. gambiae s.l. aquatic habitat locations in each study site. The Gaussian approximation spatial filter models accounted for approximately 13% to 32% redundant locational information in the ecological datasets. Spatial statistics generated in a SAS/GIS^® module can capture spatial dependency effects on the mean response term of a Poisson regression analysis of field and remotely sampled An. gambiae s.l. aquatic habitat data.     

Making direction a first‐class citizen of Tobler's first law of geography

Waldo Tobler frequently reminded us that the law named after him was nothing more than calling for exceptions. This article discusses one of these exceptions. Spatial relations between points are frequently modeled as vectors in which both distance and direction are of equal prominence. However, in Tobler's first law of geography, such a relation is described only from the perspective of distance by relating the decreasing similarity of observations in some attribute space to their increasing distance in geographic space. Although anisotropic versions of many geographic analysis techniques, such as directional semivariograms, anisotropy clustering, and anisotropic point pattern analysis, have been developed over the years, direction remains on the level of an afterthought. We argue that, compared to distance, directional information is still under‐explored and anisotropic techniques are substantially less frequently applied in everyday GIS analysis. Commonly, when classical spatial autocorrelation indicators, such as Moran's I, are used to understand a spatial pattern, the weight matrix is only built from distance, without direction being considered. Similarly, GIS operations, such as buffering, do not take direction into account either, with distance in all directions being treated equally. In reality, meanwhile, particularly in urban structures and when processes are driven by the underlying physical geography, direction plays an essential role. In this article we ask whether the development of early GIS, data (sample) sparsity, and Tobler's law lead to a theory‐induced blindness for the role of direction. If so, is it possible to envision direction becoming a first‐class citizen of equal importance to distance instead of being an afterthought only considered when the deviation from a perfect circle becomes too obvious to be ignored?     

Predictive fire occurrence modelling to improve burned area estimation at a regional scale: A case study in East Caprivi,Namibia

Fires threaten human lives, property and natural resources in Southern African savannas. Due to warming climate, fire occurrence may increase and fires become more intense. It is crucial, therefore, to understand the complexity of spatiotemporal and probabilistic characteristics of fires. This study scrutinizes spatiotemporal characteristics of fires and the role played by abiotic, biotic and anthropogenic factors for fire probability modelling in a semiarid Southern African savanna environment. The MODIS fire products: fire hot spots (MOD14A2 and MYD14A2) and burned area product MODIS (MCD45A1), and GIS derived data were used in analysis. Fire hot spots occurrence was first analysed, and spatial autocorrelation for fires investigated, using Moran's I correlograms. Fire probability models were created using generalized linear models (GLMs). Separate models were produced for abiotic, biotic, anthropogenic and combined factors and an autocovariate variable was tested for model improvement. The hierarchical partitioning method was used to determine independent effects of explanatory variables. The discriminating ability of models was evaluated using area under the curve (AUC) from the receiver operating characteristic (ROC) plot. The results showed that 19.2–24.4% of East Caprivi burned when detected using MODIS hot spots fire data and these fires were strongly spatially autocorrelated. Therefore, the autocovariate variable significantly improved fire probability models when added to them. For autologistic models, i.e. models accounting for spatial autocorrelation, discrimination was good to excellent (AUC 0.858–0.942). For models not counting spatial autocorrelation, prediction success was poor to moderate (AUC 0.542–0.745). The results of this study clearly showed that spatial autocorrelation has to be taken in to account in the fire probability model building process when using remotely sensed and GIS derived data. This study also showed that fire probability models accounting for spatial autocorrelation proved to be superior in regional scale burned area estimation when compared with MODIS burned area product (MCD45A1).     

A comprehensive framework for exploratory spatial data analysis: Moran location and variance scatterplots

Abstract

A significant Geographic Information Science (GIS) issue is closely related to spatial autocorrelation, a burning question in the phase of information extraction from the statistical analysis of georeferenced data. At present, spatial autocorrelation presents two types of measures: continuous and discrete. Is it possible to use Moran's I and the Moran scatterplot with continuous data? Is it possible to use the same methodology with discrete data? A particular and cumbersome problem is the choice of the spatial-neighborhood matrix (W) for points data. This paper addresses these issues by introducing the concept of covariogram contiguity, where each weight is based on the variogram model for that particular dataset: (1) the variogram, whose range equals the distance with the highest Moran I value, defines the weights for points separated by less than the estimated range and (2) weights equal zero for points widely separated from the variogram range considered. After the W matrix is computed, the Moran location scatterplot is created in an iterative process. In accordance with various lag distances, Moran's I is presented as a good search factor for the optimal neighborhood area. Uncertainty/transition regions are also emphasized. At the same time, a new Exploratory Spatial Data Analysis (ESDA) tool is developed, the Moran variance scatterplot, since the conventional Moran scatterplot is not sensitive to neighbor variance. This computer-mapping framework allows the study of spatial patterns, outliers, changeover areas, and trends in an ESDA process. All these tools were implemented in a free web e-Learning program for quantitative geographers called SAKWeb© (or, in the near future, myGeooffice.org).     

Multiscale mapping of burn area and severity using multisensor satellite data and spatial autocorrelation analysis

Traditional methods of recording fire burned areas and fire severity involve expensive and time-consuming field surveys. Available remote sensing technologies may allow us to develop standardized burn-severity maps for evaluating fire effects and addressing post fire management activities. This paper focuses on multiscale characterization of fire severity using multisensor satellite data. To this aim, both MODIS (Moderate Resolution Imaging Spectroradiometer) and ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer) data have been processed using geo-statistic analyses to capture pattern features of burned areas.Even if in last decades different authors tried to integrate geo-statistics and remote sensing image processing, methods used since now are only variograms, semivariograms and kriging. In this paper, we propose an approach based on the use of spatial indicators of global and local autocorrelation. Spatial autocorrelation statistics, such as Moran's I and Getis–Ord Local Gi index, were used to measure and analyze dependency degree among spectral features of burned areas. This approach enables the characterization of pattern features of a burned area and improves the estimation of fire severity.     

Detection of temporal changes in the spatial distribution of cancer rates using local Moran’s I and geostatistically simulated spatial neutral models

This paper presents the first application of spatially correlated neutral models to the detection of changes in mortality rates across space and time using the local Morans I statistic. Sequential Gaussian simulation is used to generate realizations of the spatial distribution of mortality rates under increasingly stringent conditions: 1) reproduction of the sample histogram, 2) reproduction of the pattern of spatial autocorrelation modeled from the data, 3) incorporation of regional background obtained by geostatistical smoothing of observed mortality rates, and 4) incorporation of smooth regional background observed at a prior time interval. The simulated neutral models are then processed using two new spatio-temporal variants of the Morans I statistic, which allow one to identify significant changes in mortality rates above and beyond past spatial patterns. Last, the results are displayed using an original classification of clusters/outliers tailored to the space-time nature of the data. Using this new methodology the space-time distribution of cervix cancer mortality rates recorded over all US State Economic Areas (SEA) is explored for 9 time periods of 5 years each. Incorporation of spatial autocorrelation leads to fewer significant SEA units than obtained under the traditional assumption of spatial independence, confirming earlier claims that Type I errors may increase when tests using the assumption of independence are applied to spatially correlated data. Integration of regional background into the neutral models yields substantially different spatial clusters and outliers, highlighting local patterns which were blurred when local Morans I was applied under the null hypothesis of constant risk.This research was funded by grants R01 CA92669 and 1R43CA105819-01 from the National Cancer Institute and R43CA92807 under the Innovation in Biomedical Information Science and Technology Initiative at the National Institute of Health. The views stated in this publication are those of the authors and do not necessarily represent the official views of the NCI. The authors also thank three anonymous reviewers for their comments that helped improve the presentation of the methodology.     

A Comparison of Aspatial and Spatial Measures of Segregation

The modifiable areal unit problem arises when the boundaries that define neighborhoods affect perceived levels of segregation. Scholars postulate that this problem is exacerbated when one uses a definition of neighborhoods that is based on administrative units; doing so leads to an aspatial measure of segregation, which may or may not adequately account for the spatial relationships among residential locations. In this article, we assess whether aspatial and spatial definitions of neighborhoods produce different perceived levels of income segregation. Using an original individual‐level dataset on income in San Mateo County, California, we define each individual's neighborhood in three ways – two aspatial and one spatial. On the basis of these definitions of neighborhoods, we then estimate residential income segregation using the local Moran's I statistic. We report two primary findings. First, the three measures generate different perceived levels of income segregation. Specifically, we observe less income segregation when using the aspatial measures as compared with the spatial one. Second, the inconsistencies between these measures are systematic in such a way as to lead to different inferences when used to predict individual voter turnout.     

Evaluating Local Non-Stationarity when Considering the Spatial Variation of Large-scale Autocorrelation

Multi‐scale effects of spatial autocorrelation may be present in datasets. Given the importance of detecting local non‐stationarity in many theoretical as well as applied studies, it is necessary to “remove” the impact of large‐scale autocorrelation before common techniques for local pattern analysis are applied. It is proposed in this paper to employ the regionalized range to define spatially varying sub‐regions within which the impact of large‐scale autocorrelation is minimized and the local patterns can be investigated. A case study is conducted on crime data to detect crime hot spots and cold spots in San Antonio, Texas. The results confirm the necessity of treating the non‐stationarity of large‐scale spatial autocorrelation prior to any action aiming at detecting local autocorrelation.     

Low Altitude Aerial Photography Applications for Digital Surface Models Creation in Archaeology

Low Altitude Aerial Photography (LAAP) is based on the use of small flying platforms to take photographs from very low altitudes. The acquisition of series of Digital Surface Models (DSMs) and orthoimages through photogrammetric and orthorectification processes is one of the main applications. The use of this technique in archaeological sites provides very precise and valuable data, but knowing the reliability of the method is a key to ensuring that the results are valid, since the repeatability of the method is fundamental to multitemporal studies. The present work shows an analysis of the similarity of DSMs obtained from different stereoscopic pairs from the same area. The reliability of the models has been assessed by calculating the Standard Deviation (STD) of the altitude values from the models, to obtain maps displaying the differences among them. Finally, the STD values' spatial distribution has been studied to assess if spatial autocorrelation exists by means of the Moran's Index and Anselin's Local Moran's Index. Results showed good similarity among the models and revealed clearly those areas where the model must be edited.     

Small-world characteristics on transportation networks: a perspective from network autocorrelation

Studies on small-world networks have received intensive interdisciplinary attention during the past several years. It is well-known among researchers that a small-world network is often characterized by high connectivity and clustering, but so far there exist few effective approaches to evaluate small-world properties, especially for spatial networks. This paper proposes a method to examine the small-world properties of spatial networks from the perspective of network autocorrelation. Two network autocorrelation statistics, Moran’s I and Getis–Ord’s G, are used to monitor the structural properties of networks in a process of “rewiring” networks from a regular to a random network. We discovered that Moran’s I and Getis–Ord’s G tend to converge and have relatively low values when properties of small-world networks emerge. Three transportation networks at the national, metropolitan, and intra-city levels are analyzed using this approach. It is found that spatial networks at these three scales possess small-world properties when the correlation lag distances reach certain thresholds, implying that the manifestation of small-world phenomena result from the interplay between the network structure and the dynamics taking place on the network.      

An Evaluation of Fractal Methods for Characterizing Image Complexity

Previously, we developed an integrated software package called ICAMS (Image Characterization and Modeling System) to provide specialized spatial analytical functions for interpreting remote sensing data. This paper evaluates three fractal dimension measurement methods that have been implemented in ICAMS: isarithm, variogram, and a modified version of triangular prism. To provide insights into how the fractal methods compare with conventional spatial techniques in measuring landscape complexity, the performance of two spatial autocorrelation methods, Moran's I and Geary's C, is also evaluated. Results from analyzing 25 simulated surfaces having known fractal dimensions show that both the isarithm and triangular prism methods can accurately measure a range of fractal surfaces. The triangular prism method is most accurate at estimating the fractal dimension of surfaces having higher spatial complexity, but it is sensitive to contrast stretching. The variogram method is a comparatively poor estimator for all surfaces, particularly those with high fractal dimensions. As with the fractal techniques, spatial autocorrelation techniques have been found to be useful for measuring complex images, but not images with low dimensionality. Fractal measurement methods, as well as spatial autocorrelation techniques, can be applied directly to unclassified images and could serve as a tool for change detection and data mining.     

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.     

Maps and Mapping Technologies of the Persian Gulf War

Assessing the recent Persian Gulf War from a cartographic standpoint is now possible. Unlike in previous wars, which established new technologies for postwar cartographic exploitation, the gulf war is unique in having presented a proving ground for electronic cartographic technology. An analysis is given of map coverage of the war by the media, especially magazines and newspapers, and from a military perspective. From a cartographic standpoint, the winners in the war include hand-held Global Positioning System (GPS) technology, geographic information systems (GIS), workstation-based image processing and cartographic map-production systems, and radar imaging from aircraft. More fully exploiting and building on the success of these technologies in peacetime seems to be a clear mandate for academic and professional cartography.     

中国农村居民收入时空分异

在ArcGIS和GeoDA等软件的支持下,本文利用标准差指数、变异系数法,结合重心迁移、空间自相关等探索性空间数据分析法(ESDA),首先,对2000~2014年全国整体农村居民人均纯收入进行时间演变特征分析,接着对2000~2013年全国31个省级农村居民人均纯收入的空间分异格局、重心迁移趋势和空间相关性等特征进行分析。结果表明,中国农村收入增速加快,逐渐超过城镇,贫富差距拉大;中国省级农村居民收入区域分异特征出现变化,由严格的东高西低的梯度型变为中西部较低的局部跳跃型;全局空间正相关性显著,存在空间集聚特征,形成东部沿海省份和东北地区的高值聚集区以及西部大片区域的低值聚集区;从省级收入增长率上来看,区域增速的高低发生转变;农民人均收入重心向西北迁移,有利于减小东西收入差距。     

Spatial analysis in epidemiology: Nascent science or a failure of GIS?

This paper summarizes contributions of GIS in epidemiology, and identifies needs required to support spatial epidemiology as science. The objective of spatial epidemiology is to identify disease causes and correlates by relating spatial disease patterns to geographic variation in health risks. GIS supports disease mapping, location analysis, the characterization of populations, and spatial statistics and modeling. Although laudable, these accomplishments are not sufficient to fully identify disease causes and correlates. One reason is the failure of present-day GIS to provide tools appropriate for epidemiology. Two needs are most pressing. First, we must reject the static view: meaningful inference about the causes of disease is impossible without both spatial and temporal information. Second, we need models that translate space-time data on health outcomes and putative exposures into epidemiologically meaningful measures. The first need will be met by the design and implementation of space-time information systems for epidemiology; the second by process-based disease models.     

基于ESDA-GIS的新疆县域经济时空差异研究

区域经济差异历来是国内外学者关注的热点问题。从时空角度出发,本文利用新疆1978-2004年县域人均GDP数据,采用变差系数、ESDA全局和局部空间自相关分析方法与GIS技术相结合,对新疆县域经济总体发展差异和局部空间异质性的演变特征进行了实证研究。变差系数分析显示新疆县际经济差异并不沿着"倒U字"型的轨迹变化,1978-2004年县域间的经济差距先减少,而后缓慢扩大。通过新疆各县人均GDP的空间自相关系数(Moran’sI)的计算,我们发现改革开放以来新疆经济发展的空间集聚效应增强,集聚区域间的经济差距不断拉大。对不同年度新疆各县人均GDP的局域空间自相关分析进一步揭示出北疆中、西部、南疆西、北部逐渐形成"HH"和"LL"两种类型空间集聚。实践证明空间分析方法是传统经济差异量度方法的一种有益补充,使我们更加深入理解区域经济的空间格局及其变化规律。     

基于GIS的湖北省区域经济差异空间统计分析

运用了空间统计分析和地理信息系统技术相结合的方法,分析和研究了湖北省区域经济差异,揭示了湖北省区域经济差异的空间自相关和空间集聚特征。