Understanding the Combined Impacts of Aggregation and Spatial Non‐Stationarity: The Case of Migration‐Environment Associations in Rural South Africa

Socio‐demographic data are typically collected at various levels of aggregation, leading to the modifiable areal unit problem. Spatial non‐stationarity of statistical associations between variables further influences the demographic analyses. This study investigates the implications of these two phenomena within the context of migration‐environment associations. Global and local statistical models are fit across increasing levels of aggregation using household level survey data from rural South Africa. We raise the issue of operational scale sensitivity, which describes how the explanatory power of certain variables depends on the aggregation level. We find that as units of analysis (households) are aggregated, some variables become non‐significant in the global models, while others are less sensitive to aggregation. Local model results show that aggregation reduces spatial variation in migration‐related local associations but also affects variables differently. Spatial non‐stationarity appears to be the driving force behind this phenomenon as the results from the global model mask this relationship. Operational scale sensitivity appears related to the underlying spatial autocorrelation of the non‐aggregated variables but also to the way a variable is constructed. Understanding operational scale sensitivity can help to refine the process of selecting variables related to the scale of analysis and better understand the effects of spatial non‐stationarity on statistical relationships.     

基于空间连续数据的小流域景观格局破碎化研究

基于空间连续数据，采用局部空间关联指标（LISA）——局部Moran指数（Local Moran Index, LMI），通过探测小流域内景观均质性和异质性的变化情况来反映景观格局破碎化的变化过程。作为一种空间明确的景观格局研究方法，LMI能够发现流域景观格局变化过程中的热点地区，并分析其与流域土地利用变化之间的联系，明确了土地利用变化是引起小流域景观格局变化的最主要的驱动因素。研究表明，基于空间连续数据的局部空间关联指标方法可以作为传统景观格局变化研究方法的有益补充。     

Geographically weighted regression‐based determinants of malaria incidences in northern China

Geographically weighted regression (GWR) is an important local method to explore spatial non‐stationarity in data relationships. It has been repeatedly used to examine spatially varying relationships between epidemic diseases and predictors. Malaria, a serious parasitic disease around the world, shows spatial clustering in areas at risk. In this article, we used GWR to explore the local determinants of malaria incidences over a 7‐year period in northern China, a typical mid‐latitude, high‐risk malaria area. Normalized difference vegetation index (NDVI), land surface temperature (LST), temperature difference, elevation, water density index (WDI) and gross domestic product (GDP) were selected as predictors. Results showed that both positively and negatively local effects on malaria incidences appeared for all predictors except for WDI and GDP. The GWR model calibrations successfully depicted spatial variations in the effect sizes and levels of parameters, and also showed substantially improvements in terms of goodness of fits in contrast to the corresponding non‐spatial ordinary least squares (OLS) model fits. For example, the diagnostic information of the OLS fit for the 7‐year average case is R² = 0.243 and AICc = 837.99, while significant improvement has been made by the GWR calibration with R² = 0.800 and AICc = 618.54.     

Spatial Analysis of 1991 Gulf War Troop Locations in Relationship with Postwar Health Symptom Reports Using GIS Techniques

Spatial autocorrelation analysis was used to identify spatial patterns of 1991 Gulf War (GW) troop locations in relationship to subsequent postwar diagnosis of chronic multisymptom illness (CMI). Criteria for the diagnosis of CMI include reporting from at least two of three symptom clusters: fatigue, musculoskeletal pain, and mood and cognition. A GIS‐based methodology was used to examine associations between potential hazardous exposures or deployment situations and postwar health outcomes using troop location data as a surrogate. GW veterans from the Devens Cohort Study were queried about specific symptoms approximately four years after the 1991 deployment to the Persian Gulf. Global and local statistics were calculated using the Moran's I and G statistics for six selected date periods chosen a priori to mark important GW‐service events or exposure scenarios among 173 members of the cohort. Global Moran's I statistics did not detect global spatial patterns at any of the six specified data periods, thus, indicating there is no significant spatial autocorrelation of locations over the entire Gulf region for veterans meeting criteria for severe postwar CMI. However, when applying local G* and local Moran's I statistics, significant spatial clusters (primarily in the coastal Dammam/Dharhan and the central inland areas of Saudi Arabia) were identified for several of the selected time periods. Further study using GIS techniques, coupled with epidemiological methods, to examine spatial and temporal patterns with larger sample sizes of GW veterans is warranted to ascertain if the observed spatial patterns can be confirmed.     

Spatially constrained regionalization with multilayer perceptron

In this article, multilayer perceptron (MLP) network models with spatial constraints are proposed for regionalization of geostatistical point data based on multivariate homogeneity measures. The study focuses on non‐stationarity and autocorrelation in spatial data. Supervised MLP machine learning algorithms with spatial constraints have been implemented and tested on a point dataset. MLP spatially weighted classification models and an MLP contiguity‐constrained classification model are developed to conduct spatially constrained regionalization. The proposed methods have been tested with an attribute‐rich point dataset of geological surveys in Ukraine. The experiments show that consideration of the spatial effects, such as the use of spatial attributes and their respective whitening, improve the output of regionalization. It is also shown that spatial sorting used to preserve spatial contiguity leads to improved regionalization performance.     

The Role of External Variables and GIS Databases in Geostatistical Analysis

Although many geostatistical studies only study a measured attribute in relation to its spatial coordinates, this paper argues that other layers in the GIS database can be of additional use for spatial prediction purposes. They may enter the prediction equations as predictors in a regression model, or as correlated measurements. In an example we will show how this is done for predicting PCB138, a sediment pollution variable, over the North Sea floor. Issues of exploratory data analysis, required sample size, sample configuration, local versus global neighbourhoods, non‐stationarity, non‐linear transformations, change of support and conditional simulation will be discussed in the light of this example.     

The Impact of Hurricanes on Crime: A Spatio-Temporal Analysis in the City of Houston,Texas

The impact that natural disasters have on crime is not well understood. In general, it is assumed that crime declines shortly after the disaster and slowly increases to pre-disaster levels over time. However, this assumption is not always confirmed by the few empirical studies that have been conducted to date. In this paper we analyze the impacts that Hurricane Rita, and for the purpose of comparison, Hurricane Katrina had on the temporal and spatial distributions of reported crimes in the city of Houston, TX. Crime data were collected before, during, and after the landfall of both hurricanes. The modeling part of this paper focused on primarily spatio-temporal and local regression models at the local scale. Spatio-temporal models were applied to identify potential spatio-temporal crime clusters associated with the hurricanes. A local regression model in the form of a geographically weighted regression was applied to explore relationships between crime clusters and possible underlying factors leading to the creation of said clusters.

The results show that while Hurricane Katrina did not have any apparent impact on crime, Hurricane Rita led to a significant short-term increase in burglaries and auto thefts. The post important result was the identification of a large, highly significant spatio-temporal burglary cluster located in the northeastern part of Houston. This cluster lasted from a few days before to a few days after the landfall of Hurricane Rita. Empirical evidence was found that the mandatory evacuation order that was issued prior to the arrival of Hurricane Rita led to a short-time spike in burglaries. It was assumed that these crimes were committed by individuals who did not follow the evacuation order, but instead burglarized the residences of individuals who did evacuate. No mandatory evacuation order was issued for Hurricane Katrina. Altogether, three variables including the percentage of African Americans, the percentage of persons living below the poverty level, and the distance to the nearest police station was identified as having a positive relationship with the increase in burglaries associated with Hurricane Rita     

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.     

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).     

Improving Geocode Accuracy with Candidate Selection Criteria

Geocoding systems typically use more than one geographic reference dataset to improve match rates and spatial accuracy, resulting in multiple candidate geocodes from which the single “best” result must be selected. Little scientific evidence exists for formalizing this selection process or comparing one strategy to another, leading to the approach used in existing systems which we term the hierarchy‐based criterion: place the available reference data layers into qualitative, static, and in many cases, arbitrary hierarchies and attempt a match in each layer, in order. The first non‐ambiguous match with suitable confidence is selected and returned as output. This approach assumes global relationships of relative accuracy between reference data layers, ignoring local variations that could be exploited to return more precise geocodes. We propose a formalization of the selection criteria and present three alternative strategies which we term the uncertainty‐, gravitationally‐, and topologically‐based strategies. The performance of each method is evaluated against two ground truth datasets of nationwide GPS points to determine any resulting spatial improvements. We find that any of the three new methods improves on current practice in the majority of cases. The gravitationally‐ and topologically‐based approaches offer improvement over a simple uncertainty‐based approach in cases with specific characteristics.     

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.     

基于多种空间权重矩阵的区域经济空间自相关分析——以河南省为例

在空间统计分析的应用中,空间权重矩阵的设定对空间自相关的分析结果有较大的影响。通过构建基于邻接关系和空间距离的两大类共计14组空间权重矩阵,以河南省县域经济为研究对象,计算全局和局部两种空间自相关指数,研究空间权重矩阵对区域经济空间自相关分析的影响。结果表明:1)一阶车矩阵比二阶车矩阵能更好地度量河南省县域经济的空间分布,表明河南省县域经济的空间自相关性主要发生在边界直接相邻的区域之间,空间依赖效应从邻域不断向外辐射的现象不明显。2)合理应用空间距离矩阵的关键是能够正确设定阈值距离d,当40 km<d<50 km时,河南省县域经济呈现显著的空间自相关性。3)由郑州市以及围绕郑州的环形区域共同构成了河南省唯一的大面积高GDP值聚集区域,省会城市的经济外溢现象明显;豫东北的鹤壁市和新乡市为低GDP值聚集区域。     

Is your neighbor your friend? Scan methods for spatial social network hotspot detection

GIS analyses use moving window methods and hotspot detection to identify point patterns within a given area. Such methods can detect clusters of point events such as crime or disease incidences. Yet, these methods do not account for connections between entities, and thus, areas with relatively sparse event concentrations but high network connectivity may go undetected. We develop two scan methods (i.e., moving window or focal processes), EdgeScan and NDScan, for detecting local spatial-social connections. These methods capture edges and network density, respectively, for each node in a given focal area. We apply methods to a social network of Mafia members in New York City in the 1960s and to a 2019 spatial network of home-to-restaurant visits in Atlanta, Georgia. These methods successfully capture focal areas where Mafia members are highly connected and where restaurant visitors are highly local; these results differ from those derived using traditional spatial hotspot analysis using the Getis–Ord Gi* statistic. Finally, we describe how these methods can be adapted to weighted, directed, and bipartite networks and suggest future improvements.     

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.     

SE‐KGE: A location‐aware Knowledge Graph Embedding model for Geographic Question Answering and Spatial Semantic Lifting

Learning knowledge graph (KG) embeddings is an emerging technique for a variety of downstream tasks such as summarization, link prediction, information retrieval, and question answering. However, most existing KG embedding models neglect space and, therefore, do not perform well when applied to (geo)spatial data and tasks. Most models that do consider space primarily rely on some notions of distance. These models suffer from higher computational complexity during training while still losing information beyond the relative distance between entities. In this work, we propose a location‐aware KG embedding model called SE‐KGE. It directly encodes spatial information such as point coordinates or bounding boxes of geographic entities into the KG embedding space. The resulting model is capable of handling different types of spatial reasoning. We also construct a geographic knowledge graph as well as a set of geographic query–answer pairs called DBGeo to evaluate the performance of SE‐KGE in comparison to multiple baselines. Evaluation results show that SE‐KGE outperforms these baselines on the DBGeo data set for the geographic logic query answering task. This demonstrates the effectiveness of our spatially‐explicit model and the importance of considering the scale of different geographic entities. Finally, we introduce a novel downstream task called spatial semantic lifting which links an arbitrary location in the study area to entities in the KG via some relations. Evaluation on DBGeo shows that our model outperforms the baseline by a substantial margin.     

An Adaptive Method of Non‐stationary Variogram Modeling for DEM Error Surface Simulation

Geostatistical characterization of local DEM error is usually based on the assumption of a stationary variogram model which requires the mean and variance to be finite and constant in the area under investigation. However, in practice this assumption is appropriate only in a restricted spatial location, where the local experimental variograms vary slowly. Therefore, an adaptive method is developed in this article to model non‐stationary variograms, for which the estimator and the indicator for characterization of spatial variation are a Voronoi map and the standard deviation of mean values displayed in the Voronoi map, respectively. For the adaptive method, the global domain is divided into different meshes with various sizes according to the variability of local variograms. The adaptive method of non‐stationary variogram modeling is applied to simulating error surfaces of a LiDAR derived DEM located in Sichuan province, China. Results indicate that the locally adaptive variogram model is more accurate than the global one for capturing the characterization of spatial variation in DEM errors. The adaptive model can be considered as an alternative approach to modeling non‐stationary variograms for DEM error surface simulation.     

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     

Spatial Information Divergence: Using Global and Local Indices to Compare Geographical Masks Applied to Crime Data

Advances in Geographic Information Science (GISc) and the increasing availability of location data have facilitated the dissemination of crime data and the abundance of crime mapping websites. However, data holders acknowledge that when releasing sensitive crime data there is a risk of compromising the victims' privacy. Hence, protection methodologies are primarily applied to the data to ensure that individual privacy is not violated. This article addresses one group of location protection methodologies, namely geographical masks that are applicable for crime data representations. The purpose is to identify which mask is the most appropriate for crime incident visualizations. A global divergence index (GDi) and a local divergence index (LDi) are developed to compare the effects that these masks have on the original crime point pattern. The indices calculate how dissimilar the spatial information of the masked data is from the spatial information of the original data in regards to the information obtained via spatial crime analysis. The results of the analysis show that the variable radius mask and the donut geomask should be primarily used for crime representations as they produce less spatial information divergence of the original crime point pattern than the alternative local random rotation mask and circular mask.     

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。     

ADCN: An anisotropic density‐based clustering algorithm for discovering spatial point patterns with noise

Density‐based clustering algorithms such as DBSCAN have been widely used for spatial knowledge discovery as they offer several key advantages compared with other clustering algorithms. They can discover clusters with arbitrary shapes, are robust to noise, and do not require prior knowledge (or estimation) of the number of clusters. The idea of using a scan circle centered at each point with a search radius Eps to find at least MinPts points as a criterion for deriving local density is easily understandable and sufficient for exploring isotropic spatial point patterns. However, there are many cases that cannot be adequately captured this way, particularly if they involve linear features or shapes with a continuously changing density, such as a spiral. In such cases, DBSCAN tends to either create an increasing number of small clusters or add noise points into large clusters. Therefore, in this article, we propose a novel anisotropic density‐based clustering algorithm (ADCN). To motivate our work, we introduce synthetic and real‐world cases that cannot be handled sufficiently by DBSCAN (or OPTICS). We then present our clustering algorithm and test it with a wide range of cases. We demonstrate that our algorithm can perform equally as well as DBSCAN in cases that do not benefit explicitly from an anisotropic perspective, and that it outperforms DBSCAN in cases that do. Finally, we show that our approach has the same time complexity as DBSCAN and OPTICS, namely O(n log n) when using a spatial index and O(n²) otherwise. We provide an implementation and test the runtime over multiple cases.