Crime Risk Maps: A Multivariate Spatial Analysis of Crime Data

In crime analyses, maps showing the degree of risk help police departments to make decisions on operational matters, such as where to patrol or how to deploy police officers. This study statistically models spatial crime data for multiple crime types in order to produce joint crime risk maps. To effectively model and map the spatial crime data, we consider two important characteristics of crime occurrences: the spatial dependence between sites, and the dependence between multiple crime types. We reflect both characteristics in the model simultaneously using a generalized multivariate conditional autoregressive model. As a real‐data application, we examine the number of incidents of vehicle theft, larceny, and burglary in 83 census tracts of San Francisco in 2010. Then, we employ a Bayesian approach using a Markov chain Monte Carlo method to estimate the model parameters. Based on the results, we detect the crime hotspots, thus demonstrating the advantage of using a multivariate spatial analysis for crime data.     

Exploring scale-dependent correlations between cancer mortality rates using factorial kriging and population-weighted semivariograms

This article presents a geostatistical methodology that accounts for spatially varying population size in the processing of cancer mortality data. The approach proceeds in two steps: (1) spatial patterns are first described and modeled using population-weighted semivariogram estimators, (2) spatial components corresponding to nested structures identified on semivariograms are then estimated and mapped using a variant of factorial kriging. The main benefit over traditional spatial smoothers is that the pattern of spatial variability (i.e., direction-dependent variability, range of correlation, presence of nested scales of variability) is directly incorporated into the computation of weights assigned to surrounding observations. Moreover, besides filtering the noise in the data, the procedure allows the decomposition of the structured component into several spatial components (i.e., local versus regional variability) on the basis of semivariogram models. A simulation study demonstrates that maps of spatial components are closer to the underlying risk maps in terms of prediction errors and provide a better visualization of regional patterns than the original maps of mortality rates or the maps smoothed using weighted linear averages. The proposed approach also attenuates the underestimation of the magnitude of the correlation between various cancer rates resulting from noise attached to the data. This methodology has great potential to explore scale-dependent correlation between risks of developing cancers and to detect clusters at various spatial scales, which should lead to a more accurate representation of geographic variation in cancer risk, and ultimately to a better understanding of causative relationships.     

Geostatistical Smoothing of Areal Data: Mapping Employment Density with Factorial Kriging

This article summarizes area-to-point (ATP) factorial kriging that allows the smoothing of aggregate, areal data into a continuous spatial surface. Unlike some other smoothing methods, ATP factorial kriging does not suppose that all of the data within an area are located at a centroid or other arbitrary point. Also, unlike some other smoothing methods, factorial kriging allows the user to utilize an autocovariance function to control the smoothness of the output. This is beneficial because the covariance function is a physically meaningful statement of spatial relationship, which is not the case when other spatial kernel functions are used for smoothing. Given a known covariance function, factorial kriging gives the smooth surface that is best in terms of minimizing the expected mean squared prediction error. I present an application of the factorial kriging methodology for visualizing the structure of employment density in the Denver metropolitan area.     

Analyzing Hotspots of Crime Using a Bayesian Spatiotemporal Modeling Approach: A Case Study of Violent Crime in the Greater Toronto Area

Conventional methods used to identify crime hotspots at the small‐area scale are frequentist and employ data for one time period. Methodologically, these approaches are limited by an inability to overcome the small number problem, which occurs in spatiotemporal analysis at the small‐area level when crime and population counts for areas are low. The small number problem may lead to unstable risk estimates and unreliable results. Also, conventional approaches use only one data observation per area, providing limited information about the temporal processes influencing hotspots and how law enforcement resources should be allocated to manage crime change. Examining violent crime in the Regional Municipality of York, Ontario, for 2006 and 2007, this research illustrates a Bayesian spatiotemporal modeling approach that analyzes crime trend and identifies hotspots while addressing the small number problem and overcoming limitations of conventional frequentist methods. Specifically, this research tests for an overall trend of violent crime for the study region, determines area‐specific violent crime trends for small‐area units, and identifies hotspots based on crime trend from 2006 to 2007. Overall violent crime trend was found to be insignificant despite increasing area‐specific trends in the north and decreasing area‐specific trends in the southeast. Posterior probabilities of area‐specific trends greater than zero were mapped to identify hotspots, highlighting hotspots in the north of the study region. We discuss the conceptual differences between this Bayesian spatiotemporal method and conventional frequentist approaches as well as the effectiveness of this Bayesian spatiotemporal approach for identifying hotspots from a law enforcement perspective.     

On Geocomputational Determinants of Entropic Variations for Urban Dynamics Studies

Monitoring population characteristics and their patterns of spatial evolution are fundamental components for urban management and policy decision‐making. Societal issues such as health, transport, or crime are often explored using a range of models describing the urban dynamics of population attributes at specific scales that can be seen as complementary. Using and simulating data at different scales of aggregation asks for the need to analyze and compare spatiotemporal variations in order to better understand the model behaviors and emerging properties of the geosimulation. This article analyzes the uses of the entropy measure in the literature and constraining factors needed for its potential extension to explore the variations in geographic and time scales. In particular, the article discusses the need for a truly spatial entropy that takes into account the spatial contiguities of the observations usually aggregated within a zoning system of areal units. Two generic solutions are exposed for the various geometries and attribute structures used for census‐related analyses; they are based on existing measures for point data using (i) co‐occurrences of observations and (ii) discriminant ratios of distances between groups of observations. Their extensions to areal compositional data are articulated around their conceptual changes and geocomputational challenges. A revisited and new version of the entropy decomposition theorem, encompassing a spatiality concept semantically related to correlation, is also presented as efficiently reusing the constrained hierarchical zoning system of administrative units to enable discovery of emerging spatial pattern features from the geosimulation. A comparison of the results between the classical use of entropy and the spatial entropy framework devised shows the flexibility and added capabilities of the approach for new types of analyses, thus allowing new insight into studies of population dynamics.     

The Effect on Attribute Prediction of Location Uncertainty in Spatial Data

A datum is considered spatial if it contains location information. Typically, there is also attribute information, whose distribution depends on its location. Thus, error in location information can lead to error in attribute information, which is reflected ultimately in the inference drawn from the data. We propose a statistical model for incorporating location error into spatial data analysis. We investigate the effect of location error on the spatial lag, the covariance function, and optimal spatial linear prediction (that is, kriging). We show that the form of kriging after adjusting for location error is the same as that of kriging without adjusting for location error. However, location error changes entries in the matrix of explanatory variables, the matrix of co‐variances between the sample sites, and the vector of covariances between the sample sites and the prediction location. We investigate, through simulation, the effect that varying trend, measurement error, location error, range of spatial dependence, sample size, and prediction location have on kriging after and without adjusting for location error. When the location error is large, kriging after adjusting for location error performs markedly better than kriging without adjusting for location error, in terms of both the prediction bias and the mean squared prediction error.     

基于道路网络的犯罪空间聚集特征研究

由于目前犯罪空间聚集特征研究的单元主要是地点、街区、巡逻区等,但是许多警务工作是沿道路网络开展的,因此有必要研究犯罪在道路网络上的空间聚集特征。本文以路段为分析单元对浙江省某地2011-2014年发生的16787起盗窃类犯罪进行了研究。通过分析,发现:1在道路网络中存在犯罪热点路段;2犯罪在路段上具有聚集性,少部分犯罪热点路段聚集了大部分犯罪,如19.86%的犯罪热点路段聚集了53.42%的犯罪;3犯罪热点路段在道路网络中也具有空间聚集性,主要聚集在类型为住宅区、大学、商业区等7个区域。根据犯罪在道路网络上的聚集特征,警察部门能优化相关警务工作,科学分配警力资源,从而提高治安防控、犯罪预防、侦查破案等能力和效率。     

城市犯罪风险区位因子与风险地形分析——以武汉市主城区为例

从犯罪背景空间、场所空间、联接空间和聚集空间四个层次,构建城市犯罪风险区位因子体系。以武汉市主城区为研究区域,以立案判决的“两抢一盗”犯罪为数据源,综合运用空间句法、犯罪近重复分析和地理加权回归模型方法进行犯罪风险地形建模实证研究。结果表明,犯罪风险区位因子对犯罪空间分布的影响具有显著的空间异质性;依据多层次的犯罪风险区位因子体系及其对犯罪行为的影响机制,城市犯罪高风险区域可分为城市商业中心、火车站交通枢纽、城中村和城乡结合部等几大类型。基于犯罪地理学理论构建的犯罪风险区位因子体系模拟的犯罪风险地形对实际犯罪空间分布有良好的解释度,可为城市犯罪分布环境形成机制的研究提供相关借鉴。     

Crime Exposure Along My Way Home: Estimating Crime Risk Along Personal Trajectory by Visual Analytics

Crime has been one of the notorious public threats in cities. Fortunately, the increasing digital crime data provide great opportunities to analyze and control crime incidents. However, studies that predict the risk of crime exposure for an individual’s spatiotemporal paths based on historical crime big data are still limited. In this study, we have proposed the crime risk index (CRI) for spatiotemporal trajectory and built a model to estimate the CRI. Furthermore, an online crime risk analysis platform has been developed based on the model. First, we proposed a multi-scale tile system and a novel algorithm to estimate trajectory-based CRI using big historical crime data and entropy-based weighting. Second, we created a web-based platform that allows users to provide a spatiotemporal trajectory and estimate the crime risk for such trajectory. We conducted several experiments based on the crime data in Detroit. Results demonstrate the practicability and generalizability of our platform. The proposed model and platform can be applied to multiple cities, providing useful references for crime information and public safety.     

THE IMPACT OF CRIME ON APARTMENT PRICES: EVIDENCE FROM STOCKHOLM,SWEDEN

This study uses data of about 9,000 apartment sales in Stockholm, Sweden, to assess the impact of crime on property prices. The study employs hedonic pricing modelling to estimate the impact of crime controlling for other factors (property and neighbourhood characteristics). Geographic Information System (GIS) is used to combine apartment sales by coordinates with offences, land use characteristics and demographic data of the population. The novelty of this research is threefold. First, it explores a set of land use attributes created by spatial techniques in GIS in combination with detailed geographical data in hedonic pricing modelling. Second, the effect of crime in neighbouring zones at one place can be measured by incorporating spatial lagged variables of offence rates into the model. Third, the study provides evidence of the impact of crime on housing prices in a capital city of a traditional welfare state, information otherwise lacking in the international literature. Our results indicate that apartment prices in a specific area are strongly affected by crime in its neighbouring zones, regardless of crime type. When offences were broken down by types, residential burglary, theft, vandalism, assault and robbery individually had a significant negative effect on property values. However, for residential burglary such an effect is not homogenous across space, and apartment prices in central areas are often less discounted by being exposed to crime than those in the city's outskirts.     

Nonlinear Multivariate Spatial Modeling Using NLPCA and Pair‐Copulas

A novel geostatistical modeling approach is developed to model nonlinear multivariate spatial dependence using nonlinear principal component analysis (NLPCA) and pair‐copulas. In spatial studies, multivariate measurements are frequently collected at each location. The dependence between such measurements can be complex. In this article, a multivariate geostatistical model is developed that can capture both nonlinear spatial dependence across locations and nonlinear dependence between measurements at a particular location. Nonlinear multivariate dependence between spatial variables is removed using NLPCA. Subsequently, a pair‐copula based model is fitted to each transformed variable to model the univariate nonlinear spatial dependencies. NLPCA and pair‐copulas, within the proposed model, are compared with stepwise conditional transformation (SCT) and conventional kriging. The results show that, for the two case studies presented, the proposed model that utilizes NLPCA and pair‐copulas reproduces nonlinear multivariate structures and univariate distributions better than existing methods based on SCT and kriging.     

Geography, Spatial Data Analysis, and Geostatistics: An Overview

Geostatistics is a distinctive methodology within the field of spatial statistics. In the past, it has been linked to particular problems (e.g., spatial interpolation by kriging) and types of spatial data (attributes defined on continuous space). It has been used more by physical than human geographers because of the nature of their types of data. The approach taken by geostatisticians has several features that distinguish it from the methods typically used by human geographers for analyzing spatial variation associated with regional data, and we discuss these. Geostatisticians attach much importance to estimating and modeling the variogram to explore and analyze spatial variation because of the insight it provides. This article identifies the benefits of geostatistics, reviews its uses, and examines some of the recent developments that make it valuable for the analysis of data on areal supports across a wide range of problems.     

Modelling spatial heterogeneity and nonstationarity in artifact-rich landscapes

In this paper we consider a crucial issue for survey archaeology: how we identify and make sense of the heterogeneous and often inter-dependent behaviours and processes responsible for apparent archaeological patterns across the landscape. We apply two spatial statistical tools, kriging and geographically weighted regression, to develop a model that addresses the spatial heterogeneity and spatial nonstationarity present in the pottery distributions identified by our intensive survey of the Greek island of Antikythera. Our modelling results highlight a clear spatial structure underlying different scales of pottery density as well as locally varying relationships between pottery densities and several environmental variables. This allows us to develop further testable hypotheses about long-term settlement and land-use patterns on Antikythera, including more explicit models of community organisation, and of the relationship between the island's geomorphological structure and its history of past human activity.     

A Bayesian Approach to Modeling Binary Data: The Case of High‐Intensity Crime Areas

This paper reports the fitting of a number of Bayesian logistic models with spatially structured or/and unstructured random effects to binary data with the purpose of explaining the distribution of high‐intensity crime areas (HIAs) in the city of Sheffield, England. Bayesian approaches to spatial modeling are attracting considerable interest at the present time. This is because of the availability of rigorously tested software for fitting a certain class of spatial models. This paper considers issues associated with the specification, estimation, and validation, including sensitivity analysis, of spatial models using the WinBUGS software. It pays particular attention to the visualization of results. We discuss a map decomposition strategy and an approach that examines properties of the full posterior distribution. The Bayesian spatial model reported provides some interesting insights into the different factors underlying the existence of the three police‐defined HIAs in Sheffield.     

Effects of Confidentiality-Preserving Geo-Masking on the Estimation of Semivariogram and of the Kriging Variance

Geostatistical methods, such as semivariograms and kriging are well-known spatial tools commonly employed in many disciplines such as health, mining, forestry, meteorology to name only few. They are based essentially on point-referenced data on a continuous space and on the calculation of distances between them. In many practical instances, however, the exact point location, even if exactly known, is geo-masked to preserve confidentiality. This typically happens when dealing with confidential data related to individuals-health and their biometric parameters. In these situations, the estimation of the semivariogram and, hence, the spatial prediction can become biased and highly inefficient. This paper examines the extent of the bias in the particular case when the geo-masking mechanism is known (called “intentional locational error”) and lays the ground to a full understanding of the phenomenon in more general cases. We also examine how the geo-masking affects the estimation of the kriging variance thus reducing the efficiency of spatial prediction. We pursue our aims by developing some theoretical results and by making use of simulated and real data analysis.     

A Geostatistical Analysis of Soil, Vegetation, and Image Data Characterizing Land Surface Variation

The elucidation of spatial variation in the landscape can indicate potential wildlife habitats or breeding sites for vectors, such as ticks or mosquitoes, which cause a range of diseases. Information from remotely sensed data could aid the delineation of vegetation distribution on the ground in areas where local knowledge is limited. The data from digital images are often difficult to interpret because of pixel-to-pixel variation, that is, noise, and complex variation at more than one spatial scale. Landsat Thematic Mapper Plus (ETM+) and Satellite Pour l'Observation de La Terre (SPOT) image data were analyzed for an area close to Douna in Mali, West Africa. The variograms of the normalized difference vegetation index (NDVI) from both types of image data were nested. The parameters of the nested variogram function from the Landsat ETM+ data were used to design the sampling for a ground survey of soil and vegetation data. Variograms of the soil and vegetation data showed that their variation was anisotropic and their scales of variation were similar to those of NDVI from the SPOT data. The short- and long-range components of variation in the SPOT data were filtered out separately by factorial kriging. The map of the short-range component appears to represent the patterns of vegetation and associated shallow slopes and drainage channels of the tiger bush system. The map of the long-range component also appeared to relate to broader patterns in the tiger bush and to gentle undulations in the topography. The results suggest that the types of image data analyzed in this study could be used to identify areas with more moisture in semiarid regions that could support wildlife and also be potential vector breeding sites.     

Spatiotemporal Modeling of Correlated Small‐Area Outcomes: Analyzing the Shared and Type‐Specific Patterns of Crime and Disorder

This research applies a Bayesian multivariate modeling approach to analyze the spatiotemporal patterns of physical disorder, social disorder, property crime, and violent crime at the small‐area scale. Despite crime and disorder exhibiting similar spatiotemporal patterns, as hypothesized by broken windows and collective efficacy theories, past studies often analyze a single outcome and overlook the correlation structures between multiple crime and disorder types. Accounting for five covariates, the best‐fitting model partitions the residual risk of each crime and disorder type into one spatial shared component, one temporal shared component, and type‐specific spatial, temporal, and space–time components. The shared components capture the underlying spatial pattern and time trend common to all types of crime and disorder. Results show that population size, residential mobility, and the central business district are positively associated with all outcomes. The spatial shared component is found to explain the largest proportion of residual variability for all types of crime and disorder. Spatiotemporal hotspots of crime and disorder are examined to contextualize broken windows theory. Applications of multivariate spatiotemporal modeling with shared components to ecological crime theories and crime prevention policy are discussed.     

Property and Personal Crime in Istanbul

In recent studies on urban safety, close relationships between physical and demographic characteristics have been found in crime levels in cities. In many countries social, political and economic turmoil have been the main reasons for the increase in urban crime and violence in the last 50 years. In physically deprived environments, the most important factors that increase urban crime are socially isolated communities, economic discrimination and lack of equality in political citizenship rights. In developing countries, it is difficult to obtain data about crime and safety. For this reason, there are very few studies on crime compared to developed countries. In the research in this paper, the similarities and differences of crime ratios against property and persons in Istanbul are compared with those in other countries. For this purpose, the spatial distribution of crimes committed were analysed on a comparative basis between 1998–2002 in 32 districts displaying different characteristics in terms of distance to the centre, use of land, value of land, physical and demographic features. The research revealed that the crime rates in Istanbul against property and persons were in parallel with developed countries. The districts which have mixed use (residential and commercial, residential and industrial), high population increase, high number of households, high density and high land value, property and personal crime levels are high; when date of becoming a district is recent and the size of the district is large, property and personal crime levels are low.     

基于环境犯罪学理论的入室盗窃时空分布研究——以北京市主城区案件的分析为例

以往关于犯罪时空特征的研究较多的侧重于对犯罪时空分布现象的描述分析以及从人文地理视角下的环境影响性分析,但缺少从环境要素与犯罪主体行为之间的相互作用机制下的犯罪时空特征研究。本文通过开展北京市入室盗窃案件的时空热点实证分析,总结和归纳了案件热点环境的时空要素类型,并基于环境犯罪学的基本原理,构建了基于犯罪主体与环境影响要素相互作用的犯罪时空分布机制,其中,环境对犯罪主体的影响主要表现为四类要素,即目标、交通、防范和作案时机。这些研究可以为下一步开展犯罪模拟以及犯罪预防提供借鉴。