Geostatistical methods have rarely been applied to area-level offense data. This article demonstrates their potential for improving the interpretation and understanding of crime patterns using previously analyzed data about car-related thefts for Estonia, Latvia, and Lithuania in 2000. The variogram is used to inform about the scales of variation in offense, social, and economic data. Area-to-area and area-to-point Poisson kriging are used to filter the noise caused by the small number problem. The latter is also used to produce continuous maps of the estimated crime risk (expected number of crimes per 10,000 habitants), thereby reducing the visual bias of large spatial units. In seeking to detect the most likely crime clusters, the uncertainty attached to crime risk estimates is handled through a local cluster analysis using stochastic simulation. Factorial kriging analysis is used to estimate the local- and regional-scale spatial components of the crime risk and explanatory variables. Then regression modeling is used to determine which factors are associated with the risk of car-related theft at different scales.
Areal interpolation transforms data for a variable of interest from a set of source zones to estimate the same variable's distribution over a set of target zones. One common practice has been to guide interpolation by using ancillary control zones that are related to the variable of interest's spatial distribution. This guidance typically involves using source zone data to estimate the density of the variable of interest within each control zone. This article introduces a novel approach to density estimation, the geographically weighted expectation–maximization (GWEM), which combines features of two previously used techniques, the expectation–maximization (EM) algorithm and geographically weighted regression. The EM algorithm provides a framework for incorporating proper constraints on data distributions, and using geographical weighting allows estimated control-zone density ratios to vary spatially. We assess the accuracy of GWEM by applying it with land use/land cover (LULC) ancillary data to population counts from a nationwide sample of 1980 U.S. census tract pairs. We find that GWEM generally is more accurate in this setting than several previously studied methods. Because target-density weighting (TDW)—using 1970 tract densities to guide interpolation—outperforms GWEM in many cases, we also consider two GWEM–TDW hybrid approaches and find them to improve estimates substantially.
Basic health system data such as the number of patients utilising different health facilities and the types of illness for which they are being treated are critical for managing service provision. These data requirements are generally addressed with some form of national Health Management Information System (HMIS) which coordinates the routine collection and compilation of data from national health facilities. HMIS in most developing countries are characterised by widespread under-reporting. Here we present a method to adjust incomplete data to allow prediction of national outpatient treatment burdens. We demonstrate this method with the example of outpatient treatments for malaria within the Kenyan HMIS. Three alternative modelling frameworks were developed and tested in which space-time geostatistical prediction algorithms were used to predict the monthly tally of treatments for presumed malaria cases (MC) at facilities where such records were missing. Models were compared by a cross-validation exercise and the model found to most accurately predict MC incorporated available data on the total number of patients visiting each facility each month. A space-time stochastic simulation framework to accompany this model was developed and tested in order to provide estimates of both local and regional prediction uncertainty. The level of accuracy provided by the predictive model, and the accompanying estimates of uncertainty around the predictions, demonstrate how this tool can mitigate the uncertainties caused by missing data, substantially enhancing the utility of existing HMIS data to health-service decision-makers.
This paper presents a geostatistical methodology which 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.
The analysis of health data and putative covariates, such as environmental, socioeconomic, demographic, behavioral, or occupational factors, is a promising application for geostatistics. Transferring methods originally developed for the analysis of earth properties to health science, however, presents several methodological and technical challenges. These arise because health data are typically aggregated over irregular spatial supports (e.g., counties) and consist of a numerator and a denominator (i.e., rates). This article provides an overview of geostatistical methods tailored specifically to the characteristics of areal health data, with an application to lung cancer mortality rates in 688 U.S. counties of the southeast (1970-1994). Factorial Poisson kriging can filter short-scale variation and noise, which can be large in sparsely populated counties, to reveal similar regional patterns for male and female cancer mortality that correlate well with proximity to shipyards. Rate uncertainty was transferred through local cluster analysis using stochastic simulation, allowing the computation of the likelihood of clusters of low or high cancer mortality. Accounting for population size and rate uncertainty led to the detection of new clusters of high mortality around Oak Ridge National Laboratory for both sexes, in counties with high concentrations of pig farms and paper mill industries for males (occupational exposure) and in the vicinity of Atlanta for females.
This article summarizes a spatial econometric analysis of local population and employment growth in the N etherlands, with specific reference to impacts of gender and space. The simultaneous equations model used distinguishes between population‐ and gender‐specific employment groups, and includes autoregressive and cross‐regressive spatial lags to detect relations both within and among these groups. Spatial weights matrices reflecting different bands of travel times are used to calculate the spatial lags and to gauge the spatial nature of these relations. The empirical results show that although population–employment interaction is more localized for women's employment, no gender difference exists in the direction of interaction. Employment growth for both men and women is more influenced by population growth than vice versa. The interaction within employment groups is even more important than population growth. Women's, and especially men's, local employment growth mostly benefits from the same employment growth in neighboring locations. Finally, interaction between these groups is practically absent, although men's employment growth may have a negative impact on women's employment growth within small geographic areas. In summary, the results confirm the crucial roles of gender and space, and offer important insights into possible relations within and among subgroups of jobs and people.
Este artículo presenta un análisis econométrico espacial de crecimiento de población local y empleo en los Países Bajos con atención especial a los impactos de las variables de género y espacio. El modelo de ecuaciones simultáneas utilizado aquí distingue entre grupos de empleo específicos por población y por género, e incluye lags (o retardos) espaciales autorregresivos y regresivos cruzados ( autoregressive and cross‐regressive spatial lags ) para detectar las relaciones dentro y entre dichos grupos. Para calcular los lags espaciales y para evaluar la naturaleza espacial de estas relaciones, se construyen matrices de pesos espaciales que reflejan los distintos rangos de tiempos de viaje. Los resultados empíricos muestran que aunque la interacción población‐empleo es más localizada para el empleo de mujeres, no existe diferencia de género en la dirección de la interacción. El crecimiento del empleo para hombres y mujeres está más influenciado por el crecimiento demográfico que vice versa. La interacción al interior de los grupos de empleo es aún más importante que el crecimiento de la población. El empleo local de mujeres y especialmente el de hombres se beneficia mayormente del crecimiento del empleo en localidades vecinas. Finalmente, la interacción entre estos grupos es prácticamente nula, aunque el crecimiento de empleo masculino puede tener un impacto negativo en el crecimiento del empleo de las mujeres dentro de áreas geográficas pequeñas. En resumen, los resultados confirman el papel crucial de las variables de género y espacio y ofrecen pistas importantes acerca de las posibles relaciones dentro y entre los subgrupos de empleo y la población.
One of the main tasks in analyzing pedestrian movement is to detect places where pedestrians stop, as those places usually are associated with specific human activities, and they can allow us to understand pedestrian movement behavior. Very few approaches have been proposed to detect the locations of stops in positioning data sets, and they often are based on selecting the location of candidate stops as well as potential spatial and temporal thresholds according to different application requirements. However, these approaches are not suitable for analyzing the slow movement of pedestrians where the inaccuracy of a nondifferential global positioning system commonly used for movement tracking is so significant that it can hinder the selection of adequate thresholds. In this article, we propose an exploratory statistical approach to detect patterns of movement suspension using a local indicator of spatial association (LISA) in a vector space representation. Two different positioning data sets are used to evaluate our approach in terms of exploring movement suspension patterns that can be related to different landscapes: players of an urban outdoor mobile game and visitors of a natural park. The results of both experiments show that patterns of movement suspension were located at places such as checkpoints in the game and different attractions and facilities in the park. Based on these results, we conclude that using LISA is a reliable approach for exploring movement suspension patterns that represent the places where the movement of pedestrians is temporally suspended by physical restrictions (e.g., checkpoints of a mobile game and the route choosing points of a park).
This article discusses options to allow comparative analysis of inequalities in the distribution of health workers ( HWs ) across and within countries using a single summary measure of the distribution. Income inequality generally is measured across individuals, but inequalities in the dispersion of HWs must use geographical areas or population groupings as units of analysis. The article first shows how this change of observational unit creates a resolution problem for various inequality indices and then tests how sensitive a simple ratio measure of the distribution of HWs is to changes in resolution. This ratio of inequality is illustrated first with the global distribution of HWs and then with its distributions within I ndonesia. The resolution problem is not solved through this new approach, and indicators of inequalities of access to HWs or health services more generally appear not to be comparable across countries. Investigating geographical inequalities over time in one setting is possible but only if the units of analysis remain the same over time.
Este artículo examina las opciones para realizar un análisis comparativo de las desigualdades en la distribución de los trabajadores de salud ( health workers‐HW ) a través y al interior de los países que utilizan una sola medida‐resumen para dicha distribución. Por lo general la desigualdad de ingresos se mide entre individuos, pero las desigualdades en la dispersión de HW se miden utilizando las áreas geográficas o grupos de población como unidades de análisis. El artículo presente examina cómo el cambio de la unidad de observación crea un problema de resolución espacial para varios índices de desigualdad. Luego, los autores evalúan la sensibilidad a cambios en la resolución sobre una tasa sencilla de la distribución de HWs. La tasa de desigualdad propuesta por los autores es ilustrada primero por medio de la distribución global de HWs y luego vía sus distribuciones dentro de Indonesia. Los autores concluyen que el problema de resolución no llega a ser resulto por el nuevo enfoque propuesto, y que en términos generales, los indicadores de las desigualdades de acceso a HWs o servicios de salud parecen no ser comparables entre países. La investigación de las desigualdades geográficas a través del tiempo en un mismo contexto geográfico es posible pero sólo si las unidades de análisis se mantienen constantes.
The aim of this paper is to analyze the intra-urban spatial distributions of population and employment in the agglomeration of Dijon (regional capital of Burgundy, France). We study whether this agglomeration has followed the general tendency of job decentralization observed in most urban areas or whether it is still characterized by a monocentric pattern. In that purpose, we use a sample of 136 observations at the communal and at the IRIS (infra-urban statistical area) levels with 1999 census data and the employment database SIRENE (INSEE). First, we study the spatial pattern of total employment and employment density using exploratory spatial data analysis. Apart from the CBD, few IRIS are found to be statistically significant, a result contrasting with those found using standard methods of subcenter identification with employment cut-offs. Next, in order to examine the spatial distribution of residential population density, we estimate and compare different specifications: exponential negative, spline- exponential and multicentric density functions. Moreover, spatial autocorrelation, spatial heterogeneity and outliers are controlled for by using the appropriate maximum likelihood, generalized method of moments and Bayesian spatial econometric techniques. Our results highlight again the monocentric character of the agglomeration of Dijon.
The impact of transportation networks on the location of human activities is a surprisingly neglected topic in economic geography. Using the simple plant location problem, this paper investigates such an impact in the case of a few idealized networks. It is seen that a grid network tends to foster a dispersed pattern of activities, while the center of a radial network acts as an attractor. The case of two economies characterized by different network configurations that form a custom union is then analyzed. It is shown that the structural properties of the networks still hold, though some locations are pulled toward the common border. This suggests that no much relocation should be expected within the European Union if the state members endorse similar fiscal and social policies after the formation of the single market.
In this paper we compare the relative efficiency of different forecasting methods of space-time series when variables are spatially and temporally correlated. We consider the case of a space-time series aggregated into a single time series and the more general instance of a space-time series aggregated into a coarser spatial partition. We extend in various directions the outcomes found in the literature by including the consideration of larger datasets and the treatment of edge effects and of negative spatial correlation. The outcomes obtained provide operational suggestions on how to choose between alternative forecasting methods in empirical circumstances.
This paper surveys changes in the U.S. National Airway System since the 1960s. The most appropriate measures for summarizing air traffic distributions at airports are investigated, with the Gini Index of Concentration being used extensively to analyze U.S. airport traffic patterns over a twenty-four-year period. The properties of the Gini index and other measures are compared and discussed in detail in the context of analyzing air traffic distribution. It is shown how concentration in the traffic patterns at the larger airports was at a high level prior to deregulation, but since 1978, the patterns have gradually become even more concentrated.
This paper addresses the issue of incorporating household dynamics into operational dynamic urban models. Dynamic model approaches that can be used to model urban change are introduced and discussed. We conclude that these different approaches are best combined in an accounting framework. An example of an accounting framework for a dynamic model of Amsterdam is presented. The household submodel is discussed in detail and some preliminary results are given.
One of the key assumptions in spatial econometric modelling is that the spatial process is isotropic, which means that direction is irrelevant in the specification of the spatial structure. On one hand, this assumption largely reduces the complexity of the spatial models and facilitates estimation and interpretation; on the other hand, it appears rather restrictive and hard to justify in many empirical applications. In this paper a very general anisotropic spatial model, which allows for a high level of flexibility in the spatial structure, is proposed. This new model can be estimated using maximum likelihood and its asymptotic properties are well understood. When the model is applied to the well-known 1970 Boston housing prices data, it significantly outperforms the isotropic spatial lag model. It also provides interesting additional insights into the price determination process in the properties market.
We extend the literature on Bayesian model comparison for ordinary least-squares regression models to include spatial autoregressive and spatial error models. Our focus is on comparing models that consist of different matrices of explanatory variables. A Markov Chain Monte Carlo model composition methodology labelled MC to the third by Madigan and York (1995) is developed for two types of spatial econometric models that are frequently used in the literature. The methodology deals with cases where the number of possible models based on different combinations of candidate explanatory variables is large enough that calculation of posterior probabilities for all models is difficult or infeasible. Estimates and inferences are produced by averaging over models using the posterior model probabilities as weights, a procedure known as Bayesian model averaging. We illustrate the methods using a spatial econometric model of origin-destination population migration flows between the 48 US States and District of Columbia during the 1990 to 2000 period.
The objective of this paper is to compare fractal-based parameters calculated by different fractal methods for urban built-up areas, and to link the observed spatial variations to variables commonly used in urban geography, urban economics or land use planning. Computations are performed on Brussels. Two fractal methods (correlation and dilation) are systematically applied for evaluating the fractal dimension of built-up surfaces; correlation is used to evaluate the fractal dimension of the borders (lines). Analyses show that while fractal dimension is ideal for distinguishing the morphology of Brussels, each estimation technique leads to slightly different results. Interesting associations are to be found between the fractal dimensions and rent, distance, income and planning rules. Despite its limitations, fractal analysis seems to be a promising tool for describing the morphology of the city and for simulating its genesis and planning. The model is robust: it replicates the urban spatial regularities and patterns, and could hence fruitfully be integrated into intra urban simulation processes.
Spatial weights matrices are necessary elements in most regression models where a representation of spatial structure is needed. We construct a spatial weights matrix, W, based on the principle that spatial structure should be considered in a two-part framework, those units that evoke a distance effect, and those that do not. Our two-variable local statistics model (LSM) is based on the G
* local statistic. The local statistic concept depends on the designation of a critical distance, d
, defined as the distance beyond which no discernible increase in clustering of high or low values exists. In a series of simulation experiments LSM is compared to well-known spatial weights matrix specifications – two different contiguity configurations, three different inverse distance formulations, and three semi-variance models. The simulation experiments are carried out on a random spatial pattern and two types of spatial clustering patterns. The LSM performed best according to the Akaike Information Criterion, a spatial autoregressive coefficient evaluation, and Moran’s I tests on residuals. The flexibility inherent in the LSM allows for its favorable performance when compared to the rigidity of the global models.
A strong increase in the availability of space-time data has occurred during the past decades. This has led to the development of a substantial literature dealing with the two particular problems inherent to this kind of data, i.e. serial dependence between the observations on each spatial unit over time, and spatial dependence between the observations on the spatial units at each point in time (e.g. Elhorst, 2001, 2003). Typical for spatial panel data models is that the causal direction cannot be based on instantaneous relationships between simultaneously measured variables. Rather the so-called cross-lagged panel design studies compare the effects of variables on each other across time. Although they circumvent the difficult problem of assessing causal direction in cross-sectional research, the cross-lagged panel design studies are usually performed in discrete time (Oud, 2002). Because of different discrete time observation intervals within and between studies, outcomes are often incomparable or appear to be contradictory (Gollob & Reichardt, 1987). This paper will describe the problems of cross-lagged space-time models in discrete time and propose how these problems can be solved through a continuous time approach. In this regard special attention will be paid to structural equation modelling (SEM). In addition, we shall describe how space-time dependence can he handled in a SEM framework
Spatial networks display both topologic and geometric variations in their structure. This study investigates the measurement of road network structure. Existing measures of heterogeneity, connectivity, accessibility, and interconnectivity are reviewed and three supplemental measures are proposed, including measures of entropy, connection patterns, and continuity. Proposed measures were applied to 16 test networks, which were derived from 4 idealized base networks: 90-degree, 45-degree, 30-degree, and completely connected. The results show that the differentiated structures of road networks can be evaluated by the measure of entropy; predefined connection patterns of arterial roads can be identified and quantified by the measures of ringness, webness, beltness, circuitness, and treeness. A measure of continuity evaluates the quality of a network from the perspective of travelers. Proposed measures could be used to describe the structural attributes of complicated road networks quantitatively, to compare different network structures, and to explore the structural evolution of networks in the spatial and temporal context. These measures can find their applications in urban planning and transportation practice.
This paper presents a methodology for neural spatial interaction modelling. Particular emphasis is laid on design, estimation and performance issues in both cases, unconstrained and singly constrained spatial interaction. Families of classical neural network models, but also less classical ones such as product unit neural network models are considered. Some novel classes of product unit and summation unit models are presented for the case of origin or destination constrained spatial interaction flows. The models are based on a modular connectionist architecture that may be viewed as a linked collection of functionally independent neural modules with identical feedforward topologies, operating under supervised learning algorithms. Parameter estimation is viewed as Maximum Likelihood (ML) learning. The nonconvex nature of the loss function makes the Alopex procedure, a global search procedure, an attractive and appropriate optimising scheme for ML learning. A benchmark comparison against the classical gravity models illustrates the superiority of both, the unconstrained and the origin constrained, neural network model versions in terms of generalization performance measured by Kullback and Leibler`s information criterion. Hereby, the authors make use of the bootstrapping pairs approach to overcome the largely neglected problem of sensitivity to the specific splitting of the data into training, internal validation and testing data sets, and to get a better statistical picture of prediction variability of the models. Keywords: Neural spatial interaction models, origin constrained or destination constrained spatial interaction, product unit network, Alopex procedure, boostrapping, benchmark performance tests.
Space-Time Analysis of Regional Systems (STARS) is an open source package designed for dynamic exploratory analysis of data measured for areal units at multiple points in time. STARS consists of four core analytical modules:  ESDA: exploratory spatial data analysis;  Inequality measures;  Mobility metrics;  Spatial Markov. Developed using the Python object oriented scripting language, STARS lends itself to three main modes of use. Within the context of a command line interface (CLI), STARS can be treated as a package which can be called from within customized scripts for batch oriented analyses and simulation. Alternatively, a graphical user interface (GUI) integrates most of the analytical modules with a series of dynamic graphical views containing brushing and linking functionality to support interactive exploration of the spatial, temporal and distributional dimensions of socioeconomic and physical processes. Finally, the GUI and CLI modes can be combined for use from the Python shell to facilitate interactive programming and access to the many libraries contained within Python. This paper provides an overview of the design of STARS, its implementation, functionality and future plans. A selection of its analytical capabilities are also illustrated that highlight the power and flexibility of the package.
The problem of identifying space-time processes from their autocorrelations and partial autocorrelation functions is addressed. Questions are raised concerning the assumption that time correlation functions generalize to the space-time case, that spatial lag operations are additive, and that space-time correlation functions need be identical across space even for stationary processes. -Authors