Duration Modeling of Spatial Point Patterns

This paper attempts to further the research by Odland and Ellis (1992) in applying event history methodology to the analysis of spatial point patterns (that is, event patterns). Its empirical focus is the event pattern derived from the adoption of an agricultural innovation, the Harvestore, in southern Ontario, Canada, from 1963 to 1986. Event history analysis involves the use of discrete-state, continuous-time stochastic models to investigate a temporal longitudinal record on discrete variables. Event history models are usually concerned with durations of time between events and the effects of intertemporal time dependencies on future event occurrences. As such, they are often referred to as duration models. Many of the methods used in event history analysis allow the use of other nonnegative interval measurements in place of standard temporal intervals to investigate a series of events. In particular, spatial intervals (or durations) of distances between events may also be accommodated by event history models. Our analysis extends the previous research of Odland and Ellis (1992) by using a wider range of parametric models to explore duration dependence, investigating the role of spatial censoring, and using a more extensive set of explanatory variables. In addition, simulation experiments and graphical tests are used to evaluate the empirical event pattern against one generated from Complete Spatial Randomness. Results indicate that the event pattern formed by the Harvestore adopter farms is clustered (that is, is described by positive duration dependency), the sales agent is a significant factor in the distribution of adopters, and that contrasting results are obtained from the analysis using censored data versus uncensored data.     

Local Indicators of Spatial Association—LISA

The capabilities for visualization, rapid data retrieval, and manipulation in geographic information systems (GIS) have created the need for new techniques of exploratory data analysis that focus on the “spatial” aspects of the data. The identification of local patterns of spatial association is an important concern in this respect. In this paper, I outline a new general class of local indicators of spatial association (LISA) and show how they allow for the decomposition of global indicators, such as Moran's I, into the contribution of each observation. The LISA statistics serve two purposes. On one hand, they may be interpreted as indicators of local pockets of nonstationarity, or hot spots, similar to the G_i and G*_i statistics of Getis and Ord (1992). On the other hand, they may be used to assess the influence of individual locations on the magnitude of the global statistic and to identify “outliers,” as in Anselin's Moran scatterplot (1993a). An initial evaluation of the properties of a LISA statistic is carried out for the local Moran, which is applied in a study of the spatial pattern of conflict for African countries and in a number of Monte Carlo simulations.     

A Comparison of Three Exploratory Methods for Cluster Detection in Spatial Point Patterns

This paper compares the performances of three exploratory methods for cluster detection in spatial point patterns where the at-risk population is known. After reviewing two existing methods, Openshaw et al. (1987) and Besag and Newell (1991), an alternative method is introduced. These three methods are then compared empirically using two point patterns drawn from a disaggregate housing database consisting of 28,832 observations. Each observation in the data set contains attributes of single-family detached dwellings in the City of Amherst, New York. This paper provides some new insights into the performance of the three methods, as previous applications have used spatially aggregated (and hence rather inaccurate) data. The paper also demonstrates the utility of GIS for this type of spatial analysis.     

Applying Local Indicators of Spatial Association to Analyze Longitudinal Data: The Absolute Perspective

Local Indicators of Spatial Association (LISA) are a class of spatial statistical methods that have been widely applied in various scientific fields. When applying LISA to make longitudinal comparisons of spatial data, a common way is to run LISA analysis at each time point, then compare the results to infer the distributional dynamics of spatial processes. Given that LISA hinges on the global mean value that often varies across time, the LISA result generated at time T_i reflects the spatial patterns strictly with respect to T_i. Therefore, the typical comparative cross-sectional analysis with LISA can only characterize the relative distributional dynamics. However, the relative perspective alone is inadequate to comprehend the full picture, as the patterns are not directly associated with the changes of the spatial process’s intensity. We argue that it is important to obtain the absolute distribution dynamics to complement the relative perspective, especially for tracking how spatial processes evolve across time at the local level. We develop a solution that modifies the significance test when implementing LISA analysis of longitudinal data to reveal and visualize the absolute distribution dynamics. Experiments were conducted with Mongolian livestock data and Rwanda population data.     

A Scale‐Sensitive Test of Attraction and Repulsion Between Spatial Point Patterns

There exist a variety of tests for attraction and repulsion effects between spatial point populations, most notably those involving either nearest‐neighbor or cell‐count statistics. Diggle and Cox (1981) showed that for the nearest‐neighbor approach, a powerful test could be constructed using Kendall's rank correlation coefficient. In the present paper, this approach is extended to cell‐count statistics in a manner paralleling the K‐function approach of Lotwick and Silverman (1982). The advantage of the present test is that, unlike nearest‐neighbors, one can identify the spatial scales at which repulsion or attraction are most significant. In addition, it avoids the torus‐wrapping restrictions implicit in the Monte Carlo testing procedure of Lotwick and Silverman. Examples are developed to show that this testing procedure can in fact identify both attraction and repulsion between the same pair of point populations at different scales of analysis.     

Order Distance in Regular Point Patterns

This article examines the k th nearest neighbor distance for three regular point patterns: square, triangular, and hexagonal lattices. The probability density functions of the k th nearest distance and the average k th nearest distances are theoretically derived for k =1, 2, …, 7. As an application of the k th nearest distance, we consider a facility location problem with closing of facilities. The problem is to find the optimal regular pattern that minimizes the average distance to the nearest open facility. Assuming that facilities are closed independently and at random, we show that the triangular lattice is optimal if at least 68% of facilities are open by comparing the upper and lower bounds of the average distances.     

A Genetic Approach to Detecting Clusters in Point Data Sets

Spatial analysis techniques are widely used throughout geography. However, as the size of geographic data sets increases exponentially, limitations to the traditional methods of spatial analysis become apparent. To overcome some of these limitations, many algorithms for exploratory spatial analysis have been developed. This article presents both a new cluster detection method based on a genetic algorithm, and Programs for Cluster Detection, a toolkit application containing the new method as well as implementations of three established methods: Openshaw's Geographical Analysis Machine (GAM), case point-centered searching (proposed by Besag and Newell), and randomized GAM (proposed by Fotheringham and Zhan). We compare the effectiveness of cluster detection and the runtime performance of these four methods and Kulldorf's spatial scan statistic on a synthetic point data set simulating incidence of a rare disease among a spatially variable background population. The proposed method has faster average running times than the other methods and significantly reduces overreporting of the underlying clusters, thus reducing the user's postprocessing burden. Therefore, the proposed method improves upon previous methods for automated cluster detection. The results of our method are also compared with those of Map Explorer (MAPEX), a previous attempt to develop a genetic algorithm for cluster detection. The results of these comparisons indicate that our method overcomes many of the problems faced by MAPEX, thus, we believe, establishing that genetic algorithms can indeed offer a viable approach to cluster detection.     

p‐Functional Clusters Location Problem for Detecting Spatial Clusters with Covering Approach

Regionalization or districting problems commonly require each individual spatial unit to participate exclusively in a single region or district. Although this assumption is appropriate for some regionalization problems, it is less realistic for delineating functional clusters, such as metropolitan areas and trade areas where a region does not necessarily have exclusive coverage with other regions. This paper develops a spatial optimization model for detecting functional spatial clusters, named the p‐functional clusters location problem (p‐FCLP), which has been developed based on the Covering Location Problem. By relaxing the complete and exhaustive assignment requirement, a functional cluster is delineated with the selective spatial units that have substantial spatial interaction. This model is demonstrated with applications for a functional regionalization problem using three journey‐to‐work flow datasets: (1) among the 46 counties in South Carolina, (2) the counties in the East North Central division of the US Census, and (3) all counties in the US. The computational efficiency of p‐FCLP is compared with other regionalization problems. The computational results show that detecting functional spatial clusters with contiguity constraints effectively solves problems with optimality in a mixed integer programming (MIP) approach, suggesting the ability to solve large instance applications of regionalization problems.     

Using AMOEBA to Create a Spatial Weights Matrix and Identify Spatial Clusters

The creation of a spatial weights matrix by a procedure called AMOEBA, A Multidirectional Optimum Ecotope-Based Algorithm , is dependent on the use of a local spatial autocorrelation statistic. The result is (1) a vector that identifies those spatial units that are related and unrelated to contiguous spatial units and (2) a matrix of weights whose values are a function of the relationship of the ith spatial unit with all other nearby spatial units for which there is a spatial association. In addition, the AMOEBA procedure aids in the demarcation of clusters, called ecotopes, of related spatial units. Experimentation reveals that AMOEBA is an effective tool for the identification of clusters. A comparison with a scan statistic procedure (SaTScan) gives evidence of the value of AMOEBA. Total fertility rates in enumeration districts in Amman, Jordan, are used to show a real-world example of the use of AMOEBA for the construction of a spatial weights matrix and for the identification of clusters. Again, comparisons reveal the effectiveness of the AMOEBA procedure.     

Local Forms of Spatial Analysis

Local forms of spatial analysis focus on exceptions to the general trends represented by more traditional global forms of spatial analysis. There is currently a rapid expansion in the development of such techniques but their history almost exactly parallels that of Geographical Analysis, with the first examples of local analysis appearing in the late 1960s. Indeed, Geographical Analysis has published many of the significant contributions in this field. This paper reviews the development of local forms of spatial analysis and assesses the current situation. Following a discussion on the nature and importance of local analysis, examples are given of local forms of point pattern analysis; local graphical approaches; local measures of spatial dependency; the spatial expansion method; adaptive filtering; multilevel modeling; geographically weighted regression; random coefficients models; autoregressive models; and local forms of spatial interaction models.     

Exploring Spatial Patterns Using an Expanded Spatial Autocorrelation Framework

Spatial autocorrelation (SA) is regarded as an important dimension of spatial pattern. SA measures usually consist of two components: measuring the similarity of attribute values and defining the spatial relationships among observations. The latter component is often represented by a spatial weights matrix that predefines spatial relationship between observations in most measures. Therefore, SA measures, in essence, are measures of attribute similarity, conditioned by spatial relationship. Another dimension of spatial pattern can be explored by controlling observations to be compared based upon the degree of attribute similarity. The resulting measures are spatial proximity measures of observations, meeting predefined attribute similarity criteria. Proposed measures reflect degrees of clustering or dispersion for observations meeting certain levels of attribute similarity. An existing spatial autocorrelation framework is expanded to a general framework to evaluate spatial patterns and can accommodate the proposed approach measuring proximity. Analogous to the concept of variogram, clustergram is proposed to show the levels of spatial clustering over a range of attribute similarity, or attribute lags. Specific measures based on the proposed approach are formulated and applied to a hypothetical landscape and an empirical example, showing that these new measures capture spatial pattern information not reflected by traditional spatial autocorrelation measures.     

Local Spatial Autocorrelation in a Biological Model

We review the recently developed local spatial autocorrelation statistics I_i, c_i, G_i, and G_i*. We discuss two alternative randomization assumptions, total and conditional, and then newly derive expectations and variances under conditional randomization for I_i and c_i, as well as under total randomization for c_i. The four statistics are tested by a biological simulation model from population genetics in which a population lives on a 21 × 21 lattice of stepping stones (sixty-four individuals per stone) and reproduces and disperses over a number of generations. Some designs model global spatial autocorrelation, others spatially random surfaces. We find that spatially random designs give reliable test results by permutational methods of testing significance. Globally autocorrelated designs do not fit expectations by any of the three tests we employed. Asymptotic methods of testing significance failed consistently, regardless of design. Because most biological data sets are autocorrelated, significance testing for local spatial autocorrelation is problematic. However, the statistics are informative when employed in an exploratory manner. We found that hotspots (positive local autocorrelation) and coldspots (negative local autocorrelation) are successfully distinguished in spatially autocorrelated, biologically plausible data sets.     

"The Problem of Spatial Autocorrelation" and Local Spatial Statistics

This article examines the relationship between spatial dependency and spatial heterogeneity, two properties unique to spatial data. The property of spatial dependence has led to a large body of research into spatial autocorrelation and also, largely independently, into geostatistics. The property of spatial heterogeneity has led to a growing awareness of the limitation of global statistics and the value of local statistics and local statistical models. The article concludes with a discussion of how the two properties can be accommodated within the same modelling framework.     

Transnational Flows of E-Waste and Spatial Patterns of Recycling in China

Two geographers residing in Beijing discuss the inflows, processing, and consumption of electronic waste—a topic largely neglected in the current literature on globalization. Based on extensive interviews with electronics producers and recyclers in China, the paper explores the global flows of e-waste and concentration of related recycling in coastal China. The authors suggest that recycling activities (authorized as well as illegal) grew in tandem with the dramatic increase in electronics production during the last decade. They note that the country's recycling sector has played a significant role in rural industrialization and local economic development, albeit in conflict with the objectives of environmental protection. Journal of Economic Literature, Classification Numbers: F20, L63, O17, O19. 6 figures, 23 references.     

Spatial Agglomeration of Manufacturing in Greece: Sectoral Patterns and Determinants

This article aims to demonstrate how the industry characteristics of manufacturing sectors affect the patterns of their spatial agglomeration. It also addresses several intricate issues concerning the measurement of localization economies and estimation of their main determinants in manufacturing industries. The original empirical analysis employs annual industrial data from the Hellenic Statistical Authority (ELSTAT) during the period 1993–2006 in Greece at the prefecture level, i.e. for 51 prefectures. The data processing reveals three important findings. The first is the temporal persistence of localization economies in the Greek manufacturing. The second refers to the high level of agglomeration associated with the high-technology industries as well as the resource- and scale-intensive industries. Lastly, there are significant effects of industry characteristics related to knowledge externalities, labour skills and productivity, scale economies and own-transport expenditure on spatial agglomeration, as resulted from the use of alternative geographic concentration indices and panel data models. Results obtained have implications for policy-makers, who can enhance the regional manufacturing activity by affecting these industry-specific factors. Amongst others, planning measures and policies which aim at promoting the local development and regional convergence should focus on reducing transport costs for firms or sectors, by improving the infrastructure capacity, interconnectivity and quality of services.     

The Spatial Patterns of Networks,Hierarchies and Subsidiaries

This article reviews evidence and arguments linking the networking behaviour of firms with geographic distance, before examining the spatial relationships of electronics firms in the three major electronics centres in Spain. The focus is on the spatial pattern and extent of different types of inter-firm relations. Based on the analysis of 184 surveyed establishments, displaying different ownership and organization characteristics, the results show that while regional linkages are important, significant extra-regional linkages are also maintained by firms in regional clusters. The spatial extent of linkages depends on the mode of relations; arm's length, network and hierarchy relations show different spatial patterns, as do different types of cooperation. The importance of extra-regional linkages also varies with firm- and plant-specific characteristics. Extra-regional linkages are more common among larger and more R&D-intensive firms, firms with greater presence in the rest of the country and firms with more experience of cooperation and more stable relationships.