Exploring Goodness-of-Fit and Spatial Correlation Using Components of Tango's Index of Spatial Clustering

The ability to detect anomalies such as spatial clustering in data sets plays an important role in spatial data analysis, leading to interest in test statistics identifying patterns exhibiting significant levels of clustering. Toward this end, Tango (1995) proposed a statistic (and its associated distribution under a null hypothesis of no clustering) assessing overall patterns of spatial clustering in a set of observed regional counts. Rogerson (1999) observed that Tango's index may be decomposed into the summation of two distinct statistics, the first mirroring standard tests of goodness-of-fit (GOF), and the second an index of spatial association (SA) similar to Moran's I . In this article, we investigate the effectiveness of Rogerson's expression of Tango's statistic in separating GOF from SA in data sets containing clusters. We simulate data under the null hypothesis of no clustering as well as two alternative hypotheses. The first alternative hypothesis induces a poor fit from the null hypothesis while maintaining independent observations and the second alternative hypothesis induces spatial dependence while maintaining fit. Using Rogerson's decomposition and leukemia incidence data from upstate New York, we show graphically that one is unable to statistically distinguish poor fit from autocorrelation.     

The Assessment of Spatial Autocorrelation through Constrained Multiple Regression

Most published measures of spatial autocorrelation (SA) can be recast as a (normalized) cross-product statistic that indexes the degree of relationship between corresponding entries from two matrices—one specifying the spatial connections among a set of n locations, and the other reflecting a very explicit definition of similarity between the set of values on some variable x realized over the n locations. We first give a very brief sketch of the basic cross-product approach to the evaluation of SA, and then generalize this strategy to include less restrictive specifications for the notion of similarity between the values on x. Using constrained multiple regression, the characterization of variate similarity basic to any assessment of SA can itself be framed according to the information present in the measure of spatial separation. These extensions obviate the inherent arbitrariness in how SA is usually evaluated, which now results from the requirement of a very restrictive definition of variate similarity before a cross-product index can be obtained.     

Using Spatial Filters and Exploratory Data Analysis to Enhance Regression Models of Spatial Data

Residual spatial autocorrelation is a situation frequently encountered in regression analysis of spatial data. The statistical problems arising due to this phenomenon are well‐understood. Original developments in the field of statistical analysis of spatial data were meant to detect spatial pattern, in order to assess whether corrective measures were required. An early development was the use of residual autocorrelation as an exploratory tool to improve regression analysis of spatial data. In this note, we propose the use of spatial filtering and exploratory data analysis as a way to identify omitted but potentially relevant independent variables. We use an example of blood donation patterns in Toronto, Canada, to demonstrate the proposed approach. In particular, we show how an initial filter used to rectify autocorrelation problems can be progressively replaced by substantive variables. In the present case, the variables so retrieved reveal the impact of urban form, travel habits, and demographic and socio‐economic attributes on donation rates. The approach is particularly appealing for model formulations that do not easily accommodate positive spatial autocorrelation, but should be of interest as well for the case of continuous variables in linear regression.     

Exploring Nonlinear Spatial Dependence in the Tails

In many instances it is of interest to measure the degree of similarity between neighboring regions. Spatial autocorrelation measures are the most popular means of doing it. However, such measures only capture a global linear relationship between regions, whereas in many circumstances a more general instrument is required. For instance, in economic poverty analysis or environmental applications (and in other cases where we are interested in extreme events and threshold exceedances) we should be more interested in the spatial pattern in the tails of the joint distributions. In this article we introduce some exploratory tool that focuses on the bivariate joint tails behavior to detect a pattern of spatial regularities. The method will be illustrated with reference to simulated environmental data.     

Impact of Cliff and Ord (1969, 1981) on Spatial Epidemiology

The influence in spatial epidemiology of the seminar work on autocorrelation by Cliff and Ord is discussed. Quantifying the evidence of spatial clustering was an important step in the development of modern statistical methods for analyzing spatial variations of diseases. Autocorrelation is nowadays mostly accounted for at a latent level within a hierarchical framework to small area disease mapping. The importance of accounting for autocorrelation in geographical correlation studies is also reviewed.     

Spatial Cluster Detection in Spatial Flow Data

As a typical form of geographical phenomena, spatial flow events have been widely studied in contexts like migration, daily commuting, and information exchange through telecommunication. Studying the spatial pattern of flow data serves to reveal essential information about the underlying process generating the phenomena. Most methods of global clustering pattern detection and local clusters detection analysis are focused on single‐location spatial events or fail to preserve the integrity of spatial flow events. In this research we introduce a new spatial statistical approach of detecting clustering (clusters) of flow data that extends the classical local K‐function, while maintaining the integrity of flow data. Through the appropriate measurement of spatial proximity relationships between entire flows, the new method successfully upgrades the classical hot spot detection method to the stage of “hot flow” detection. Several specific aspects of the method are discussed to provide evidence of its robustness and expandability, such as the multiscale issue and relative importance control, using a real data set of vehicle theft and recovery location pairs in Charlotte, NC.     

A Surface-Based Approach to Measuring Spatial Segregation

Quantitative indices of residential segregation have been with us for half a century, but suffer significant limitations. While useful for comparison among regions, summary indices fail to reveal spatial aspects of segregation. Such measures generally consider only the population mix within zones, not between them. Zone boundaries are treated as impenetrable barriers to interaction between population subgroups, so that measurement of segregation is constrained by the zoning system, which bears no necessary relation to interaction among population subgroups. A segregation measurement approach less constrained by the chosen zoning system, which enables visualization of segregation levels at the local scale and accounts for the spatial dimension of segregation, is required. We propose a kernel density estimation approach to model spatial aspects of segregation. This provides an explicitly geographical framework for modeling and visualizing local spatial segregation. The density estimation approach lends itself to development of an index of spatial segregation with the advantage of functional compatibility with the most widely used index of segregation (the dissimilarity index D ). We provide a short review of the literature on measuring segregation, briefly describe the kernel density estimation method, and illustrate how the method can be used for measuring segregation. Examples using a simulated landscape and two empirical cases in Washington, DC and Philadelphia, PA are presented.     

Measuring Spatial Autocorrelation of Vectors

This article introduces measures to quantify spatial autocorrelation for vectors. In contrast to scalar variables, spatial autocorrelation for vectors involves an assessment of both direction and magnitude in space. Extending conventional approaches, measures of global and local spatial associations for vectors are proposed, and the associated statistical properties and significance testing are discussed. The new measures are applied to study the spatial association of taxi movements in the city of Shanghai. Complications due to the edge effect are also examined.     

"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.     

Spatial autocorrelation tests and the Classic Maya collapse: Methods and inferences

Spatial autocorrelation, resulting in pattern or structure in geographically distributed data, is discussed in theoretical and practical terms. Tests for spatial autocorrelation are presented, along with an explication of the relationship between autocorrelation models, the product-moment correlation coefficient and the spatial autocorrelation test statistic. Two archaeological examples illustrate the application of the auto-correlation test statistic. The first uses a hypothetical data set, which shows the type of map patterns that appear with various levels of spatial autocorrelation, and the second examines the terminal distribution of long-count-dated monuments at lowland Classic Maya sites. The results of the second example fail to support arguments for simple patterning in the cessation of the erection of these monuments and, by inference, in the Maya collapse itself. Finally, it is argued that while the identification of spatial autocorrelation is often the goal of spatial analyses, the presence of autocorrelation violates the assumptions of certain statistics used in such analyses.     

Knowledge Spillovers and Total Factor Productivity: Evidence Using a Spatial Panel Data Model

This article investigates the impact of knowledge capital stocks on total factor productivity (TFP) through the lens of the knowledge capital model proposed by Griliches (1979) , augmented with a spatially discounted cross-region knowledge spillover pool variable. The objective is to shift attention from firms and industries to regions and to estimate the impact of cross-region knowledge spillovers on TFP in Europe. The dependent variable is the region-level TFP, measured in terms of the superlative TFP index suggested by Caves, Christensen, and Diewert (1982) . This index describes how efficiently each region transforms physical capital and labor into output. The explanatory variables are internal and out-of-region stocks of knowledge, the latter capturing the contribution of cross-region knowledge spillovers. We construct patent stocks to proxy annual regional knowledge capital stocks for N =203 regions during 1997–2002. In estimating the effects, we implement a spatial panel data model that controls for spatial autocorrelation as well as individual heterogeneity across regions. The findings provide a fairly remarkable confirmation of the role of knowledge capital contributing to productivity differences among regions and add an important spatial dimension to discussions in the literature by showing that productivity effects of knowledge spillovers increase with geographic proximity.     

Policy Coalitions in the U.S. Congress: A Spatial Duration Modeling Approach

This paper applies spatial duration models to the analysis of cosponsorship coalitions in the U.S. House of Representatives. This approach provides a unique and simultaneous statistical analysis of ideological space (specifically, coalition formation) and geographical space. Typically, duration models are associated with temporal longitudinal data, but recently have been adapted to the spatial domain (Pellegrini and Reader 1996). In this paper, spatial duration models are further adapted to examine ideological space including a consideration of unobserved sources of spatial variation (or omitted variable bias). We examine two features of cosponsorship coalitions, breadth and clustering. Breadth is defined as the ideological distance between the two most extreme members of the coalition which is an important “signal” to the rest of Congress regarding the scope and broad appeal of the proposed legislation. In contrast, clustering refers to the distance between individual members of a coalition and reveals the tendency, or not, of ideologically similar members of Congress to support various bills. To examine breadth and clustering, we employ spatial duration models of cosponsorship that permit a multivariate analysis incorporating both the characteristics of members of Congress and the geographical regions they represent. Results indicate that cosponsorship coalition patterns are primarily determined by the content of the legislation, not the actions of the coalition leadership. While the leadership characteristics of sponsors have a limited effect on cosponsorship breadth, the size of the coalition is the primary determinent. Leadership characteristics also have little effect on cosponsorship clustering. Rather, clustering is due to members' policy preferences, as measured by distance to the coalition leader. In addition, the duration analysis results suggest that geographical proximity between members of Congress “overcomes” ideological distance. Finally, the spatial duration approach is noted as a fruitful methodology for examining explicitly spatial patterns in both ideological or geographical space.     

Outsmarting geography: implementing territorial innovation strategies in sparsely populated regions

The smart specialization literature has hardly addressed the role of geography in promoting novel approaches to local and regional innovation processes beyond classic clustering approaches. Based on empirical observations from five sparsely populated regions, the present article proposes original insights that contribute to the theoretical debate on the place-based nature and spatial dimension of entrepreneurial discovery, the key functional mechanism behind smart specialization. First, it advocates the added-value of integrating strategic spatial planning approaches at different stages of smart specialization implementation, from design to operationalization. Second, it suggests that more effective ways of creating domains through shared knowledge bases of existing sectors should aim at promoting collaboration between second-tier economic agents. Finally, the specificity of the territorial preconditions found in sparsely populated regions brings to the fore new forms of proximity relations based on institutional, cognitive and organizational proximity rather than on geographical clustering.     

Power of the Rank Adjacency Statistic to Detect Spatial Clustering in a Small Number of Regions

The rank adjacency statistic D is a statistical method for assessing spatial autocorrelation or clustering of geographical data. It was originally proposed for summarizing the geographical patterns of cancer data in Scotland (IARC 1985). In this paper, we investigate the power of the rank adjacency statistic to detect spatial clustering when a small number of regions is involved. The investigations were carried out using Monte Carlo simulations, which involved generating patterned/clustered values and computing the power with which the D statistic would detect it. To investigate the effects of region shapes, structure of the regions, and definition of weights, simulations were carried out using two different region shapes, binary and nonhinary weights, and three different lattice structures. The results indicate that in the typical example of considering Canadian total mortality at the electoral district level, the D statistic had adequate power to detect general spatial autocorrelation in twenty‐five or more regions. There was an inverse relationship between power and the level of connectedness of the regions, which depends on the weighting function, shape, and arrangement of the regions. The power of the D statistic was also found to compare favorably with that of Moran's I statistic.     

An Exploratory and Reflective Process of Urban Spatial Morphology within Social Sustainability: Lessons from Middle Eastern Islamic Tradition

This article outlines the significant role of ideologies and values that lie beneath the physicality of the city, in reforming urban spatial morphology within a framework of social sustainability. We focus on the urban morphology of Middle Eastern cities, which have evolved within the framework of Islamic tradition, to illuminate the relationship between the ideological and physical dimensions of spatial morphology in all urban contexts. We examine the process by which a collective of religious, political, and cultural values underlying the physicality of the city have evolved into aesthetic conventions. This process played a crucial role in the maintenance of social and urban sustainability. We propose a form of “pattern language,” here termed the anatomical approach, that brings together the ideological dimension of a city's inhabitants and the physical characteristics of urban morphology. Such a model may help urban designers and architects to understand and create more responsive and friendly cities. It furthermore contributes to the planning education process by providing the essential knowledge and analytical foundation for site analysis and conservation of valuable contexts.     

Tobler’s Law in a Multivariate World

Tobler’s first law of geography is widely recognized as reflecting broad empirical realities in geography. Its key concepts of “near” and “related” are intuitive in a univariate setting. However, when moving to the joint consideration of spatial patterns among multiple variables, the combination of attribute similarity and geographical similarity that underlies the concept of spatial autocorrelation is much harder to deal with. This article uses the notion of distance in multiattribute space to explore and visualize the connection between “near” and “related” in a multivariate context. We approach this from a global, local, and regional perspective. We outline a number of ways to combine different visualization techniques and introduce a new local neighbor match test for multivariate local clusters. We illustrate the methods by means of Guerry’s classic data set on moral statistics in 1833 France.     

Interaction among High-tech Talent and its Impact on Innovation Performance: A Comparison of Taiwanese Science Parks at Different Stages of Development

Numerous studies have studied how knowledge spillovers and various other factors influence industrial clusters in terms of geographical proximity. Related studies have generally confirmed significant positive correlations between firm innovative activities and factors such as spatial proximity and degree of industrial clustering. This study elucidates on an individual level, based on the relationship between proximity dimension and innovative activity, the interactive relationships between the mobility and interaction of high-tech talent and innovation performance. Survey results indicate that the spatial proximity of firms clustering within the Hsinchu and Tainan Science-based Industrial Park increases the interaction among high-tech personnel and the expansion of their professional networks, thus promoting innovation. Gradually organizational and social proximity evolve from physical proximity within high-tech districts via the evolution of industrial networks and interactions among high-tech talent. Additionally survey results demonstrate the value of mobility and informal relationships involving high-tech talent, as well as the effect of these relationships on innovation performance during the various stages of science park development. However, how to avoid lock-in in the future development of high-tech districts remains a critical issue. The results of this investigation provide a useful reference for planning and managing industrial districts.