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.     

Population pressure,political institutions,and protests: A multilevel analysis of protest events in African cities

Why do some of Africa's urban areas experience higher rates of protest incidence than others? Numerous authors have highlighted the role of urbanisation and democratisation in determining cross-national variation in the rates of urban protest. Yet understanding has been hindered by failures to measure mechanisms at the appropriate spatial scale, analyse a sufficiently representative sample of urban centres, de-confound local and country-level factors, and consider what it is about specific urban centres that shapes variation in protest incidence. This paper presents new evidence on the determinants of protests in African urban centres by linking georeferenced data on urban settlements from the Urban Centres Database to the location of protest events taken from the Armed Conflict Location and Event Dataset. Fitting a series of multilevel regression models with cross-level effects, we simultaneously estimate variation in protest incidence as a function of local- and country-level factors and the interactions between them. Our results indicate that variation in protest incidence between urban centres can be explained by a combination of local-specific and country-level contextual factors including population size and growth, regime type, civil society capacity, and whether an urban centre is politically significant. These findings advance our understanding of how political and demographic factors interact and influence protest incidence in urban Africa.     

Loglinear Residual Tests of Moran's I Autocorrelation and their Applications to Kentucky Breast Cancer Data

This article bridges the permutation test of Moran's I to the residuals of a loglinear model under the asymptotic normality assumption. It provides the versions of Moran's I based on Pearson residuals ( I _PR) and deviance residuals ( I _DR) so that they can be used to test for spatial clustering while at the same time account for potential covariates and heterogeneous population sizes. Our simulations showed that both I _PR and I _DR are effective to account for heterogeneous population sizes. The tests based on I _PR and I _DR are applied to a set of log-rate models for early-stage and late-stage breast cancer with socioeconomic and access-to-care data in Kentucky. The results showed that socioeconomic and access-to-care variables can sufficiently explain spatial clustering of early-stage breast carcinomas, but these factors cannot explain that for the late stage. For this reason, we used local spatial association terms and located four late-stage breast cancer clusters that could not be explained. The results also confirmed our expectation that a high screening level would be associated with a high incidence rate of early-stage disease, which in turn would reduce late-stage incidence rates.     

Cultural transmission, copying errors, and the generation of variation in material culture and the archaeological record

Archaeologists are adept at analyzing variation in artifacts. The discipline has well established and tested methods to track change through time and to evaluate the function of artifacts that depend upon measures of variation in the archaeological record. Although a critical concept, the means by which variation in material culture is generated is not well understood. This paper explores one source of variation, copying errors, and systematically examines how cultural transmission processes act to amplify, reduce, or maintain such variation. Using simple models, we generate expected distributions for the amount of variation that occurs through time under varying circumstances. This variation is caused by small errors that are transmitted from one person to another in the propagation and replication of cultural traits. These baseline values provide useful null models for explaining variation in prehistoric assemblages of artifacts. We use measurements of projectile points from Owens Valley and Woodland ceramics from Illinois to demonstrate the value of this approach.     

MULTIVARIATE MIXTURE OF NORMALS WITH UNKNOWN NUMBER OF COMPONENTS: AN APPLICATION TO CLUSTER NEOLITHIC CERAMICS FROM AEGEAN AND ASIA MINOR USING PORTABLE XRF*

Multivariate techniques and especially cluster analysis have been commonly used in archaeometry. Exploratory and model‐based techniques of clustering have been applied to geochemical (continuous) data of archaeological artefacts for provenance studies. Model‐based clustering techniques such as classification maximum likelihood and mixture maximum likelihood have been used to a lesser extent in this context and, although they seem to be suitable for such data, they either present practical difficulties—such as high dimensionality of the data—or their performance gives no evidence that they are superior to standard methods. In this paper standard statistical methods (hierarchical clustering, principal components analysis) and the recently developed model‐based multivariate mixture of normals with an unknown number of components, are applied and compared. The data set provides chemical compositions of 188 ceramic samples derived from the Aegean islands and surrounding areas.     

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.     

In search of a better method to distinguish artefacts from geofacts

Archaeologists use a method of evaluating the characteristics of flakes, called scoring, to distinguish geofacts (pseudo-artefacts or eoliths) from artefacts. Lower total scores are considered indicative of a natural source of the finds, while higher ones support the opposite. However, this method has some limitations. The most important are the small quantity of assemblages subject to such an analysis and the unclear boundary drawn by a ranking within a point-based score evaluation between collections with finds of cultural and anthropic origin. Here, we present a method that minimizes these limitations. It consists of a statistical approach using scoring percentages, a new method of visualizing them and the application of clustering. This way, we obtained clear differences between pseudo-artefacts and artefacts by considering flakes from six flint assemblages from Central Europe as well as an experimental assemblage.     

Dependence of seasonal variation of absorption on solar activity in the equatorial ionosphere

From data for the absorption of radio waves at oblique incidence in Lagos, and at vertical incidence at Colombo, the seasonal variation of absorption at the two sites are examined. It is shown that, if subsolar absorption be assumed to depend upon sunspot number, the cos X law gives the same index for both the diurnal and the seasonal variation of absorption.     

Exploring the clustering of creative industries

During the last decades, a large body of literature has been published on the clustering of creative industries, but it has not been reviewed in a systematic way. In this review paper, we fill this gap. The review leads to the identification of several deficiencies of current research. Based on that, we distil avenues for future empirical research on the drivers of the clustering of creative industries, which are embedded in a comprehensive analytical framework.     

A Supplemental Indicator of High-Value or Low-Value Spatial Clustering

Most test statistics for detecting spatial clustering cannot distinguish between low-value spatial clustering and high-value spatial clustering, and none is designed to explicitly detect high-value clustering, low-value clustering, or both. To fill this void in practice, we introduce an adjustment procedure that can supplement common two-sided spatial clustering tests so that a one-sided conclusion can be reached. The procedure is applied to Moran's I and Tango's C _G in both simulated and real-world spatial patterns. The results show that the adjustment procedure can account for the influence of low-value clusters on high-value clustering and vice versa. The procedure has little effect on the original global testing methods when there is no clustering. When there is a clustering tendency, the procedure can unambiguously distinguish the existence of high-value clusters or low-value clusters or both.     

Refining correspondence analysis-based ceramic seriation of regional data sets

Ceramic seriation is one of the primary tools used by archaeologists to create chronologies, especially for surface survey data. In this article, we outline a bootstrapped approach to correspondence analysis-based seriation designed to help assess and improve the stability of relative orderings produced through such analyses. This procedure systematically identifies and removes small samples and sites with unusual samples, such as those with multiple components, which are not handled well by seriation and require secondary interpretation. Our approach combines data from multiple projects in the Zuni region of the American Southwest in order to gauge the effects of intraregional variation in ceramic distributions and reexamine prior interpretations of demographic change based on individual projects. This analysis highlights two previously unknown regional trends, including variation in the distribution of multicomponent sites and potential short-term depopulation of a significant part of the region. Based on this example, we further suggest that our method may be particularly useful in situations where little prior chronological information is available.     

THE MAX‐P‐REGIONS PROBLEM*

ABSTRACT In this paper, we introduce a new spatially constrained clustering problem called the max‐p ‐regions problem. It involves the clustering of a set of geographic areas into the maximum number of homogeneous regions such that the value of a spatially extensive regional attribute is above a predefined threshold value. We formulate the max‐p ‐regions problem as a mixed integer programming (MIP) problem, and propose a heuristic solution.     

Symmetry and Perfection of Form

Abstract

Objects in space are here considered from the point of view of geometrical symmetry. Accordingly, only their shape or form is important, and their size or position in space may be ignored. By comparing the symmetry of a given object with that of nearby objects of the same kind, we can identify those objects that are 'perfect' of their kind in a precise, technical sense. Among convex polyhedra with given incidence structure, there are exactly nine instances of such perfection of form.     

Geological constraints on the use of lead isotopes for provenance in archaeometallurgy

The first part of this paper is a brief critical history of the use of Pb isotopes for inferring the geological provenance of archaeological materials, with an emphasis on non-ferrous metals. The second part examines variation in the Pb isotopic ratios of oxide and sulphide ore minerals in selected regions of the world, and relates these to the geological histories of ore formation in each region. This exercise shows that in regions where most ore deposits are of similar geological age—as in the Andes, Europe and the circum-Mediterranean—provenance analysis with Pb isotopes is inherently difficult because geographically distant sources often exhibit similar isotopic ratios. Conversely, regions with many periods of ore formation—such as southern Africa—appear to be very promising regions for future studies of provenance with Pb isotopes. The wider implication of this exploratory survey is that archaeologists should carefully consider the range and clustering of geological Pb isotopic ratios in their regions of interest before investing large sums of money into Pb isotopic analysis of artefacts.     

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.     

Ecological Inference and Spatial Variation of Individual Behavior: National Divide and Elections in Catalonia

When in geography one reconstructs individual behavior starting from aggregated data through ecological inference, a crucial aspect is the spatial variation of individual behavior. Basic ecological inference methods treat areas as if they were all exchangeable, which in geographical applications is questionable due to the existence of contextual effects that relate to area location and induce spatial dependence. Here that assumption is avoided by basing ecological inference on a model that simultaneously does a cluster analysis, grouping together areas with similar individual behavior, and an ecological inference analysis in each cluster, estimating the individual behavior in the areas of each group. That allows one to capture most of the spatial dependence and summarize the individual behavior at a local level through the behavior estimated for each cluster. This approach is used to investigate vote switching in Catalonia, where voters split across a national allegiance divide on top of the ideological divide. That leads to Catalans having a lot of options to choose from, and to them voting differently depending on whether the election is for the Catalan parliament or for the Spanish parliament. To investigate that, the results in the two most recent pairs of such elections are analyzed by simultaneously clustering areas based on the similarity of their vote and vote switch patterns, and estimating one vote switch pattern for each cluster. As a result, Catalonia is partitioned into four clusters that have a strong spatial structure, with all the areas in the same cluster having similar demographic composition. The estimated vote switch patterns are quite different across clusters but very similar across pairs of elections, and they help assess how the differential voter turnout and the strategic dual vote effects vary in space.     

Electron content measurements in the auroral zone using GPS: preliminary observations of the main trough and a survey of the degree of irregularity in summer

Ionospheric electron content was monitored from sites in or near Tromsø, Norway, for six months of 1993, using the transmissions from the satellites of the Global Positioning System (GPS). The data have been used for preliminary studies of two important phenomena of the high-latitude ionosphere: the main trough and the incidence of large irregularities. The latitude and motion of the trough were determined on several occasions during the spring period, and the results compared with previous data. Best agreement is with the formula of Collis and Haggstrom (1988). The incidence of large irregularities was surveyed during a four-month period, approximately from the summer solstice to the autumnal equinox, and the variation with time of day and magnetic activity has been determined. It was found that irregularities are considerably larger by night than by day, but that they are enhanced during both periods by increased magnetic activity. Statistical results are presented. It is suggested that these irregularities are the same as the “auroral blobs” previously studied by incoherent-scatter radar.     

Comparing Outsourcing Patterns in Domestic and FDI Manufacturing Plants: Empirical Evidence from Spain

To fully understand the local linkages of Foreign Direct Investment (FDI) plants, we argue it would be useful to analyze the outsourcing patterns of such plants in comparison to domestic plants. Consequently, we examined 1031 industrial plants, both domestic and foreign, located in Spain. The FDI plants show patterns similar to those of domestic plants with regard to the level of outsourcing, the incidence of outsourced production on the companies’ total sales and the economic content of outsourcing relationships. Further, our results show that levels of embeddedness in the local and regional economy of FDI plants are not significantly different from domestic plants. However, FDI plants are highly concentrated spatially in the largest industrial agglomerations. For such plants, Barcelona not only seems a preferred site for location but also for contracting manufacturing tasks.     

MEASURING THE LOCALIZATION OF ECONOMIC ACTIVITY: A PARAMETRIC APPROACH*

ABSTRACT The index proposed by Ellison and Glaeser (1997) is now well established as the preferred method for measuring the localization of economic activity. In this paper we develop an alternative localization measure that is consistent with the theoretical framework originally proposed by Ellison and Glaeser. Our measure follows directly from the Random Utility (Profit) Maximization (RUM) location decision model. Because the distributional assumptions in our model are fully compatible with RUM, we are able to offer a more efficient measure of industry clustering.