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 Empirical Comparison of Edge Effect Correction Methods Applied to K‐function Analysis

This paper explores various edge correction methods for K‐function analysis via Monte Carlo simulation. The correction methods discussed here are Ripley's circumference correction, a toroidal correction, and a guard area correction. First, simulation envelopes for a random point pattern are constructed for each edge correction method. Then statistical powers of these envelopes are analyzed in terms of the probability of detecting clustering and regularity in simulated clustering/regularity patterns. In addition to the K‐function, K(h), determined for individual distances, h, an overall statistic k is also examined. A major finding of this paper is that the K‐function method adjusted by either the Ripley or toroidal edge correction method is more powerful than what is not adjusted or adjusted by the guard area method. Another is that the overall statistic k outperforms the individual K(h) across almost the entire range of potential distances h.     

The Colocation Quotient: A New Measure of Spatial Association Between Categorical Subsets of Points. 协同区位商：点集分类子集间空间关联性的新度量标准

This article presents a new metric we label the colocation quotient (CLQ), a measurement designed to quantify (potentially asymmetrical) spatial association between categories of a population that may itself exhibit spatial autocorrelation. We begin by explaining why most metrics of categorical spatial association are inadequate for many common situations. Our focus is on where a single categorical data variable is measured at point locations that constitute a population of interest. We then develop our new metric, the CLQ, as a point‐based association metric most similar to the cross‐k‐function and join count statistic. However, it differs from the former in that it is based on distance ranks rather than on raw distances and differs from the latter in that it is asymmetric. After introducing the statistical calculation and underlying rationale, a random labeling technique is described to test for significance. The new metric is applied to economic and ecological point data to demonstrate its broad utility. The method expands upon explanatory powers present in current point‐based colocation statistics.     

Voluntary regions and the case of Las Vegas

A shifting American cultural geography, stemming from clustering of like-minded people, has been much-discussed in recent years. The “voluntary region”, proposed by Wilbur Zelinsky in his path-breaking The cultural geography of the United States, is a regional construct relatively unexplored by cultural geographers that may help in their contributions to such conversations. As described by Zelinsky, voluntary regions are places that attract individual, like-minded people away from long-standing “traditional regions” based on a desire for amenity and economic opportunity. I review the concept and its sparse embrace in the literature and suggest that it has much to offer our discipline. Using Las Vegas as a paradigmatic example, I explore methods that can be used to explore the formation and character of voluntary regions. I argue that the voluntary region framework is an encompassing lens through which cultural geographers can examine the complex nature of place and regional construction at the hands of dynamic forces that lead people to resettle in new places.     

ARTIFICIAL NEURAL NETWORKS AS A TOOL FOR ARCHAEOLOGICAL DATA ANALYSIS*

Artificial neural networks (ANN) offer a supplement to traditional classification algorithms applied to archaeological data. Because of their flexible architecture, non-linearity and independence from the distribution of the underlying data, neural networks have unique advantages for such applications. In particular, ANN models are well suited for use with the sparse data sets common in archaeological work. Combining multivariate techniques with networks for data validation, pre-processing and classification exploits the merits of both and provides a comprehensive approach to the analysis and classification of archaeological data.     

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.     

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.     

Statistical Methods for Evaluating the Geometrical Hierarchy of a Network

The objective of this paper is to present statistical methods for evaluating the geometrical hierarchy of a network in comparison with a random hierarchy network. First, the random hierarchy network is explicitly formulated by four stochastic processes in which line segments or lines, which represent roads, are randomly placed and their placement is independent of their ranks. Second, under these stochastic processes, this paper derives the expected value and variance of i) the number of intersections between roads of different ranks; and ii) the distance from an arbitrary point to the nearest highest-ranked road through two kinds of routes. Using these expected values, the intersection index and the detour index are proposed, and it is shown that these indicators are useful for evaluating the geometrical hierarchy of a network. As calculation of these indices is laborious, an efficient computational method is developed, and its application to an actual example is described.     

A Note on the Extremities of Local Moran's Iis and Their Impact on Global Moran's I

By defining local Moran's I_i as a ratio of quadratic forms and making use of its overall additivity to match global Moran's I, we can identify spatial objects with a strong impact on global Moran's I. First, we concentrate on the spatial properties of local Moran's I_i expressed by the local linkage degree. Depending on whether we use the W- or C-coding of the spatial connectivity matrix, the variance of local Moran's I_i for a small local linkage degree will be either large or small. Note that spatial objects associated with a local Moran's I_i with a large variance affect the global statistic much more than spatial objects associated with a local Moran's I_i with a small variance. Counterintuitively, global Moran's I defined in the W-coding is most influenced by spatial objects with a small number of spatial neighbors. In contrast, spatial objects with a large number of spatial neighbors exert more impact on global Moran's I setup in the C-coding. Second, we investigate the impact of the empirical data on local Moran's I_i and show that local Moran's I_i will only be significant for extreme absolute residuals at and around the reference location. Clusters of average regression residuals cannot be detected by local Moran's I_i. Consequently, spatial cliques of extreme residuals contribute more to significance tests on global autocorrelation.     

Computing the Jacobian in Gaussian Spatial Autoregressive Models: An Illustrated Comparison of Available Methods

When estimating spatial regression models by maximum likelihood using spatial weights matrices to represent spatial processes, computing the Jacobian, ln(|I ? λW|), remains a central problem. In principle, and for smaller data sets, the use of the eigenvalues of the spatial weights matrix provides a very rapid resolution. Analytical eigenvalues are available for large regular grids. For larger problems not on regular grids, including those induced in spatial panel and dyadic (network) problems, solving the eigenproblem may not be feasible, and a number of alternatives have been proposed. This article surveys selected alternatives, and comments on their relative usefulness, covering sparse Cholesky and sparse LU factorizations, and approximations such as Monte Carlo, Chebyshev, and using lower‐order moments with interpolation. The results are presented in terms of component‐wise differences between sets of Jacobians for selected data sets. In conclusion, recommendations are made for a number of analytical settings. Al estimar modelos de regresión espacial con el método del máxima verosimilitud (máximum likelihood) y usando matrices de pesos espaciales para representar procesos espaciales, cálculo del término jacobiano (jabobian)—ln(| I ?λ W |)‐ sigue siendo un problema central. En principio, y para bases de datos más pequeñas, el uso de los valores propios (eigenvalues) de la matriz de pesos espaciales proporciona una solución muy rápida. Los eigenvalues analíticos para retículas o grillas grandes y regulares son ya conocidos. Para problemas más grandes, que no se presentan en mallas regulares ‐incluyendo aquellos que se inducen en problemas de paneles espaciales y en problemas de (redes) diádicas‐, es posible que resolver el eigenproblem no sea posible. Este artículo estudia una selección de alternativas y comenta acerca de su relativa utilidad. Se cubren las facorizaciones de tipo Cholesky disperso (sparse Cholesky) y de tipo LU dispersas (sparse LU), las aproximaciones Monte Carlo, y Chebyshev, así mismo se utiliza momentos de bajo‐orden (lower‐order) con interpolación. Los resultados se presentan en términos de diferencias de componentes entre sets de términos jacobianos para bases de datos seleccionadas. En conclusión, se hacen recomendaciones para una serie de contextos analíticos. 当采用表征空间过程的空间权重矩阵对空间回归模型进行最大似然估计时,雅可比矩阵ln(|I?λW|)的计算仍是核心问题。对于小数据集,原则上可利用空间权重矩阵的特征值提供一种快速的解决方案,对于大型规则格网数据特征值分析同样有效。但对于不规则格网大型问题,包括从空间面板和二元（网络）问题中引伸的问题,利用特征值的解决方案可能不适用,对此学术界提出了多种可选替代方案。本文选取已有的几种替代方案并评论各自的相对有效性,其中包括稀疏Cholesky分解和稀疏LU分解法,Monte Carlo和 Chebyshev近似模拟法以及低阶矩插值法。结果以所选数据集雅可比矩阵间特定组份的差异方式显示。最后,推荐了一些分析设定。     

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.     

Modelling tourism and hospitality employment clusters: a spatial econometric approach

ABSTRACT

Geographic clustering of industries for mutual economic benefit has long been recognised. The concept of ‘externalities’ introduced by Alfred Marshall early last century rely on agglomeration of specialised industry within a geographic area. However, only recently has cluster modelling been applied to the tourism and hospitality (T&H) industry. The aim of this paper, therefore, is twofold: first is to develop a cluster-based theoretical framework for delineating geographic boundaries of T&H clusters, and second is to identify the underlying factors that drive their form and shape.

Drawing on employment data as the basis for co-location of T&H firms, spatial econometrics techniques are applied to model the spatial clustering of T&H employment in Victoria, Australia. Results show that rural tourism regions have higher levels of employment in tourism operational services whereas employment in city-based regions is more concentrated in hospitality services. Our findings, when normalised as a percentage of total employment, show that rural and regional Victoria ranks most highly as employers in the T&H industry. Adopting a range of spatial metrics, we show that T&H clustering throughout Victoria is largely driven by six location-specific factors: (1) the availability of tourism attractions; (2) proximity to the coast; (3) the road density network; (4) accessibility to employment within the Melbourne CBD; (5) the scale of the regional economy; and, (6) the advantages and disadvantages associated with economic resources. We conclude that the cluster-led strategy pose a number of challenges for tourism planners to promote regional tourism. Nevertheless, results from this study indicate that T&H employment clustering creates a more cohesive spatial structure that could support economic development and better connectedness of tourism destinations. These clusters could act as service hubs to their wider catchment areas where visitors are encouraged to stay overnight and travel to specific sights during the day.     

OLS ESTIMATION AND THE t TEST REVISITED IN RANK‐SIZE RULE REGRESSION*

ABSTRACT The rank‐size rule and Zipf's law for city sizes have been traditionally examined by means of OLS estimation and the t test. This paper studies the accurate and approximate properties of the OLS estimator and obtains the distribution of the t statistic under the assumption of Zipf's law (i.e., Pareto distribution). Indeed, we show that the t statistic explodes asymptotically even under the null, indicating that a mechanical application of the t test yields a serious type I error. To overcome this problem, critical regions of the t test are constructed to test the Zipf's law. Using these corrected critical regions, we can conclude that our results are in favor of the Zipf's law for many more countries than in the previous researches such as Rosen and Resnick (1980) or Soo (2005) . By using the same database as that used in Soo (2005) , we demonstrate that the Zipf law is rejected for only one of 24 countries under our test whereas it is rejected for 23 of 24 countries under the usual t test. We also propose a more efficient estimation procedure and provide empirical applications of the theory for some countries.     

Maximum Getis–Ord Statistic Adjusted for Spatially Autocorrelated Data

Local statistics test the null hypothesis of no spatial association or clustering around the vicinity of a location. To carry out statistical tests, it is assumed that the observations are independent and that they exhibit no global spatial autocorrelation. In this article, approaches to account for global spatial autocorrelation are described and illustrated for the case of the Getis–Ord statistic with binary weights. Although the majority of current applications of local statistics assume that the spatial scale of the local spatial association (as specified via weights) is known, it is more often the case that it is unknown. The approaches described here cover the cases of testing local statistics for the cases of both known and unknown weights, and they are based upon methods that have been used with aspatial data, where the objective is to find changepoints in temporal data. After a review of the Getis–Ord statistic, the article provides a review of its extension to the case where the objective is to choose the best set of binary weights to estimate the spatial scale of the local association and assess statistical significance. Modified approaches that account for spatially autocorrelated data are then introduced and discussed. Finally, the method is illustrated using data on leukemia in central New York, and some concluding comments are made.     

DOES FIRM OWNERSHIP AFFECT SPILLOVER OPPORTUNITIES? EVIDENCE FROM CHINESE MANUFACTURING

The clustering of economic activity is believed to generate both positive own‐industry (localization) spillovers and negative competitive pressures. Using data on manufacturing enterprises operating in China during 1998–2006, this paper provides evidence on the net effect of opposing spillovers from nearby economic activity. Central to the analysis is the opportunity to distinguish local manufacturing enterprises by state, private, or foreign ownership. Systematic differences in average productivity of these firms enable inferences about differences in the strength of spillovers from one type of firm to another type. Results indicate that spillovers are larger within the same ownership type than they are across them, consistent with localization economies that operate within segmented channels of influence.     

A New Artefact Typology for the Study of Medieval Arrowheads

ARCHAEOLOGICALLY recovered arrowheads from the British Isles. dated to between the roth and 16th centuries are examined. Hie exisiting arrowhead typology in the London Museum Medieval Catalogue is assessed and a new typology consisting of 28 generic forms, and subdivided into functional groups, is suggested.     

Spatial Entropy

A major problem in information theory concerns the derivation of a continuous measure of entropy from the discrete measure. Many analysts have shown that Shannon's treatment of this problem is incomplete, but few have gone on to rework his analysis. In this paper, it is suggested that a new measure of discrete entropy which incorporates interval size explicitly is required; such a measure is fundamental to geography and this statistic has been called spatial entropy. The use of the measure is first illustrated by application to one-and two-dimensional aggregation problems, and then the implications of this statistic for Wilson's entropy-maximizing method are traced. Theil's aggregation statistic is reinterpreted in spatial terms, and finally, some heuristics are suggested for the design of real and idealized spatial systems in which entropy is at a maximum.     

Weathering evidence for an additional glacial stage in Tasmania

Quantitative studies of relative dating parameters, including subsurface dolerite weathering rind thickness and weathering front penetration, permit the differentiation of three broad groupings of till deposits in several valleys in north-central, western, western-central and south-western Tasmania. An early cold climatic phase–the Linda Glacial Stage–is recognised on the basis of this weathering evidence which also indicates that there have been at least two more recent Glacial Stages of decreasing severity, termed here the Henty and Margaret Glacial Stages respectively. This three-fold model bears a striking similarity to that of Lewis (1945) which was rejected nearly three decades ago. However, whereas Lewis' model was founded upon erosional evidence, the present study is based entirely upon depositional and weathering evidence.     

Reconnaissance of Prehistoric Sites in the Red Sea Coastal Region of the Sudan,NE Africa

This paper reports results of a recent Stone Age-focused archaeological survey in the Red Sea coastal region of the Republic of Sudan, northeast Africa. Bifaces (handaxes) are the most conspicuous artifact class encountered during the survey and are characteristic of the Acheulean technocomplex. Other recorded artifact types include points, scrapers, and prepared core products referable to the Nubian and recurrent Levallois methods. Most of the artifact-bearing localities lie landward—outside of the coastal margin—thus, the evidence does not signify direct coastal adaptation per se. Our preliminary findings suggest that multiple Pleistocene-age hominin settlements tied to a terrestrial niche existed in the region. The western margin of the Red Sea occupies a pivotal location, linking the Horn of Africa and the Levant, two vital regions in human evolutionary research. Thus, the Stone Age data from the Sudan region has direct relevance for assessing hominin dispersal routes out of Africa.