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.     

Minimum-Cost Distances in Spatial Analysis

An axiomatic approach to distance is developed which focuses on those behavioral concepts of distance related to movement in space. In particular, spatial movement by behaving units is postulated to involve a choice from among some set of abstract trips in space, and implicitly, to involve the minimization of some relevant notion of trip costs. In this context, the relevant behavioral notion of distance in space is taken to be the minimum-cost distance generated by this choice process. These trip-cost concepts extend the classical notions of paths, path lengths, and shortest paths in metric spaces. Hence many of the analytical results of the paper involve extensions of classical shortest-path distance properties to minimum-cost distances. In addition to these extensions, a characterization theorem is given which specifies the possible functional relationships between trip costs and their associated path lengths. These relationships include most functional forms which are commonly employed in the literature.     

On the accuracy of estimating living stature from skeletal length in the grave and by linear regression

This study evaluates a method for obtaining stature estimates for populations represented by skeletal material, with individuals buried in a supine position. During the excavation of a Danish mediaeval cemetery, in situ skeletal length in the grave was measured from a point above the cranial point farthest from the body to the most distal point of the talus. The measurement was made with a folding rule placed on the sagittal midline of the skeleton, allowed to follow any curvature of the skeleton in situ. In the laboratory, stature was reconstructed anatomically, and this stature was regarded as an accurate estimate of living stature. Stature was also reconstructed from femur length by two linear regression procedures: 1) by sample and sex specific formulae, employing a leave‐one‐out approach, and 2) by sex wise formulae for Euro‐Americans from Trotter & Gleser (1952, American Journal of Physical Anthropology 10 : 463–514). Skeletal length in the grave and the two stature estimates based on linear regression were compared to anatomically reconstructed stature. Skeletal length in the grave estimated anatomically reconstructed stature with practically no bias (95% CI: −1.3–1.5 cm). Sample specific regression formulae estimated anatomically reconstructed stature also with no bias (95% CI: −1.2–1.1 cm). In contrast, statures calculated from Trotter & Gleser's regression formulae estimated anatomically reconstructed stature with a bias of about 4 cm (95% CI: 3.3–5.0 cm). Estimates of stature variance were biased for all three estimation procedures. However, for samples of adults, an adjusted variance estimate can be obtained by subtracting 8.7 cm² from the variance obtained from skeletal lengths in the grave. It is recommended to measure skeletal length in the grave whenever possible, and use this measurement for estimating statures for prehistoric and early historic populations. Copyright © 2005 John Wiley & Sons, Ltd.     

The Absolute Speed of Change: Multidimensional Scaling and Innovation Rates

The evaluation of societal developments depends on a clear determination of the rate of change that occurs within societies. While many statistical approaches are able to indicate similarity/dissimilarity distances between archaeological assemblages, only a few can be linked to linear timescales. In the following approach, the advantages of non‐metric multidimensional scaling (NMDS) are described as a method that produces gradients for a quantitative measurement of cultural change on a linear timescale. Thus, the speed of innovations or the regression of cultural developments could be quantified. In consequence, a quantified proxy of societal developments on a linear timescale is provided. In two examples, the usefulness of such a proxy is described in relation to other data.     

Shortest-Path Distances: An Axiomatic Approach

An axiomatic approach to distance is developed which focuses on those concepts of distance related to movement in space. The most fundamental types of such distances generally involve some notion of shortest paths between points, where the relevant concept of path length can be any additive attribute of paths (such as physical miles, hours spent in traveling, or gallons of fuel consumed). In particular, the shortest-path distance between any two points in space is here taken to be the greatest lower bound on all path lengths between these points. This notion of shortest-path distance is shown to be formally equivalent to a quasimetric, i.e., a distance which satisfies only the classical triangularity axiom for metrics. The main analysis of the paper focuses on the question of whether or not such shortest-path distances can actually be realized, i.e., on whether there exist shortest paths in space. The central result is to establish a general set of conditions under which such shortest paths always exist. In addition, a condition for the uniqueness of these paths is also established.     

Designs for Detecting Spatial Dependence

The aim of this article is to find optimal or nearly optimal designs for experiments to detect spatial dependence that might be in the data. The questions to be answered are: how to optimally select predictor values to detect the spatial structure (if it is existent) and how to avoid to spuriously detect spatial dependence if there is no such structure. The starting point of this analysis involves two different linear regression models: (1) an ordinary linear regression model with i.i.d. error terms—the nonspatial case and (2) a regression model with a spatially autocorrelated error term, a so-called simultaneous spatial autoregressive error model. The procedure can be divided into two main parts: The first is use of an exchange algorithm to find the optimal design for the respective data collection process; for its evaluation an artificial data set was generated and used. The second is estimation of the parameters of the regression model and calculation of Moran's I , which is used as an indicator for spatial dependence in the data set. The method is illustrated by applying it to a well-known case study in spatial analysis.     

Modeling Distance Decay Effects in Web Server Information Flows

Previous studies have shown that there is a direct correlation between the popularity of a medium and the cost in transmitting information through that medium. On this basis the World Wide Web may become more important as a mass medium than radio and television. Yet despite the enormous growth in Internet information and Internet-supported businesses, there has been, as yet, little in the way of quantitative spatial analysis of information flows on the WWW. One major issue is whether or not distance influences the web sites that a user may visit. If distance is a factor, then the location of servers delivering content becomes important. In this paper an analysis of information flows from U.K. academic web servers to the rest of the world is carried out. Using a UNIX utility called ping, the average time taken for a defined amount of information to travel between the United Kingdom and sixty-six other countries across the Internet was measured. This time measurement known as latency is used as a measure of distance on the Internet. The latency measurements are combined with counts of visitors from each of these countries to approximately one hundred U. K. academic WWW servers and used to build a simple gravity model of WWW information flows. The latency measurements between the United Kingdom and the other countries were gathered over a week in 1996. The counts of visitors relate to the total number of visits to the web servers over various time-scales for the years 1995 and 1996. We make the assumption that the distance measurements used are relevant to the visit counts. We also assume that all visitors from the .edu domain are geographically located in the United States. The gravity model is used to determine the effect of Internet distance on the number of expected visits to a web server. The study shows that latency values are a useful metric for measuring Internet distance. The results also demonstrate that the number of visitors to a web site falls off with distance on the Internet, as measured by latency values.     

GPS-based measurement of geographic spillovers in tourism – example of Polish districts

The agglomeration phenomenon in tourism often spreads beyond the borders of territorial units what is referred to as geographic spillovers. However, the measurement of spatial concentration of tourism demand and economic activity is usually based on statistics collected within regional administrative boundaries and omits the spatial interdependency between neighboring regions. Recognition of such spatial interdependency in the standard procedure to define neighborhood relies on the distance between geometric means (centroids) of territorial units which, however, rarely reflects real ‘centers’ of tourism agglomerations and leads to errors and biased results. Hence, we propose to modify the measures of the neighborhood with the use of GPS coordinates of tourism firms and attractions in order to designate their regional central tendencies and thus to correct (shift in space) localization of centroids of territorial units. We test the usefulness of the new approach to obtain a more precise measurement of spatial concentration when tourism spills over beyond the boundaries of territorial units using the example of Polish districts. We employ the exploratory spatial data analysis (spatial statistics) and spatial regression models – to assess the difference between using traditional centroids and GPS coordinates in defining neighborhood and determining spillover effects in regional analysis. Furthermore we apply the new method into the model of tourism potential in order to identify spillover effects in Polish regions. We use the data collected by Central Statistical Office (tourists staying overnight in 379 districts in 2014) and by Polish Tourist Organization (14,390 GPS coordinates of individual entities: tourism firms and attractions). The neighborhood determined with the use of GPS coordinates to measure the distance between centers of tourism agglomerations eliminates the dependence of the results on the administrative boundaries – but only to some degree. The challenge is to identify tourism agglomeration phenomenon as such, based on the mobility of tourists in space.     

THE MAPPING OF TRAVEL TIME IN EDMONTON, ALBERTA

T ime - distance is defined as the time required to travel a specific distance. Consider the time-distances among n places. They are tabulated in an n by n matrix and it is assumed that each element of the square array represents the minimum travel time to go from one place to another. Usually the matrix will be non-symmetrical with all diagonal elements equal to zero. Imagine a graphic representation of those places in a two-dimensional space. Theoretically it is possible to determine two configurations, one arising from trip i to j , the other from trip j to i , such that the locations of all n points approximate the n ( n -1)/2 time-distance relations.¹ In practice, however, the geographer will not be satisfied with a solution that does not preserve geographic neighbourliness. He will argue that geographical order is a necessary ingredient to the understanding of place relations. In most cases, a total solution that reconciles the geography with the metric is unattainable and only segments of the time-distance matrix are mapped. On polar isochronic maps, for instance, places are located according to their geographic azimuth and their time-distance with respect to one single origin. Therefore only one row or one column of the original matrix is plotted. The number of maps required for representing the entire data would be twice as large as the number of observations.     

GRAVITY AND SPATIAL STRUCTURE: THE CASE OF INTERSTATE MIGRATION IN MEXICO*

ABSTRACT The estimation of gravity models of internal (aggregate) place‐to‐place migration is plagued with endogeneity (omitted‐variable) biases if the unobserved effects of spatial structure are not accounted for. To address this econometric problem, this paper presents a more general specification of the gravity model, which allows for (bilateral) parameter heterogeneity across individual migration paths—along with (unilateral) origin‐ and destination‐specific effects. The resultant “three‐way fixed‐effects” (3FE) model is applied for an analysis of interstate migration in Mexico based on cross‐sectional data. To overcome parameter‐dimensionality problems (due to limited or incomplete information), the 3FE model is estimated using the Generalized Maximum Entropy (GME) estimator. The empirical implications of this new modeling strategy are illustrated by contrasting the 3FE‐GME estimates with those for the traditional and two‐way fixed‐effects (2FE) models. The former are far more plausible and intuitively interpretable than their traditional and 2FE counterparts, with parameter estimates changing in expected directions. The (average) effect of the migrant stock is markedly smaller than usually estimated, providing a more realistic measure of network‐induced migration. Migration outflows from centrally located origins have significantly steeper distance decay. Path‐specific distance effects exhibit directional asymmetries and spatial similarities.     

中国国内观光旅游线路设计中的游时研究

旅游线路是旅行社销售的主要产品,也是目的地旅游开发和市场营销的重要对象,其中游时是旅游线路设计中的核心要素之一。本文通过对北京、上海和广州为旅游出发地的旅游线路的统计分析表明,在中国国内观光旅游线路设计中,游时(出游时间与游览时间的统称)随客源地-目的地之间的距离呈对数增长,其中出游时间T₀(一次旅游的总耗时,单位:天)与出行直线距离D₁(客源地与目的地之间的球面距离,单位:公里)之间具有方程T₀=-4.5769+1.31611n(D₁)所描述的统计关系,而游览时间T₁(游客在目的地逗留的时间,单位:天)与出行直线距离D₁之间具有方程T₁=-4.2188+1.1220ln （D₁）所描述的统计关系。研究还发现,旅行社每日安排游览的景区(点)数目具有随出行距离呈"U"型曲线的特点,平均而言,在目的地逗留期间每天安排游览的景区(点)约为5个;从交通方式上看,随着出行距离的增加,呈现出汽车-火车-飞机交替演变的特点;旅游报价P与出行直线距离D₁之间存在线性相关性,关系式为:P=293.81+1.184 D₁。     

SPATIAL PRICE COMPETITION WITH CONSUIMERS ON A PLANE,AT INTERSECTIONS,AND ALONG MAIN ROADWAYS*

ABSTRACT. This paper examines two-dimensional price competition on a plane, with a block metric and a square grid of main roadways. One store is located at each intersection of main roadways. Consumer locations include a uniform distribution over the plane, linear concentrations along main roadways, and point concentrations at intersections. Bertrmd-Nash mill price competition is examined first. The equilibrium price depends on the relative numbers of consumers in the three types of locations (and on travel costs per mile and the spacing between stores). If too many consumers are in each point concentration, then the price equilibrium is undermined by a high-price strategy or by mill-price undercutting. Spatial competition with price discrimination is examined next, and compared to Bertrand-Nash mill price competition.     

A Shape‐Based Local Spatial Association Measure (LISShA): A Case Study in Maritime Anomaly Detection

The explicit consideration of the shape of geographic features has been largely ignored in existing spatial association measures. The primary contribution of this work is the development of a new local spatial association measure—a Local Indicator of Spatial and Shape Association (LISShA). The LISShA measure is modeled after local Geary's Spatial Autocorrelation measure with distance between shapes, calculated using the Small–Le metric, replacing difference between attribute values and the spatial neighborhood defined by Fréchet distance. We provide some explanation of these metrics and show, in detail, how the LISShA and proposed moments are calculated in a one‐dimensional context in a case study of maritime anomaly detection.     

Recursive Algorithm for Determination of Proximal (Thiessen) Polygons in Any Metric Space

A new and recursive algorithm for determining proximal polygons is based on quadtree concepts. The algorithm can use any distance metric, and produces a quadtree of the image of the proximal polygons. This can be converted to vector form, or be incorporated directly into a quadtree-based geographic information system, in order to solve a number of closest-point problems. The algorithm can also produce the Delaunay triangulation, which is the dual of the proximal polygons. Empirically, the running time of the algorithm is proportional to the number of centers raised to the 1.6 power.     

Approximating the Length of Vehicle Routing Problem Solutions Using Complementary Spatial Information

Accurately estimating the length of Vehicle Routing Problem (VRP) distances can inform transportation planning in a wide variety of delivery and service provision contexts. This study extends the work of previous research where multiple linear regression models were used to estimate the average distance of VRP solutions with various customer demands and capacity constraints. This research expands on that approach in two ways: first, the point patterns used in estimation have a wider range of customer clustering or dispersion values as measured by the Average Nearest Neighbor Index (ANNI) as opposed to just using a Poisson or random point process; second, the tour coefficient adjusted by this complementary spatial information is shown to exhibit statistically more accurate estimations. To generate a full range of ANNI values, point patterns were simulated using a Poisson process, a Matern clustering process, and a simple sequential inhibition process to obtain random, clustered, and dispersed point patterns, respectively. The coefficients of independent variables in the models were used to explain how the spatial distributions of customers influence the VRP distances. These results demonstrate that complementary spatial data can be used to improve operational results, a concept that could be applied more broadly.     

TRANSPORTATION COSTS IN REGIONAI,MODELS OF FOREIGN TRADE: AN APPLICATION TO CANADA-U.S. TRADE*

ABSTRACT. This paper outlines some arguments about the role of transportation costs in determining the welfare consequences of trade restrictions. The analysis uses a computable general equilibrium (CGE) model and presents the relevant features for trade analysis. The model has two alternative spatial formulations. In the first, all production and trade occur at one point, while in the second the regions are separated by distance. The calculated effects of a unilateral tariff increase are compared using the CGE model with the “point” and “distance” formulation. While the presence of transportation costs is crucial to some sectoral trade and production results, most welfare results are relatively insensitive to the spatial structure of the model.     

Biological Kinship,Postmarital Residence and the Emergence of Cemetery Formalisation at Prehistoric Marathon

This paper examines the role of kinship and postmarital residence in the emergence of organised cemeteries during the transition from the Final Neolithic to the Early Bronze Age at Marathon, Attica. Focusing on the cemetery of Tsepi, we performed intra‐cemetery biodistance analysis to test whether biological relatedness structured spatial organisation of tombs, and whether postmarital residence was matrilocal or patrilocal. Dental metric, dental morphological and cranial non‐metric data were collected from 293 individuals and subjected to multivariate analysis (principal component analysis, Euclidean distance ordination via multidimensional scaling), binomial probability calculations, Ripley's K analysis and determinant ratio analysis. Results indicated phenotypic similarity among some tomb co‐interments; however, outliers suggested that within‐tomb burial depended on a variety of factors that could include affinal, fictive or practical kinship. There was strong evidence for phenotypic patterning by tomb row, indicating that cemetery structure at Tsepi was organised according to biological lineages. This was especially evident for females. Male phenotypic variation was higher than that of females, though not significantly so. The results of intra‐cemetery biodistance analysis at Tsepi reveal a complex mortuary programme that emphasised biological kinship within an exogamous and likely matrilocal system of mate exchange. When considered in light of ethnographic evidence, the practice of male exogamy may correlate with the coastal location of the community and the maritime activities that structured the economy during the emergence of social complexity in the region. This paper illustrates the potential of biodistance analyses for elucidating aspects of social life in the Aegean. Copyright © 2017 John Wiley & Sons, Ltd.     

Crime and disorder, and house sales and prices around the casino sites in Windsor, Ontario, Canada

This study is an analysis of the impact of the opening or closure of a new urban casino on crime and disorder, and house sales and prices in its neighbourhood. The two sets of time-series data were the calls to the police about three types of offences and the house sales through the Multiple Listing Service in two neighbourhoods near the casinos in Windsor, Ontario, Canada. Temporally, the weekly numbers of offences and the mean monthly house prices were oscillating almost randomly around their respective declining or stationary long-term averages with no impulse from when a casino either opened or closed. Geographically, only two types of offences increased in number nearer to a casino site, but their respective distance decays neither moderated nor steepened after a casino had closed or opened. Even so, the conclusion is premature that the open or closed casinos have had benign effects on offences and house sales in the neighbourhoods.