An Approximation for the Rank Adjacency Statistic for Spatial Clustering with Sparse Data

The rank adjacency statistic D provides a simple method to assess regional clustering. It is defined as the weighted average absolute difference in ranks of the data, taken over all possible pairs of adjacent regions. In this paper the usual normal approximation to the D statistic is found to give inaccurate results if the data are sparse and some regions have tied ranks. Adjusted formulae for the moments of D that allow for the existence of ties are derived. An example of analyses of sparse mortality data (with many regions having no deaths, and hence tied ranks) showed satisfactory agreement between the adjusted formulae and the empirical distribution of the D statistic. We conclude that the D statistic, when used with adjusted moments, provides a valid approximate method to evaluate spatial clustering, even in sparse data situations.     

Composition,Similarity, and the Measurement of Economic Homogeneity*

Abstract. The concept of economic homogeneity in regional science is based on two very different notions: composition and similarity. In the case of the states of the US, measures of homogeneity based on these different notions are negatively correlated with each other, suggesting that the results of studies that use measures of economic homogeneity are likely to be sensitive to the conceptual basis of the specific measure. In order to overcome this problem, a portfolio‐theoretic measure of economic homogeneity with some attractive properties is presented. It is naturally decomposable into two components reflecting each of these notions and easy to construct using widely available data. Using this measure, patterns of homogeneity for the states of the US are illustrated and discussed, and hypotheses about the relationship between homogeneity and economic instability are tested.     

SPATIAL DEPENDENCE AND SPATIAL STRUCTURAL INSTABILITY IN APPLIED REGRESSION ANALYSIS*

The stability of regression coefficients over the observation set (“regional homogeneity”) is typically assessed by means of a Chow test or within a seemingly unrelated regression (SUR) framework. When spatial error autocorrelation is present in cross-sectional equations the traditional tests are no longer applicable. I evaluate this both in formal terms as well as empirically. I introduce a taxonomy of spatial effects in models for structural instability, and discuss its implication for testing. I compare the performance of traditional tests, robust approaches, maximum-likelihood procedures and pretest techniques by means of a series of simple Monte Carlo experiments.     

The Size-adjusted Critical Region of Moran's I Test Statistics for Spatial Autocorrelation and Its Application to Geographical Areas

In this article, we explore the expression of the asymptotic approximation of the distribution function of Moran's I test statistic for the check of spatial autocorrelation, and we derive a more accurate critical value, which gives the rejection region similar to significant level α to the order of N^?1 (N = sample size). We show that in some cases our procedure effectively finds the significance of positive spatial autocorrelation in the problem testing for the lack of the spatial autocorrelation. Compared with our method, the testing procedure of Cliff and Ord (1971) is clearly ad hoc and should not be applied blindly, as they pointed out. Our procedure is derived from the theory of asymptotic expansion. We numerically analyze four types of county systems with rectangular lattices and three regional areas with irregular lattices.     

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.     

The Detection of Clusters Using a Spatial Version of the Chi-Square Goodness-of-Fit Statistic

A test statistic for the detection of spatial clusters is developed by generalizing the common chi-square goodness-of-fit test. The paper includes a discussion of the relationship between the statistic and other associated statistics, and provides an analysis of both its null distribution and power. The paper concludes with the development of a local version of the statistic and an application to leukemia clustering in central New York.     

The Detection of Clusters Using a Spatial Version of the Chi-Square Goodness-of-Fit Statistic

A test statistic for the detection of spatial clusters is developed by generalizing the common chi-square goodness-of-fit test. The paper includes a discussion of the relationship between the statistic and other associated statistics, and provides an analysis of both its null distribution and power. The paper concludes with the development of a local version of the statistic and an application to leukemia clustering in central New York.     

A Quantitative Approach to Designing a System of Economic Regions of the USSR

The authors state the rationale and describe the technique used to devise a system of seven economic macroregions of the USSR for long-term planning purposes. Since broad resource groups determine the specialization of regional complexes and their specialization in the geographical division of labor, the macroregions were constructed on the basis of homogeneity in key resources, such as manpower, fuels, land, water and transport geography. The new regional system preserves the basic division of the USSR into western and eastern economic zones, and reflects the lower labor and transport costs in the west, and the lower natural-resource costs in the east. The seven-region system, which is already being used in the 15-year plan 1975–1990, is expected to help determine optimal directions of regional development depending on whether regions have surpluses or are short of fuels, electric power, land, water or manpower. The new macroregions were designed by consolidating existing basic economic regions and union republics into larger entities, but the republics may be set apart as subzones for more detailed planning purposes.     

Testing for Local Spatial Autocorrelation in the Presence of Global Autocorrelation

A fundamental concern of spatial analysts is to find patterns in spatial data that lead to the identification of spatial autocorrelation or association. Further, they seek to identify peculiarities in the data set that signify that something out of the ordinary has occurred in one or more regions. In this paper we provide a statistic that tests for local spatial autocorrelation in the presence of the global autocorrelation that is characteristic of heterogeneous spatial data. After identifying the structure of global autocorrelation, we introduce a new measure that may be used to test for local structure. This new statistic Oi is asymptotically normally distributed and allows for straightforward tests of hypotheses. We provide several numerical examples that illustrate the performance of this statistic and compare it with another measure that does not account for global structure.     

Beyond Moran's I: Testing for Spatial Dependence Based on the Spatial Autoregressive Model

The statistic known as Moran's I is widely used to test for the presence of spatial dependence in observations taken on a lattice. Under the null hypothesis that the data are independent and identically distributed normal random variates, the distribution of Moran's I is known, and hypothesis tests based on this statistic have been shown in the literature to have various optimality properties. Given its simplicity, Moran's I is also frequently used outside of the formal hypothesis-testing setting in exploratory analyses of spatially referenced data; however, its limitations are not very well understood. To illustrate these limitations, we show that, for data generated according to the spatial autoregressive (SAR) model, Moran's I is only a good estimator of the SAR model's spatial-dependence parameter when the parameter is close to 0. In this research, we develop an alternative closed-form measure of spatial autocorrelation, which we call APLE , because it is an approximate profile-likelihood estimator (APLE) of the SAR model's spatial-dependence parameter. We show that APLE can be used as a test statistic for, and an estimator of, the strength of spatial autocorrelation. We include both theoretical and simulation-based motivations (including comparison with the maximum-likelihood estimator), for using APLE as an estimator. In conjunction, we propose the APLE scatterplot, an exploratory graphical tool that is analogous to the Moran scatterplot, and we demonstrate that the APLE scatterplot is a better visual tool for assessing the strength of spatial autocorrelation in the data than the Moran scatterplot. In addition, Monte Carlo tests based on both APLE and Moran's I are introduced and compared. Finally, we include an analysis of the well-known Mercer and Hall wheat-yield data to illustrate the difference between APLE and Moran's I when they are used in exploratory spatial data analysis.     

INDUSTRIAL DISPERSION IN THE SOVIET UNION: AN APPLICATION OF ENTROPY MEASURES

Industrial dispersion across the republics of the USSR between 1926 and 1974 is described through the use of entropy measures. Ostensibly, a set of location principles would guide such dispersion, and several of them stress regional equalization as an important consideration in locating industry. Therefore, trends in regional inequality (in industrialization) are investigated through the use of inequality statistics derived from entropy measures at three different spatial scales. Between 1926 and 1960, inequality among the republics decreased, but has increased between 1960 and 1974. However, inequality has decreased between the economic regions of the USSR between 1940 and 1975, and at the oblast level, there has been a tendency toward greater equality (homogeneity) within each economic region or republic since 1960. In attempting to account for these diverse trends, it is suggested that they are largely the result of the priority of efficiency considerations in location decisions rather than those of regional equity per se.     

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.     

经济发达地区地方性博物馆旅游发展研究--以广州南越王墓博物馆为例

本文以广州南越王墓博物馆为例,在游客行为分析的基础上,探讨了其发展规律和动因.作者采用结构性问卷调查的方法现场收集游客行为问卷,运用SPSS软件进行统计分析,并辅之以案例地博物馆游客结构的二手资料.在对所收集资料进行定性定量分析后,作者认为,南越王墓博物馆作为地方性博物馆,属于区域性的文化观光旅游产品,重游率低,潜在市场规模有限,且呈现随出游游客增加而不断萎缩的特点,因此形成持续下滑的接待曲线.与Butler旅游产品生命周期曲线对比发现,南越王墓博物馆缺少探查、参与、发展和巩固阶段,而直接进入衰退阶段.这一结论对于经济发达地区地方性博物馆旅游开发管理具有重要意义.     

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.     

USING THE GETIS STATISTIC TO EXPLORE AGGREGATION EFFECTS IN METROPOLITAN TORONTO CENSUS DATA

In an earlier paper by the same authors (Amrhein and Reynolds 1996), the variation of the G statistic (Getis 1991; Getis and Ord 1992) was demonstrated to correlate very highly with calculated aggregation effects. In the conclusions to this earlier paper, we called for experiments with different data sets, different aggregation rules, and different definitions of the connectivity matrix. In this paper, we explore the behaviour of census data from enumeration areas of the Toronto Census Metropolitan Area. Experiments are conducted that describe the aggregation effects that creep into the data at different scales, and the effect of the aggregation algorithm on the results. Finally, we test the ability of a modified G statistic, our Getis statistic, to predict aggregation effects     

旅游产业集聚会影响地区收入差距吗？——基于中国省际面板数据的门槛回归分析

本文利用中国30个省市区1999年～2009年面板数据,分别从线性和非线性两个角度实证检验了旅游产业集聚对地区收入差距的影响,估计结果显示：一方面,旅游产业集聚对地区收入差距具有显著线性负向影响效应;另一方面,通过构建非线性面板门槛模型,进一步检验了旅游产业集聚对地区收入差距影响效应的门槛特征,具体而言,旅游产业集聚对地区收入差距负向影响效应不仅存在基于旅游产业集聚的单一门槛特征,而且也存在基于经济发展水平、基础设施建设与产业结构升级的三重门槛特征。     

A Descriptive Analysis of Discrete U.S. Industrial Complexes*

Abstract. We use the Getis/Ord local G statistic and detailed county‐level industry employment data from the U.S. Bureau of Labor Statistics to isolate discrete industrial complexes—or groups of nominally linked industries clustered in particular locations—for two recent years: 1989 and 1997. We describe the characteristics of the complexes in terms of their number, spatial extent, broad regional distribution, and other factors. Data from the two periods help illustrate key shifts in industrial locations, including the continuing concentration of the apparel industry in the Southeast and the ongoing southern shift in U.S. vehicle production.     

浅谈区域地名研究

区域地名研究是从不同角度对一个地区地名的研究。它是地名学研究的组成部分 ,并对中国地名学的发展具有重要意义。区域地名研究的主要任务是 :研究一个地域地名的总体特征 ,地名的命名、含义、分类、分布、价值、演变、管理以及不同区域地名的比较等。区域地名研究的主要方法是文献考证、数据统计、比较分析、实地调查、运用地图等     

On the homogeneity of fluids forming bedding‐parallel veins

A group of 400–500 m long, bedding‐parallel calcite veins are exposed in the central La Popa Basin of northeastern Mexico. These veins provide a unique opportunity to determine the kilometer‐scale fluid–rock system associated with bedding‐parallel vein formation, and to test for sampling bias in studies that often use one or two samples to constrain the characteristics of regional‐scale paleohydrogeological systems. We use fluid inclusion microthermometry in conjunction with measurements of δ¹³C, δ¹⁸O, and ⁸⁷Sr/⁸⁶Sr ratios to constrain the vein‐forming fluid temperatures, compositions and sources, and compare these values along and between the veins to establish the homogeneity of the vein‐forming fluids and fluid–rock system. The δ¹³C values of the veins are close to those of the host rock, and average – 3.96‰ (PDB). The δ¹⁸O values of the veins are typically 1‰ lower than those of the host rocks, and average – 9.54‰ (PDB). Fluid inclusion homogenization temperatures average 137°C and inclusion salinities are all <6 wt% NaCl equivalent. The ⁸⁷Sr/⁸⁶Sr ratios of the veins average 0.70731 and are substantially lower than the values expected for the host rock. Calculated fluid δ¹⁸O values range from 4 to 10‰ (SMOW). The isotopic and microthermometric data indicate the veins most likely formed at depths of 3–4 km when meteoric water mixed with upward migrating, warm basinal brines. Vein microstructures and field characteristics indicate they formed from multiple slip events that most likely were associated with transport of individual fluid pulses that migrated along bedding planes. The large‐scale homogeneity of vein geochemistry is remarkable and demonstrates that only one or two samples would be sufficient to accurately characterize the kilometer‐scale paleohydrogeological system for these veins.     

Continuity and change in regional disparities in Belgium during the twentieth century

This paper presents estimates of regional GDP per capita for certain benchmark years during the first half of the twentieth century using the method proposed by Geary and Stark. After testing the robustness of the Geary and Stark methodology for the Belgian situation, these estimates are linked to the official regional GDP figures, available since 1955, so that we can cover the whole of the twentieth century. Next we test the suggestion put forward by many historians of a contrast between a ‘poor Flanders’ and a relatively ‘prosperous Wallonia’ around 1900. For the remainder of the analysis Belgium’s nine provinces are used as a geographical unit to take a broader view than just the Flanders/Wallonia controversy. The analysis shows a dramatic reversal of fortune between the northern and southern provinces. We explain the main causes of this process and assess the effect of state policies on regional development. Finally, the paper considers whether the twentieth century witnessed a process of convergence.