"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.     

基于ESDA的新疆旅游经济发展空间分异规律研究

在ArcGIS空间分析技术支持下,借助GeoDA空间自相关分析方法,以新疆85个县(市)旅游总收入及其空间差异为研究对象,分析新疆旅游经济发展空间分异格局,并用地学统计方法研究其空间分异规律,得出:(1)新疆旅游经济具有较强的空间依赖性,全局空间自相关特征明显,表现为集聚度高、异质性强、差异性大的空间极化分异态势;(2)局部上则表现为高高相聚和低低相随的两极分化格局,热点区以乌鲁木齐为中心,以昌吉州和吐鲁番、阿勒泰地区为延伸,沿交通网络向周边地区递减的空间分异格局,喀什、和田地区为冷点区;(3)交通可达性及旅游基础设施数量对新疆旅游经济发展起决定性作用,高速公路尤其是铁路对旅游经济影响最大;旅游资源优势度对旅游实现更加重要;交通区位对新疆旅游经济空间分异起着基础性作用.     

New Developments in the Use of Spatial Technology in Archaeology

Spatial technology is integral to how archaeologists collect, store, analyze, and represent information in digital data sets. Recent advances have improved our ability to look for and identify archaeological remains and have increased the size and complexity of our data sets. In this review we outline trends in visualization, data management, archaeological prospecting, modeling, and spatial analysis, as well as key advances in hardware and software. Due to developments in education, information technology, and landscape archaeology, the implementation of spatial technology has begun to move beyond superficial applications and is no longer limited to environmental deterministic approaches. In the future, spatial technology will increasingly change archaeology in ways that will enable us to become better practitioners, scholars, and stewards.     

Rethinking the Spatiality of Spatial Planning: Methodological Territorialism and Metageographies

This paper argues for increased attention to the role of territory and territoriality in framing sociospatial discourses in the context of spatial plan making. In particular, it is suggested that the engagement of political actors with processes of spatial planning tends to be framed within particular spatial imaginaries which reflect established political-administrative and territorial boundaries. It is contended that a critical analysis of the territorial framing of processes of spatial planning is necessary in order to understand the capacity for spatial strategies to effectively challenge and reconfigure established sociospatial imaginaries in functional or relational terms. It is suggested that spatially explicit public policy statements, such as planning strategies, may be characterized by specific assumptions of territorial space, in a similar manner to which mainstream social science has contained implicit assumptions of state-centrism. The salience of territorial spatial imaginaries is demonstrated in the case of European spatial planning and through a local case study of city-regional spatial planning and politics in the Greater Dublin Area.     

A Programming Approach to Minimizing and Maximizing Spatial Autocorrelation Statistics

A programming approach is presented for identifying the form of the weights matrix W which either minimizes or maximizes the value of Moran's spatial autocorrelation statistic for a specified vector of data values. Both nonlinear and linear programming solutions are presented. The former are necessary when the sum of the links in W is unspecified while the latter can be used if this sum is fixed. The approach is illustrated using data examined in previous studies for two variables measured for the counties of Eire. While programming solutions involving different sets of constraints are derived, all yield solutions in which the number of nonzero elements in W is considerably smaller than that in W defined using the contiguity relationships between the counties. In graph theory terms, all of the Ws derived define multicomponent graphs. Other characteristics of the derived Ws are also presented.     

Local Spatial Autocorrelation Statistics: Distributional Issues and an Application

The statistics G_i(d) and G_i*(d), introduced in Getis and Ord (1992) for the study of local pattern in spatial data, are extended and their properties further explored. In particular, nonbinary weights are allowed and the statistics are related to Moran's autocorrelation statistic, I. The correlations between nearby values of the statistics are derived and verified by simulation. A Bonferroni criterion is used to approximate significance levels when testing extreme values from the set of statistics. An example of the use of the statistics is given using spatial-temporal data on the AIDS epidemic centering on San Francisco. Results indicate that in recent years the disease is intensifying in the counties surrounding the city.     

针对我国省际旅游业发展与经济增长间关系的空间计量方法应用

本研究利用空间计量模型研究中国省际旅游业发展与经济增长的关系。结果表明：1999～2007年各省级行政区的旅游发展对经济增长具有长期推动作用;各省级行政区的经济增长受到本区域旅游业发展水平、邻近区域的旅游业发展水平和经济增长的共同影响;并且入境旅游对经济增长的作用效果比国内旅游更为显著。因此,建议各省级行政区在旅游产业布局和功能分区的基础上加强区域间旅游合作和开拓国际国内旅游市场。     

Toward a Theory of Spatial Statistics: Another Step Forward

An update is presented to an earlier piece outlining some steps that needed to be taken toward the establishment of a theory of spatial statistics. Findings that have appeared since this first paper are summarized and interpreted, and extensions and suggestions are offered for the further establishment of a basis for a theory of spatial statistics. Topics include boundary considerations, the role of latent spatial dependencies, and small-sample-size issues. These topics embrace the problems of data transformations, edge effect bias, reference sampling distributions, multivariate autocorrelation models, conditional expectations, and higher-order autoregressive structures. In part, a course is charted for the next step to be taken.     

The Analysis of Spatial Association by Use of Distance Statistics

Introduced in this paper is a family of statistics, G, that can be used as a measure of spatial association in a number of circumstances. The basic statistic is derived, its properties are identified, and its advantages explained. Several of the G statistics make it possible to evaluate the spatial association of a variable within a specified distance of a single point. A comparison is made between a general G statistic and Moran's I for similar hypothetical and empirical conditions. The empirical work includes studies of sudden infant death syndrome by county in North Carolina and dwelling unit prices in metropolitan San Diego by zip-code districts. Results indicate that G statistics should be used in conjunction with I in order to identify characteristics of patterns not revealed by the I statistic alone and, specifically, the G_i and G_i* statistics enable us to detect local “pockets” of dependence that may not show up when using global statistics.     

Spatial Autocorrelation Statistics of Areal Prevalence Rates under High Uncertainty in Denominator Data

We propose a new estimator of spatial autocorrelation of areal incidence or prevalence rates in small areas, such as crime and health indicators, for correcting spatially heterogeneous sampling errors in denominator data. The approach is dubbed the heteroscedasticity‐consistent empirical Bayes (HC‐EB) method. As American Community Survey (ACS) data have been released to the public for small census geographies, small‐area estimates now form the demographic landscape of neighborhoods. Meanwhile, there is growing awareness of the diminished statistical validity of global and local Moran’s I when such small‐area estimates are used in denominator data. Using teen birth rates by census tracts in Mecklenburg County, North Carolina, we present comparisons of conventional and new HC‐EB estimates of Global and Local Moran’s I statistics created on ACS data, along with estimates on ground truth values from the 2010 decennial census. Results show that the new adjustment method dramatically enhances the statistical validity of global and local spatial autocorrelation statistics.     

Large Sample-Size Distribution of Statistics Used In Testing for Spatial Correlation

Test statistics for testing for spatial correlation in continuous variables have been given by both Moran and Geary and have subsequently been generalized. It has been conjectured for a long time that under the hypothesis of no spatial correlations all these statistics are normally distributed when the sample size is large. This paper proves a very general theorem on the large sample normality of quadratic forms. As corollaries to the theorem the asymptotic normality, under the hypothesis, of all the above-mentioned statistics is established. The necessary conditions are quite unrestrictive. It is also shown, by means of a counter example, that the conditions given in a similar theorem (Cliff and Ord) are inadequate to ensure normality.     

Methodological Problems in Economic Geography

The author uses the techniques of paleogeography and archeology to trace climatic fluctuations in inner Asia and the rise of nomadism in the 1st millennium B. C. replacing a settled mode of stock herding and agriculture. Previous papers in this series appeared in Soviet Geography, June 1964 and February 1966.     

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.     

Basic Methodological Problems in Ethnic Mapping

The following excerpt from a speech delivered October 18, 1963, before the Presidium of the Academy of Sciences USSR by a leading ideological spokesman of the Communist party is relevant to the discussion surrounding V. A. Anuchin's advocacy of a unified geography. Ilyichev denounces the Stalinist definition of the environment as a purely natural category. He charges that some Soviet scholars have used this definition as a “theoretical foundation” for erecting an insurmountable wall between the natural and social sciences. A briefer version of his remarks appeared in the journal Voprosy Filosofi, 1963, No. 11, pp. 6–7.