"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.     

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.     

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。     

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.     

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.     

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.     

Controlling the False Discovery Rate: A New Application to Account for Multiple and Dependent Tests in Local Statistics of Spatial Association

Assessing the significance of multiple and dependent comparisons is an important, and often ignored, issue that becomes more critical as the size of data sets increases. If not accounted for, false-positive differences are very likely to be identified. The need to address this issue has led to the development of a myriad of procedures to account for multiple testing. The simplest and most widely used technique is the Bonferroni method, which controls the probability that a true null hypothesis is incorrectly rejected. However, it is a very conservative procedure. As a result, the larger the data set the greater the chances that truly significant differences will be missed. In 1995, a new criterion, the false discovery rate (FDR), was proposed to control the proportion of false declarations of significance among those individual deviations from null hypotheses considered to be significant. It is more powerful than all previously proposed methods. Multiple and dependent comparisons are also fundamental in spatial analysis. As the number of locations increases, assessing the significance of local statistics of spatial association becomes a complex matter. In this article we use empirical and simulated data to evaluate the use of the FDR approach in appraising the occurrence of clusters detected by local indicators of spatial association. Results show a significant gain in identification of meaningful clusters when controlling the FDR, in comparison to more conservative approaches. When no control is adopted, false clusters are likely to be identified. If a conservative approach is used, clusters are only partially identified and true clusters are largely missed. In contrast, when the FDR approach is adopted, clusters are fully identified. Incorporating a correction for spatial dependence to conservative methods improves the results, but not enough to match those obtained by the FDR approach.     

Recent Directions and Developments in Geographical Information Systems

Geographical information systems (GIS) are tools for handling and processing spatially referenced information that have permeated all facets of archaeology, frequently revolutionizing research by allowing easy access to vast amounts of information, new ways of data visualization that promote insight through pattern recognition, and unique methodologies that allow entirely new approaches to the study of the past. This comprehensive review examines and critiques recent advances achieved through GIS in regional and within-site databases, locational analysis and modeling, regional simulation, studies of landscape perception through intervisibility analysis, and models of spatial allocation, territoriality, and site access. The future prospects of GIS are enormous with the growth of the Internet, the resultant linking of databases, expected enhancements in satellite remote sensing, and the increasing pervasiveness of global positioning systems for spatial data capture. If there is a persistent theme that emerges from the chronicles of contemporary scientific cartography, it is that the creation of a map almost inevitably leads to unexpected revelations. — Hall, Mapping the Next Millenium: How Computer-Driven Cartography Is Revolutionizing the Face of Science