What Problem? Spatial Autocorrelation and Geographic Information Science

In retrospect it is the word "problem" in the title that seems most remarkable about the Cliff and Ord article. Spatial autocorrelation is indeed a problem in standard inferential statistics, which was developed to handle controlled experiments, when these methods are used to generalize from natural experiments. From the perspective of geographic information science, however, spatial dependence is a defining characteristic of geographic data that makes many of the functions of geographic information systems possible. The almost universal presence of spatial heterogeneity in such data also argues against generalization and is made explicit in the recent development of place-based analytic techniques. The final section argues for a new approach to the teaching of quantitative methods in the environmental and social sciences that treats natural experiments, spatial dependence, and spatial heterogeneity as the norm.     

Spatial Autocorrelation in Ecological Studies: A Legacy of Solutions and Myths

A major aim of including the spatial component in ecological studies is to characterize the nature and intensity of spatial relationships between organisms and their environment. The growing awareness by ecologists of the importance of including spatial structure in ecological studies (for hypothesis development, experimental design, statistical analyses, and spatial modeling) is beneficial because it promotes more effective research. Unfortunately, as more researchers perform spatial analysis, some misconceptions about the virtues of spatial statistics have been carried through the process and years. Some of these statistical concepts and challenges were already presented by Cliff and Ord in 1969. Here, we classify the most common misconceptions about spatial autocorrelation into three categories of challenges: (1) those that have no solutions, (2) those where solutions exist but are not well known, and (3) those where solutions have been proposed but are incorrect. We conclude in stressing where new research is needed to address these challenges.     

Spatial Autoregression

The paper by Cliff and Ord (1969) caused us to think more about the W matrix and the concept of spatial autoregression. This article reviews some applications of W , reinforcing the point that autoregression in time series is similar to, but not the same as, autoregression in spatial series.     

Impact of Cliff and Ord (1969, 1981) on Spatial Epidemiology

The influence in spatial epidemiology of the seminar work on autocorrelation by Cliff and Ord is discussed. Quantifying the evidence of spatial clustering was an important step in the development of modern statistical methods for analyzing spatial variations of diseases. Autocorrelation is nowadays mostly accounted for at a latent level within a hierarchical framework to small area disease mapping. The importance of accounting for autocorrelation in geographical correlation studies is also reviewed.     

Network Autocorrelation

Even though Cliff and Ord (1969) do not question "network autocorrelation," their paper contains an interesting ambiguity that is here discussed. Hence, this article aims at discussing the problem of spatial autocorrelation in (perhaps preferably on) a network as well as at giving an overview of the existing relevant literature. A typology of network autocorrelations is suggested and it is hoped that this discussion initiates debates and points to new research challenges.     

A SPATIAL CLIFF‐ORD‐TYPE MODEL WITH HETEROSKEDASTIC INNOVATIONS: SMALL AND LARGE SAMPLE RESULTS*

ABSTRACT In this paper, we specify a linear Cliff‐and‐Ord‐type spatial model. The model allows for spatial lags in the dependent variable, the exogenous variables, and disturbances. The innovations in the disturbance process are assumed to be heteroskedastic with an unknown form. We formulate multistep GMM/IV‐type estimation procedures for the parameters of the model. We also give the limiting distributions for our suggested estimators and consistent estimators for their asymptotic variance‐covariance matrices. We conduct a Monte Carlo study to show that the derived large‐sample distribution provides a good approximation to the actual small‐sample distribution of our estimators.     

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.     

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.     

Book Reviews

Book reviewed in this article: Spatial Diffusion: An Historical Geography of Epidemics in an Island Community, by A. D. Cliff, P. Haggett, J. K. Ord, and G. R. Versey. Catastrophe Theory and Bifurcation: Applications to Urban and Regional Systems, by A. G. Wilson. Spatial Processes: Models and Applications, by A. D. Cliff and J. K. Ord. Statistical Applications in the Spatial Sciences, edited by N. Wrigley.     

A History of the Concept of Spatial Autocorrelation: A Geographer's Perspective

Spatial autocorrelation is a concept that helps to define the field of spatial analysis. It is central to studies using spatial statistics and spatial econometrics. In this paper, we trace the early development of the concept and explain the academic links that brought the concept to the fore in the late 1960s. In geography, the importance of the work of Michael F. Dacey, Andrew D. Cliff, and J. Keith Ord is emphasized. Later, with the publication of a volume on spatial econometrics by Luc Anselin, spatial research and the use of the concept of spatial autocorrelation received a considerable boost. These developments are outlined together with comments about recent and possible future trends in spatial autocorrelation-based research.     

BOOK REVIEWS

Book reviews in this article: Urban and Regional Models in Geography and Planning, by Alan G. Wilson. Planning and Urban Growth: An Anglo-American Comparison, by Marion Clawson and Peter Hall. New Towns: Why-And for Whom?, by H. S. Pcrloff and N. C. Sandberg (eds.). Spatial Autocorrelation, by A. D. Cliff and J. R. Ord.     

北京房地产中介空间格局演化特征及驱动因素分析

本文基于微观企业数据,采用泰森多边形、核密度及空间自相关方法,多尺度考察2001-2010年北京房地产中介门店空间格局演化特征,通过构建地理加权回归模型（GWR）,探究2010年房地产中介空间格局驱动因素。研究表明：①房地产中介集中分布在城六区,数量增速最快功能区是城市发展新区。②空间格局不均衡性增大,空间集聚态势加强。③集聚主核心点出现由"东城"向"朝阳"方向的东推位移,集聚程度加深,主核心区团块面积扩大,次级核心点增多,"两轴、两带、多中心"基本版图形成。④空间集聚现象明显,热点区域扩张,但始终集中在区域中心。⑤驱动效应最大的因素为常住人口,多种驱动因素效应均比较强的街区（乡镇）基本上属于各区县经济水平相对发达的区域。此外,政府政策对其影响也较大。     

Spatial Autocorrelation and Impacts on Criminology

Despite criminology's widespread application of geography, the full implications of Cliff and Ord's article have yet to be realized. In this essay the major types of spatial studies in criminology are outlined, followed by a depiction of the context of criminological research at the time the article was published. Next the major changes to the field occurring after the publication of Cliff and Ord's paper, focusing on technology advances and theory, are set out. Fortunately these changes mean the discipline is well placed to move beyond seeing the presence of spatial autocorrelation as a methodological issue that needs to be explained away.     

Book Reviews

Book reviewed in this article: The Office: A Facet of Urban Growth, by Peter Cowan, Daniel Fine, John Ireland, Clive Jordan, Dilys Mercer, and Angela Sears. The Office Industry: Patterns of Growth and Location, by Regina Belz Armstrong and Boris Pushkarev. Office Linkages and Location: A Study of Communications and Spatial Patterns in Central London, by J. B. Goddard. Spatial Autocorrelation, by A. D. Cliff and J. K. Ord     

Canadian foreign direct investment in the United States by type: mergers and acquisitions, greenfield, real estate, joint ventures and investment increases

This paper provides an overview of Canadian foreign direct investment (FDI) in the United States by type. Mergers and acquisitions (M&As), greenfield investments, joint ventures, real estate purchases and increases to existing investments are compared spatially, through time (using a data set that consists of transactions from 1977 to 1994) and by industrial classification. Over this study's time-frame, direct investors from Canada were most likely to perform a real estate or M&A transaction in the United States (and least likely to be involved in a joint venture). The most consequential years for real estate purchases were the 1970s and early 1980s; whereas M&A and greenfield transactions have gained in proportionate importance through time. M&As, greenfield and investment increases were most often enumerated as manufacturing transactions, but mining and consumer and business services were also very common. A series of bivariate regression models established that growing state economies significantly increased M&A, real estate, greenfield and investment increase activity from Canada. Relative regional specializations (as given by location quotients) provided additional spatial information. M&As formed a pattern of specialization that emphasized the Great Lakes region and also the central portion of the US (roughly following the Mississippi River). Greenfield and investment increase transactions favoured states along the east coast and those adjacent to the Canada-US border. Real estate investors were most attracted to the US south and extreme west.     

A General Misspecification Test for Spatial Regression Models: Dependence, Heterogeneity, and Nonlinearity

There is an increasing awareness of the potentials of nonlinear modeling in regional science. This can be explained partly by the recognition of the limitations of conventional equilibrium models in complex situations, and also by the easy availability and accessibility of sophisticated computational techniques. Among the class of nonlinear models, dynamic variants based on, for example, chaos theory stand out as an interesting approach. However, the operational significance of such approaches is still rather limited and a rigorous statistical-econometric treatment of nonlinear dynamic modeling experiments is lacking. Against this background this paper is concerned with a methodological and empirical analysis of a general misspecification test for spatial regression models that is expected to have power against nonlinearity, spatial dependence, and heteroskedasticity. The paper seeks to break new research ground by linking the classical diagnostic tools developed in spatial econometrics to a misspecification test derived directly from chaos theory—the BDS test, developed by Brock, Dechert, and Scheinkman (1987). A spatial variant of the BDS test is introduced and applied in the context of two examples of spatial process models, one of which is concerned with the spatial distribution of regional investments in The Netherlands, the other with spatial crime patterns in Columbus, Ohio.     

我国城市街区单元平面形态的演替:现状、动因及规律

论文基于相关城市的土地利用数据对城市街区单元平面形态的变化规律进行理论模拟和定量分析。研究结果表明,在外向型城市扩张模式或内向型城市更新模式下,城市街区单元的空间尺度都有明显的增大趋向,区域范围内街区单元的数量也相应减少。造成这一趋势的主要原因在于在经济和社会需求驱动下的建设模式,以房地产企业为代表的社会力量成为城市街区成型的主导力量,基于成本-收益等经济利益考虑,企业倾向于扩大开发项目的空间体量,从而造成了城市街区单元尺度的增大;这一变化本身也深刻影响了城市的居民生活和产业活动。     

城市企业主义视角下的中国城市增长机制研究

我国城市发展自本世纪以来呈现出加快发展的趋势。然而,这一进程尚不均衡和协调。本文通过城市企业主义这一视角,分析中国城市实现空间与经济迅速增长的机制及其所面临的问题。文章首先考察了2001-2009年间的公共财政结构,揭示出中国地方政府治理模式,并对其背后的制度原因进行了分析,以体现出城市企业主义是如何受到高度集中的行政考评体系和分税制这一转型期财政体制的影响。文章接着对地方政府为实现其城市企业主义战略而采用的土地驱动型发展模式进行了研究,最后提出了中国城市发展亟待转型的呼吁。     

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.     

抗战时期的上海华商房地产公司

抗战时期,因人口暴增、游资汇聚、地价暴涨等因素共同作用,上海华商房地产公司有了根本性的发展,第一次主导了上海的房地产市场。本文对抗战时期上海华商房地产公司的崛起及原因、经营内容和业绩、华商房地产同业公会的活动等内容进行了探讨。文章认为,此时期上海华商房地产公司的崛起和活动,是近代中国市场经济进入发展阶段的标志之一。