The Saddlepoint Approximation of Moran's I's and Local Moran's Ii's Reference Distributions and Their Numerical Evaluation

Global Moran's I and local Moran's I_i are the most commonly used test statistics for spatial autocorrelation in univariate map patterns or in regression residuals. They belong to the general class of ratios of quadratic forms for whom a whole array of approximation techniques has been proposed in the statistical literature, such as the prominent saddlepoint approximation by Offer Lieberman (1994). The saddlepoint approximation outperforms other approximation methods with respect to its accuracy and computational costs. In addition, only the saddlepoint approximation is capable of handling, in analytical terms, reference distributions of Moran's I that are subject to significant underlying spatial processes. The accuracy and computational benefits of the saddlepoint approximation are demonstrated for a set of local Moran's Ii statistics under either the assumption of global spatial independence or subject to an underlying global spatial process. Local Moran's I_i is known to have an excessive kurtosis and thus void the use of the simple approximation methods of its reference distribution. The results demonstrate how well the saddlepoint approximation fits the reference distribution of local Moran's I_i. Furthermore, for local Moran's I_i under the assumption of global spatial independence several algebraic simplifications lead to substantial gains in numerical efficiency. This makes it possible to evaluate local Moran's I_i's significance in large spatial tessellations.     

A Simulation Study to Explore Inference about Global Moran's I with Random Spatial Indexes

Inference procedures for spatial autocorrelation statistics assume that the underlying configurations of spatial units are fixed. However, sometimes this assumption can be disadvantageous, for example, when analyzing social media posts or moving objects. This article examines for the case of point geometries how a change from fixed to random spatial indexes affects inferences about global Moran's I, a popular spatial autocorrelation measure. Homogeneous and inhomogeneous Matérn and Thomas cluster processes are studied and for each of these processes, 10,000 random point patterns are simulated for investigating three aspects that are key in an inferential context: the null distributions of I when the underlying geometries are varied; the effect of the latter on critical values used to reject null hypotheses; and how the presence of point processes affects the statistical power of Moran's I. The results show that point processes affect all three characteristics. Inferences about spatial structure in relevant application contexts may therefore be different from conventional inferences when this additional source of randomness is taken into account.     

志书凡例琐谈——从《龙岩市志·凡例》说起

社会主义新方志第一轮编纂已经基本完成,第二轮编纂全面展开又有若干年了,目前已出版的两轮各类志书数量几近万种。毫无疑问,自20世纪70年代末以来至今,出现了在中国方志史上最大的一次修志高潮。在这个高潮中所取得的成就,无论是修成出版志书数量之多,还是志书覆盖地域范围之广阔、志书种类之多样,对促进社会文明建设的贡献,对方志理论的丰富和发展,对方志人才的培养和造就,都是历史上任何朝代无法与之伦比的。     

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.     

Comparison of Moran's I and Geary's c in Multivariate Spatial Pattern Analysis

This article compares multivariate spatial analysis methods that include not only multivariate covariance, but also spatial dependence of the data explicitly and simultaneously in model design by extending two univariate autocorrelation measures, namely Moran's I and Geary's c. The results derived from the simulation datasets indicate that the standard Moran component analysis is preferable to Geary component analysis as a tool for summarizing multivariate spatial structures. However, the generalized Geary principal component analysis developed in this study by adding variance into the optimization criterion and solved as a trace ratio optimization problem performs as well as, if not better than its counterpart the Moran principal component analysis does. With respect to the sensitivity in detecting subtle spatial structures, the choice of the appropriate tool is dependent on the correlation and variance of the spatial multivariate data. Finally, the four techniques are applied to the Social Determinants of Health dataset to analyze its multivariate spatial pattern. The two generalized methods detect more urban areas and higher autocorrelation structures than the other two standard methods, and provide more obvious contrast between urban and rural areas due to the large variance of the spatial component.     

Loglinear Residual Tests of Moran's I Autocorrelation and their Applications to Kentucky Breast Cancer Data

This article bridges the permutation test of Moran's I to the residuals of a loglinear model under the asymptotic normality assumption. It provides the versions of Moran's I based on Pearson residuals ( I _PR) and deviance residuals ( I _DR) so that they can be used to test for spatial clustering while at the same time account for potential covariates and heterogeneous population sizes. Our simulations showed that both I _PR and I _DR are effective to account for heterogeneous population sizes. The tests based on I _PR and I _DR are applied to a set of log-rate models for early-stage and late-stage breast cancer with socioeconomic and access-to-care data in Kentucky. The results showed that socioeconomic and access-to-care variables can sufficiently explain spatial clustering of early-stage breast carcinomas, but these factors cannot explain that for the late stage. For this reason, we used local spatial association terms and located four late-stage breast cancer clusters that could not be explained. The results also confirmed our expectation that a high screening level would be associated with a high incidence rate of early-stage disease, which in turn would reduce late-stage incidence rates.     

试论地方文献对文学创作的影响——以越地为例

地方文献是反映地域的历史资料,这类资料对于文学创作来说,无论在题材上还是在素材上,都是一座取之不尽的宝库。将地方文献用于文学创作,可以促进文化繁荣,同时又能增加地方文献的积累。那些反映地域特色的文献,有时对文学创作能起到意想不到的重要作用。     

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.     

Local Histories in Global Perspective: A Local Elite Fellowship in the Port City of Quanzhou in Seventeenth-Century China

The Great Mosque of Quanzhou, as a distinctive community center, bound its residents through religious, professional, and educational ties; it also linked the mosque community to other communities with bonds of shared Muslim identity and minority status. The Great Mosque was rebuilt in 1609 under the supervision of the Confucian scholar Li Guangjin. This significant event is evidence of a local elite fellowship in seventeenth-century Quanzhou consisting of three well-known Confucian scholars—Li Zhi, Li Guangjin, and He Qiaoyuan—who had close ties to their Muslim neighbors. They left meticulous records of merchants, particularly Muslim traders. This paper focuses on the fellowship among the three men in order to investigate Quanzhou’s connections to the broader world of global commercial and religious networks and to look more closely at local community life.     

Impact of the Global Economic Crisis on China's Migrant Workers: A Survey of 2,700 in 2009

An Australian geographer examines the effects of the global financial crisis on China's migrant workers, based on a recent survey of over 2,700 such workers conducted during January-February 2009. The author focuses on the number of migrant workers returning to their home villages for the annual New Year holiday period, the types of workers that were laid off, options available to such workers upon losing employment, and the reasons underlying their subsequent moves. Implications of the findings for labor policy in China are briefly outlined and several directions for future research identified. Journal of Economic Literature, Classification Numbers: E240, G010, J610, J690. 7 tables, 68 references.