Measuring Global Spatial Autocorrelation with Data Reliability Information

Assessing spatial autocorrelation (SA) of statistical estimates such as means is a common practice in spatial analysis and statistics. Popular SA statistics implicitly assume that the reliability of the estimates is irrelevant. Users of these SA statistics also ignore the reliability of the estimates. Using empirical and simulated data, we demonstrate that current SA statistics tend to overestimate SA when errors of the estimates are not considered. We argue that when assessing SA of estimates with error, one is essentially comparing distributions in terms of their means and standard errors. Using the concept of the Bhattacharyya coefficient, we proposed the spatial Bhattacharyya coefficient (SBC) and suggested that it should be used to evaluate the SA of estimates together with their errors. A permutation test is proposed to evaluate its significance. We concluded that the SBC more accurately and robustly reflects the magnitude of SA than traditional SA measures by incorporating errors of estimates in the evaluation. Key Words: American Community Survey, Geary ratio, Moran’s I, permutation test, spatial Bhattacharyya coefficient.     

Patterns and causes of uncertainty in the American Community Survey

In 2010 the American Community Survey (ACS) replaced the long form of the United States decennial census. The ACS is now the principal source of high-resolution geographic information about the U.S. population. The margins of error on ACS census tract-level data are on average 75 percent larger than those of the corresponding 2000 long-form estimate. The practical implications of this increase is that data are sometimes so imprecise that they are difficult to use. This paper explains why the ACS tract and block group estimates have large margins of error. Statistical concepts are explained in plain English. ACS margins of error are attributed to specific methodological decisions made by the Census Bureau. These decisions are best seen as compromises that attempt to balance financial constraints against concerns about data quality, timeliness, and geographic precision. In addition, demographic and geographic patterns in ACS data quality are identified. These patterns are associated with demographic composition of census tracts. Understanding the fundamental causes of uncertainty in the survey suggests a number of geographic strategies for improving the usability and quality ACS.     

空间数据统计分析的思想起源与应用演化

系统总结了空间数据统计分析的发展历程,并分为五个时期：① 早期孕育（计量革命之前）,其重要思想是19世纪初德国的区位论;② 计量革命（1950-1960年代）,主要是经典统计学的应用和理论探索;③ 空间统计学（1970-1980年代）,重点是空间点数据、面数据和空间连续性数据的分析;④ 成熟与扩散（1990-2000年代）,空间数据统计分析发展成熟并快速向其他领域扩散;⑤ 时空大数据（2010年以后）。换句话说,计量革命开始后的空间数据统计分析大约每20年有重要的新技术或方法出现,到现在已经具有成熟、系统化的方法和显著的社会效益。而在当前的时空大数据时期,其发展需要计算机科学家、统计学家和地理学家等不同学科领域人员的共同努力。     

中国省级人口增长率及其空间关联分析

分析了1982－1990年和1990－1998年2个时期的人口增长率，并用空间统计分析方法研究了2个时期人口增长率的空间关联关系。1982－1990年中国可分为北部人口低增长、中西部高人口增长率、中东部低人口增长率和南部高人口增长率等4个区域，1990－1998年中国可分为北部低人口增长率和南部高人口增长率2个区域，2个时期的空间聚类虽然不完全相同，但它们有共同的特点，南部和西部的人口增长率都比较高，北部地区的人口增长率都比较低，但它们有共同的特点，南部和西部的人口增长率都比较高，北部地区的人口增长率都比较低。最后对实证研究的结果进行了分析。     

Forthcoming events

Spatial data uncertainty models (SDUM) are necessary tools that quantify the reliability of results from geographical information system (GIS) applications. One technique used by SDUM is Monte Carlo simulation, a technique that quantifies spatial data and application uncertainty by determining the possible range of application results. A complete Monte Carlo SDUM for generalized continuous surfaces typically has three components: an error magnitude model, a spatial statistical model defining error shapes, and a heuristic that creates multiple realizations of error fields added to the generalized elevation map. This paper introduces a spatial statistical model that represents multiple statistics simultaneously and weighted against each other. This paper's case study builds a SDUM for a digital elevation model (DEM). The case study accounts for relevant shape patterns in elevation errors by reintroducing specific topological shapes, such as ridges and valleys, in appropriate localized positions. The spatial statistical model also minimizes topological artefacts, such as cells without outward drainage and inappropriate gradient distributions, which are frequent problems with random field-based SDUM. Multiple weighted spatial statistics enable two conflicting SDUM philosophies to co-exist. The two philosophies are ‘errors are only measured from higher quality data’ and ‘SDUM need to model reality’. This article uses an automatic parameter fitting random field model to initialize Monte Carlo input realizations followed by an inter-map cell-swapping heuristic to adjust the realizations to fit multiple spatial statistics. The inter-map cell-swapping heuristic allows spatial data uncertainty modelers to choose the appropriate probability model and weighted multiple spatial statistics which best represent errors caused by map generalization. This article also presents a lag-based measure to better represent gradient within a SDUM. This article covers the inter-map cell-swapping heuristic as well as both probability and spatial statistical models in detail.     

Spatial and Longitudinal Patterns in County Age-Specific Net Migration in the United States 1950–2010

Many migration studies describe various counties by adopting a priori county typologies, such as the U.S. Department of Agriculture Economic Research Service county typology, which might not be suitable for identifying different age migration patterns of the U.S. counties. This study employs a spatial clustering method that exhaustively compares all U.S. counties on their age migration similarity and spatial proximity to investigate signature age-specific net migration profiles across six decades of U.S. county age-specific net migration data from 1950 to 2010. All of the six-decade data are integrated into a common spatial county boundary on which counties below a population threshold are merged with the nearest county to mitigate the small population problem in net migration rates. As counties are merged by increasing large population thresholds, the Getis-Ord Gi* spatial autocorrelation statistic is applied to examine how the spatial migration patterns are affected. It is found that U.S. county age-specific net migration profiles exhibit four signature patterns. Although these patterns are persistent across the past six decades, their spatial distributions have experienced dramatic variation. The small population problem in net migration rates affects the extent and location of the significant spatial migration patterns.     

Relationships between String Bag Craft Distributions,Language and Geographical Distance in the Upper Sepik and Border Mountains of Papua New Guinea

This paper describes analyses involving patterned string bags collected in the upper Sepik in Papua New Guinea. The Mantel test and correspondence analysis were used to explore whether variability in craft repertoires exhibits any covariance with the region's complex linguistic picture, and if so, whether this relationship is more significant than any spatial autocorrelation the data may exhibit. Bag construction techniques exhibited strong spatial autocorrelation, while for colour patterns the effect was weaker. An effect for language remained for both dependents after statistical control, but colour pattern characteristics had a slightly stronger association with language overall. The weaker spatial autocorrelation for colour pattern variability is argued to be due to higher rates of dissemination facilitated by the visibility of the patterns and their compatibility with a broad range of construction techniques. The effect for language, on the other hand, is argued to have resulted from of a higher rate of inter-settlement migration along a particular stretch of the Sepik where people speak the same language.     

Measuring Research Data Uncertainty in the 2010 NRC Assessment of Geography Graduate Education

Abstract

This article characterizes and measures errors in the 2010 National Research Council (NRC) assessment of research-doctorate programs in geography. This article provides a conceptual model for data-based sources of uncertainty and reports on a quantitative assessment of NRC research data uncertainty for a particular geography doctoral program. Findings indicate that important variables, including faculty totals and allocations and publication counts, are substantially undercounted, with important and negative impacts on program research activity measures. Further, these research measures are highly sensitive to small changes in counts and are particularly problematic for interdisciplinary fields such as geography. We caution against using the 2010 NRC data or metrics for any assessment-oriented study of research productivity.     

Sample surveying to estimate the mean of a heterogeneous surface: reducing the error variance through zoning

One of the major sources of uncertainty associated with geographical data in GIS arises when they are the outcome of a sampling process. It is well known that when sampling from a spatially autocorrelated homogeneous surface, stratification reduces the error variance of the estimator of the population mean. In this study, we evaluate the efficiency of different spatial sampling strategies when the surface is not homogeneous. When the surface is first-order heterogeneous (the mean of the surface varies across the map), we examine the effects of stratifying it into first-order homogeneous zones prior to the usual stratification for a systematic or stratified random sample. We investigate the effect of this form of spatial heterogeneity on the performance of different methods for estimating the population mean and its error variance. We do so by distinguishing between the real surface to be surveyed (?), the sampling frame (?) including the choice of zoning, and the statistical estimators (Ψ). The study shows that zoning improves estimator efficiency when sampling a heterogeneous surface. Systematic comparison provides rules of thumb for choice of sample design, sample statistics and uncertainty estimation, based on considering different spatial heterogeneities on real surfaces.     

A Spatial View of How United States Cesarean Section Rates Changed from 1990 to 2014

The overuse of cesarean sections (C-sections) in the United States is a contested issue. The rate of C-section births in 2015 at 32 percent was over double the World Health Organization recommendation of 10 to 15 percent. We employed spatial statistical methods and data visualization techniques to assess the temporal and spatial trends in C-section rates by county across the United States. Although the national rate of C-section remained stable at the beginning and end of this study period, an increase in rates from 1997 to 2009 was reflected simultaneously in national, state, and individual county rates. Local indicators of spatial dependence did not show spatial clustering as being connected to, or driving, the change, yet the visualization methods used here show details on individual county deviance from local temporal trends. By highlighting counties that do not follow the trends of their neighbors, we identify exceptional locations that could help further the study of the determinants of changing C-section rates in the United States. Key Words: cesarean sections, exploratory spatial data analysis, medical geography, spatial statistics.     

Urban Heat and Climate Justice: A Landscape of Thermal Inequity in Pinellas County,Florida

The combined effects of two global trends, urbanization and climate change, have generated considerable concern regarding their adverse and disproportionate impacts on the health of urban populations. This study contributes to climate‐justice research by determining whether elevated levels of urban heat, indicated by land surface temperature (LST), are distributed inequitably with respect to race/ethnicity, age, and socioeconomic status in Pinellas County, Florida. Our study utilizes 2010 MODIS and Landsat medium‐resolution, remotely sensed thermal data, census socio‐demographic information, and both conventional and spatial statistical methods. Results indicate that LST is significantly greater in census tracts characterized by higher percentages of certain racial/ethnic minorities and higher poverty rates, even after controlling for contextual factors and the effects of spatial autocorrelation. This reveals the presence of a landscape of thermal inequity: uneven distribution of heat within the built urban environment and a community structure with varying vulnerability.     

我国省域创新产出的空间特征和时空演化——基于探索性空间数据分析的实证

以我国31个省域作为空间观测单元,以专利申请受理数作为创新产出的衡量指标,对我国1997～2008年期间省域创新产出的空间分布进行了探索性空间数据分析(ESDA)。通过计算区位基尼系数和集中度指数,发现我国的创新活动显示了相当高水平的空间集中,并且这种集中程度在过去的十多年里表现出了稳定的增长趋势;对全局的Moran’s I统计分析表明:省际创新活动之间存在着显著的空间自相关(空间依赖性),证明了知识溢出的存在性和空间局限性;对局部的Moran’s I分析进一步揭示了省际创新活动水平的相关模式,Moran散点图刻画了创新活动的空间集聚模式及其时空演变态势。研究结果说明经过十几年的发展,我国省域创新活动的地域性特征十分显著。     

Weight matrices and spatial autocorrelation statistics using a topological vector data model

Abstract

This paper reports on software to construct alternative weight matrices and to compute spatial autocorrelation statistics, namely the Moran coefficient and the Geary coefficient using Arc/Info’s data structure. As such it is an addition to recent efforts in linking GIS with exploratory spatial data analysis. The software is interfaced with Arc/Info via the Arc Macro Language (AML) so that it can be run in the ARC environment. This allows the user to perform exploratory analysis within GIS which may provide insights in subsequent spatial analysis and modelling.     

A spatial heterogeneity-based rough set extension for spatial data

When classical rough set (CRS) theory is used to analyze spatial data, there is an underlying assumption that objects in the universe are completely randomly distributed over space. However, this assumption conflicts with the actual situation of spatial data. Generally, spatial heterogeneity and spatial autocorrelation are two important characteristics of spatial data. These two characteristics are important information sources for improving the modeling accuracy of spatial data. This paper extends CRS theory by introducing spatial heterogeneity and spatial autocorrelation. This new extension adds spatial adjacency information into the information table. Many fundamental concepts in CRS theory, such as the indiscernibility relation, equivalent classes, and lower and upper approximations, are improved by adding spatial adjacency information into these concepts. Based on these fundamental concepts, a new reduct and an improved rule matching method are proposed. The new reduct incorporates spatial heterogeneity in selecting the feature subset which can preserve the local discriminant power of all features, and the new rule matching method uses spatial autocorrelation to improve the classification ability of rough set-based classifiers. Experimental results show that the proposed extension significantly increased classification or segmentation accuracy, and the spatial reduct required much less time than classical reduct.     

空间自相关的可塑性面积单元问题效应

可塑性面积单元问题(modifiable areal unit problem,MAUP) 效应是对空间数据分析结果产生不确定性影响的主要原因之一,在空间自相关分析中也不例外.本文分别利用网格模拟数据和中国人均GDP实例数据为数据源,以全局Moran's I 系数来探究空间自相关统计中的MAUP效应,分析结果表明,变量的空间自相关程度依赖于空间的粒度大小与单元的划分方法,但空间单元的变化与自相关性并不存在某种函数关系.因此,在进行空间自相关研究时必须选择合适的地理单元的粒度大小和分区.最后本文给出一种基于地统计内插方法来降低MAUP对空间自相关分析影响.     

近25年来塔里木河流域区域经济空间关联及演化特征分析

以塔里木河流域为研究对象,借助Arcgis8.5及Geoda等软件平台,引入空间自相关模型,对塔里木河流域42县(市)1980-2005年近25年的区域经济空间关联类型、动态演化特征及动力机制进行研究,结果表明:(1)25年来塔里木河流域经济全局空间自相关系数增长了近1.7倍,总体呈现出空间正相关特征,且为波动上升的动态过程,在5%的显著性水平下,经济在空间上表现为显著的正相关性.(2)局部区域空间自相关特征显著,区域经济显著负相关的区域逐渐消失,正相关显著区域日趋加强,最终演化为低一低及高一高两种类型区在东北和西南集中分布格局,且差距不断增大,各类型区域面积消长在起始,震荡和稳定三个阶段呈现出不同特点.(3)区域经济增长的近邻效应不断增强,2004年低-低和高-高两种类型区域面积是1980的1.66倍,但经济空间集聚效应主要是由于低-低区域面积的迅速增加所致.(4)工业化初期阶段,矿产资源条件和区位因素及交通条件两大因素是促进区域经济空间集聚与演化的动力.文章最后探讨了流域经济空间关联特点及演化特征对区域经济集聚扩散过程、区域政策选择、空间开发模式及区域协调发展等问题的影响.     

Activity patterns,socioeconomic status and urban spatial structure: what can social media data tell us?

ABSTRACT

Individual activity patterns are influenced by a wide variety of factors. The more important ones include socioeconomic status (SES) and urban spatial structure. While most previous studies relied heavily on the expensive travel-diary type data, the feasibility of using social media data to support activity pattern analysis has not been evaluated. Despite the various appealing aspects of social media data, including low acquisition cost and relatively wide geographical and international coverage, these data also have many limitations, including the lack of background information of users, such as home locations and SES. A major objective of this study is to explore the extent that Twitter data can be used to support activity pattern analysis. We introduce an approach to determine users’ home and work locations in order to examine the activity patterns of individuals. To infer the SES of individuals, we incorporate the American Community Survey (ACS) data. Using Twitter data for Washington, DC, we analyzed the activity patterns of Twitter users with different SESs. The study clearly demonstrates that while SES is highly important, the urban spatial structure, particularly where jobs are mainly found and the geographical layout of the region, plays a critical role in affecting the variation in activity patterns between users from different communities.     

Combining spatial transition probabilities for stochastic simulation of categorical fields

Categorical spatial data, such as land use classes and socioeconomic statistics data, are important data sources in geographical information science (GIS). The investigation of spatial patterns implied in these data can benefit many aspects of GIS research, such as classification of spatial data, spatial data mining, and spatial uncertainty modeling. However, the discrete nature of categorical data limits the application of traditional kriging methods widely used in Gaussian random fields. In this article, we present a new probabilistic method for modeling the posterior probability of class occurrence at any target location in space-given known class labels at source data locations within a neighborhood around that prediction location. In the proposed method, transition probabilities rather than indicator covariances or variograms are used as measures of spatial structure and the conditional or posterior (multi-point) probability is approximated by a weighted combination of preposterior (two-point) transition probabilities, while accounting for spatial interdependencies often ignored by existing approaches. In addition, the connections of the proposed method with probabilistic graphical models (Bayesian networks) and weights of evidence method are also discussed. The advantages of this new proposed approach are analyzed and highlighted through a case study involving the generation of spatial patterns via sequential indicator simulation.