A linear regression solution to the spatial autocorrelation problem

The Moran Coefficient spatial autocorrelation index can be decomposed into orthogonal map pattern components. This decomposition relates it directly to standard linear regression, in which corresponding eigenvectors can be used as predictors. This paper reports comparative results between these linear regressions and their auto-Gaussian counterparts for the following georeferenced data sets: Columbus (Ohio) crime, Ottawa-Hull median family income, Toronto population density, southwest Ohio unemployment, Syracuse pediatric lead poisoning, and Glasgow standard mortality rates, and a small remotely sensed image of the High Peak district. This methodology is extended to auto-logistic and auto-Poisson situations, with selected data analyses including percentage of urban population across Puerto Rico, and the frequency of SIDs cases across North Carolina. These data analytic results suggest that this approach to georeferenced data analysis offers considerable promise. Received: 18 February 1999/Accepted: 17 September 1999     

Application of integration of spatial statistical analysis with GIS to regional economic analysis

This paper summarizes a few spatial statistical analysis methods for to measuring spatial autocorrelation and spatial association, discusses the criteria for the identification of spatial association by the use of global Moran Coefficient, Local Moran and Local Geary. Furthermore, a user-friendly statistical module, combining spatial statistical analysis methods with GIS visual techniques, is developed in Arcview using Avenue. An example is also given to show the usefulness of this module in identifying, and quantifying the underlying spatial association patterns between economic units.     

Application of integration of spatial statistical analysis with GIS to regional economic analysis

This paper summarizes a few spatial statistical analysis methods for to measuring spatial autocorrelation and spatial association, discusses the criteria for the identification of spatial association by the use of global Moran Coefficient, Local Moran and Local Geary. Furthermore, a user-friendly statistical module, combining spatial statistical analysis methods with GIS visual techniques, is developed in Arcview using Avenue. An example is also given to show the usefulness of this module in identifying and quantifying the underlying spatial association patterns between economic units.     

A comprehensive framework for exploratory spatial data analysis: Moran location and variance scatterplots

Abstract

A significant Geographic Information Science (GIS) issue is closely related to spatial autocorrelation, a burning question in the phase of information extraction from the statistical analysis of georeferenced data. At present, spatial autocorrelation presents two types of measures: continuous and discrete. Is it possible to use Moran's I and the Moran scatterplot with continuous data? Is it possible to use the same methodology with discrete data? A particular and cumbersome problem is the choice of the spatial-neighborhood matrix (W) for points data. This paper addresses these issues by introducing the concept of covariogram contiguity, where each weight is based on the variogram model for that particular dataset: (1) the variogram, whose range equals the distance with the highest Moran I value, defines the weights for points separated by less than the estimated range and (2) weights equal zero for points widely separated from the variogram range considered. After the W matrix is computed, the Moran location scatterplot is created in an iterative process. In accordance with various lag distances, Moran's I is presented as a good search factor for the optimal neighborhood area. Uncertainty/transition regions are also emphasized. At the same time, a new Exploratory Spatial Data Analysis (ESDA) tool is developed, the Moran variance scatterplot, since the conventional Moran scatterplot is not sensitive to neighbor variance. This computer-mapping framework allows the study of spatial patterns, outliers, changeover areas, and trends in an ESDA process. All these tools were implemented in a free web e-Learning program for quantitative geographers called SAKWeb© (or, in the near future, myGeooffice.org).     

空间统计分析与GIS在区域经济分析中的应用

首先概述了度量空间自相关、空间关联的一些空间统计分析方法以及识别区域空间关联的标准,然后探讨了将空间统计分析嵌入到一个GIS系统中的可行性,开发了一个分析空间关联的模块,并举例说明其在区域经济分析中的应用。     

不同比例尺下DEM的地形特征空间自相关性差异——以川渝地区和长三角区为例

采用局部Moran’s I模型对川渝地区和长三角区1∶250 000和1∶1 000 000两种尺度DEM以及全国1∶1 000 000 DEM地形信息进行了空间自相关的计算分析与比较,研究发现两种尺度下,高程自相关存在一致性,而坡度自相关差异性较大。1∶250 000地形自相关特性多呈随机分布,反映地势较平稳,具有均...     

基于Geoda 095i区域经济增长率的空间统计分析研究

空间统计分析的核心是认识与地理位置相关的数据间的空间依赖、空间关联或空间自相关,通过空间位置建立数据间的统计关系。本文利用空间分析的相关知识,通过对河南省各辖市2006年第一季度GDP增长速度及其相关因素的分析,发现该时期内河南省各辖市GDP增长率水平的空间分布并非表现出完全随机性,而是表现出空间相似值之间的空间聚集。基于对Moran散点图的分析和空间滞后回归模型的回归分析,得出空间统计分析对于分析区域经济发展的空间结构形态以及政策制定具有参考价值。     

城镇地价的空间相关性研究

空间自相关(spatial autocorrelation)是指变量在空间上表现出一定的规律性,空间回归是考虑了空间相关性的回归技术。本文将空间自相关性理论应用于地价样点价格分析,发现地价分布规律,并通过地价样点和地价影响因素建立空间线性回归模型的方法估算土地的价值,改进了传统的回归估价方法,从而提高了地价评估的准确程度。     

Assessment of regression kriging for spatial interpolation – comparisons of seven GIS interpolation methods

As an important GIS function, spatial interpolation is one of the most often used geographic techniques for spatial query, spatial data visualization, and spatial decision-making processes in GIS and environmental science. However, less attention has been paid on the comparisons of available spatial interpolation methods, although a number of GIS models including inverse distance weighting, spline, radial basis functions, and the typical geostatistical models (i.e. ordinary kriging, universal kriging, and cokriging) are already incorporated in GIS software packages. In this research, the conceptual and methodological aspects of regression kriging and GIS built-in interpolation models and their interpolation performance are compared and evaluated. Regression kriging is the combination of multivariate regression and kriging. It takes into consideration the spatial autocorrelation of the variable of interest, the correlation between the variable of interest and auxiliary variables (e.g., remotely sensed images are often relatively easy to obtain as auxiliary variables), and the unbiased spatial estimation with minimized variance. To assess the efficiency of regression kriging and the difference between stochastic and deterministic interpolation methods, three case studies with strong, medium, and weak correlation between the response and auxiliary variables are compared to assess interpolation performances. Results indicate that regression kriging has the potential to significantly improve spatial prediction accuracy even when using a weakly correlated auxiliary variable.     

广东省县域经济实力差异空间自相关分析

以2005年广东省87个县（市、区）级区域为研究对象,选取总人口、国民生产总值等8个指标作为评价因子,通过因子分析和主成分分析法获得各县级单元经济实力综合得分。对综合得分为变量进行空间自相关分析,计算得出全局相关Moran＇s值和LISA值。结果显示：广东省的县域经济具有明显的空间集聚特征,86.21%的县市经济表现为空间正相关,但仍有少部分县市的经济发展存在异质性。     

澜沧江流域(云南段)人口密度空间自相关分析

本文介绍了空间自相关的理论方法,利用澜沧江流域(云南段)人口分布数据计算了MoranI和Local Moran I.详细论述了自相关分析的技术路线,对人口分布的空间特征进行研究探讨,把GIS技术的空间拓扑关系及可视化制图功能等很好地融合于地理现象的空间模式中,分析了研究区域人口分布的时空特征,反映了该区域人口地理分布的...     

中国人口生育率的时空演变与空间差异研究

将探索性空间数据分析应用于低生育水平下的全国生育率区域差异研究,分析了1990～2000年省级总和生育率的时空演变趋势。研究表明,省级生育水平表现为显著正的空间自相关,且呈上升趋势,其中西藏、贵州两个潜在的极高值区域对空间自相关模式有很大的影响;全国仍呈现明显的东西差异,高值聚集模式由西部、中部向西部边缘收缩,西北、西南地区呈现显著性的高值聚集模式,空间差异较小,但四川比邻近地区的生育水平低;低值聚集模式从北部、沿海向中部扩张集中,空间差异较大,仅吉林、北京-天津、江苏表现显著。     

Eigenvector selection with stepwise regression techniques to construct eigenvector spatial filters

Because eigenvector spatial filtering (ESF) provides a relatively simple and successful method to account for spatial autocorrelation in regression, increasingly it has been adopted in various fields. Although ESF can be easily implemented with a stepwise procedure, such as traditional stepwise regression, its computational efficiency can be further improved. Two major computational components in ESF are extracting eigenvectors and identifying a subset of these eigenvectors. This paper focuses on how a subset of eigenvectors can be efficiently and effectively identified. A simulation experiment summarized in this paper shows that, with a well-prepared candidate eigenvector set, ESF can effectively account for spatial autocorrelation and achieve computational efficiency. This paper further proposes a nonlinear equation for constructing an ideal candidate eigenvector set based on the results of the simulation experiment.     

西安市住宅价格空间结构和分异规律分析

利用ESDA方法对西安市城区的291个普通住宅项目均价数据进行研究,通过计算Moran指数和半变异函数分析了其空间自相关性和变异性,并进行了趋势分析。应用Kriging空间插值方法对西安市普通住宅价格空间分布进行了模拟。研究结果表明:西安市房价存在显著的空间自相关性,大部分住宅价格呈空间集聚格局,少部分因存在空间异质性而呈离散分布;房价变异函数表现出各向异性,不同方向有不同结构特征,空间自相关尺度为14.2km;西安市房价空间分异规律明显,房价分布格局受城市功能区划和交通影响较大。     

基于GIS的福建省区域经济发展差异研究

分析福建省区域经济发展的差异,对提高经济发展水平具有重要意义。本文以福建省9个地市为研究单元,以2003—2017年人均GDP为基础数据,采用ArcGIS10.1和Geoda软件进行区域经济发展差异研究。通过计算和分析各市人均GDP的空间自相关系数Moran’s I和变异系数C.V,福建省各地市与其自身相邻近的地市之间存在着正空间自相关关系,并且福建省区域经济发展差异在增大。GIS技术用于分析区域经济空间差异性具有自身的优势,已成为区域经济研究领域的方向和趋势之一。     

基于ArcGIS的房地产价格空间分布研究

首先以深圳市福田区部分普通住宅的房地产价格为数据基础,利用空间分布分析中的最近邻距离分析法确定了各住宅的空间分布情况,即呈簇状分布状态;然后,运用空间自相关理论和方法,选用Moran,指数对研究区域的房价自相关关系进行测度和实证分析,从而得到深圳市景田区部分住宅房地产价格的空间自相关性情况;最后,利用ArcGIS中的地统计分析工具对整个区域的房地产价格进行了拟合,得到研究区域房价的空间分布情况。     

Modelling coastal land use change by incorporating spatial autocorrelation into cellular automata models

This paper presents a spatial autoregressive (SAR) method-based cellular automata (termed SAR-CA) model to simulate coastal land use change, by incorporating spatial autocorrelation into transition rules. The model captures the spatial relationships between explained and explanatory variables and then integrates them into CA transition rules. A conventional CA model (LogCA) based on logistic regression (LR) was studied as a comparison. These two CA models were applied to simulate urban land use change of coastal regions in Ningbo of China from 2000 to 2015. Compared to the LR method, the SAR model yielded smaller accumulated residuals that showed a random distribution in fitting the CA transition rules. The better-fitting SAR model performed well in simulating urban land use change and scored an overall accuracy of 85.3%, improving on the LogCA model by 3.6%. Landscape metrics showed that the pattern generated by the SAR-CA model has less difference with the observed pattern.     

DEM误差的空间自相关特征分析

采用空间自相关分析方法,从空间角度对数字高程数据误差的空间分布特征进行了研究。实验表明,利用双线性曲面表示地形表面时,产生的数字高程数据误差的全局Moran’sI指数趋近于0,在整个区域单元上的分布不存在显著的全局空间自相关,邻近区域单元上高程数据误差之间的关系在整体上既不综合表现为趋同,也不综合表现为趋异,高程数据误差的整体空间格局为随机格局;而且数字高程数据误差在空间上的分布与地形坡度和地表粗糙度有一定的联系,一般情况下,平均坡度、地表粗糙度越大,高程数据的全局Moran’sI指数偏离0稍远一些;否则,距离0近一些,但全局空间自相关仍不显著,在整体上表现为随机格局。     

基于衰减因子的虚拟应答器信息融合方法研究

针对虚拟应答器(VB)信息融合时使用Kalman滤波易出现滤波发散的问题,提出了基于改进Sage-Husa自适应滤波算法的信息融合方法. 首先采用自适应滤波动态调节噪声统计特性参数,抑制滤波发散,在预测误差方差矩阵中引入衰减因子,减小陈旧数据的影响进而提高滤波精度,最后进行仿真实验,将所提出的滤波算法与Kalman滤波和Sage-Husa自适应滤波在VB的位置误差和速度误差上进行对比. 仿真结果证明:在相同的时间内,本文所述算法在VB的定位误差上具有显著优势,具有较好地稳定性.