Spatial Data Analysis：空间数据分析

1、Spatial Data AnalysisWhy Geography is important.What is spatial analysis? From Data to Information beyond mapping: added value transformations, manipulations and application of analytical methods to spatial (geographic) data Lack of locational invariance analyses where the outcome changes when the l

2、ocations of the objects under study changes median center, clusters, spatial autocorrelation where mattersIn an absolute sense (coordinates)In a relative sense (spatial arrangement, distance)Components of Spatial AnalysisVisualization Showing interesting patternsExploratory Spatial Data Analysis (ES

3、DA) Finding interesting patterns Spatial Modeling, Regression Explaining interesting patternsImplementation of Spatial AnalysisBeyond GIS Analytical functionality not part of typical commercial GIS Analytical extensions Exploration requires interactive approach Training requirements Software require

4、ments Spatial modeling requires specialized statistical methods Explicit treatment of spatial autocorrelation Space-time is not space + time ESDA and Spatial EconometricsWhat Is Special About Spatial Data?Location, Location, Location“where” mattersDependence is the rulespatial interaction, contagion

5、, externalities, spill-overs, copycattingFirst Law of Geography (Tobler)everything depends on everything else, but closer things more soSpatial heterogeneityLack of stationarity in first-order statisticsPertains to the spatial or regional differentiation observed in the value of a variableSpatial dr

6、ift (e.g., a trend surface)Spatial associationNature of Spatial DataSpatially referenced data “georeferenced” “attribute” data associated with location where matters Example: Spatial Objects points: x, y coordinates cities, stores, crimes, accidents lines: arcs, from node, to node road network, tran

7、smission lines polygons: series of connected arcs provinces, cities, census tractsGIS Data ModelDiscretization of geographical reality necessitated by the nature of computing devices (Goodchild) raster (grid) vs. vector (polygon) field view (regions, segments) vs. object view (objects in a plane)Dat

8、a model implies spatial sampling and spatial errors3 Classes of Spatial DataGeostatistical Data points as sample locations (“field” data as opposed to “objects”)Continuous variation over space Lattice/Regional Data polygons or points (centroids)Discrete variation over space, observations associated

9、with regular or irregular areal unitsPoint Patterns points on a map (occurrences of events at locations in space)Observations of a variable are made at location XAssumption that the spatial arrangement is directly related to the interaction between units of observationVisualization and ESDA Objectiv

10、e highlighting and detecting pattern Visualization mapping spatial distributions outlier detection smoothing rates ESDA dynamically linked windows linking and brushingMapping patterns :/ ESDA :/ /arcview-xgobi/Spatial ProcessSpatial Random Field Z(s): s D s Rd : generic data locati

11、on (vector of coordinates) D Rd : index set(subset of potential locations) Z(s) random variable at s, with realization z(s)Exampless are x, y coordinates of house sales, Z sales price at ss are counties, Z is crime rate in sPoint Pattern AnalysisObjectiveassessing spatial randomnessInterest in locat

12、ion itselfcomplete spatial randomnessclustering, dispersionDistance-based statisticsnearest neighborsnumber of events within given radiusPoint PatternsSpatial processindex set D is point process, s is randomDatamapped pattern examples: location of disease, gang shootingsResearch questioninterest foc

13、uses on detecting absence of spatial randomness (cluster statistics)clustered points vs dispersed pointsGeostatistical DataSpatial Processindex set D is fixed subset of Rd (continuous)Datasample points from underlying continuous surface examples: mining, air quality, house sales priceResearch Questi

14、oninterest focuses on modeling continuous spatial variationspatial interpolation (kriging)Variogram Modeling (Geostatistics)Objectivemodeling continuous variation across spaceVariogramestimating how spatial dependence varies with distancemodeling distance decayKrigingoptimal spatial predictionLattic

15、e or Regional DataSpatial processindex set D is fixed collection of countably many points in Rdfinite, discrete spatial unitsDatafixed points or discrete locations (regions) examples: county tax rates, state unemploymentResearch questioninterest focuses on statistical inferenceestimation, specificat

16、ion testsSpatial AutocorrelationObjectivehypothesis test on spatial randomness of attributes = value and locationGlobal and local autocorrelation statistics: Morans I, Gearys c, G(d), LISAVisualization of spatial autocorrelationMoran scatterplotLISA mapsSpatial process modelsHow is the spatial assoc

17、iation generated?Spatial autoregressive process (SAR)Y = WY + Spatial moving average process (SMA)Y = (I + W) vector of independent errorsW = distance weights matrixIn SAR, correlation is fairly persistent with increasing distance, whereas with SMA is decays to zero fairly quickly.Spatial processthe

18、 rule governing the trajectory of the system as a chain of changes in state.Spatial patternthe map of a single realization of the underlying spatial process (the data available for analysis).Say you conduct a regression analysis. If the residuals do not display spatial autocorrelation, then there is no need to add “space” to the model. Examine . in the residuals using Morans I or Gearys c or G