Spatial Analysis 1 Introduction
Geo-referenced Data (not any data) x, y coordinates (e.g., lat., long.) ------------------------------------------------------ - Table of Data: Obs. # x y Variables ------------------------------------- 1 2
Temporal vs. Spatial Data Temporal 1 dimension Units: day,week, month Lag: t-1, t-2, Durbin-Watson Spatial 2-3 dimension Units: county, mile, region Lag: near neighbor, networks, etc. Moran s I (W) Differencing Maps (distortions)
Ways to Study Space Map Spatial Data (GIS) Explore Properties of Geographical Space (ESDA- GIS/GEODA) Visualization techniques Spatial Modeling Spatial Statistics (Global/Local) Geostatistics Spatial Econometrics Spatial Choice / Agent Based Modeling All can be done within a GIS framework
Spatial Analysis Examples From a Variety of Fields Geography: Patterns of human spatial interaction, Distance decay, Segmentation of remotely sensed images, Clustering Earth Sciences: Climate, Geologic variables, Environmental issues, Water systems Ecology: Invasive species, Plant and animal regions, Fires Homeland Security: Mapped intelligence information Public Health, Epidemiology: Disease diffusion; Patterns of care; Clustering of disease; Risk factors Sociology and Demography: Behavior in space; Ethnic patterns; Spatial patterns of criminal activities; Spatial manifestation of demographic trends Political Science: Spatial patterns of voting; Redistricting; Diffusion of political movements Anthropology and Archaeology: Patterns of human activities (usually local in scale); Re-creation of past settlement patterns Economics: Spatial aspects of economic variables, Trends, Location patterns (sectors), Economic concentrations, Trade patterns History: Patterns of change, Political control, Migrations, Voyages, Ethnic conflict patterns over time Transportation: Movement, Accidents, Interaction, Flows
Spatial Analysis: Schools of Thought Exploratory Spatial Data Analysis (ESDA) Spatial Statistics Geostatistics Spatial Econometrics
ESDA GIS Functionality (buffers, distances, etc) Histograms, Box Plots, Leaf and Stem Plots Multiple Scatter Diagrams, Surfaces General Measures of Map Patterns Density, Surfaces, Clustering, Association Spatial Autocorrelation GWR Patterns of Residuals from Regression Visualization, 3-D, Fly-through Data Mining
Spatial Statistics Applications of Conventional Statistical Theory to Spatial Data Chance or Non-chance Occurrences in Space Measures of Spatial Association, Segregation Nearest Neighbors All Interevent Distances: K-functions Spatial Autocorrelation Statistics: I, G, c, etc. Specially Developed Tests on Spatial Randomness (or Normal) Hypotheses Clustering Spatial Filtering Spatially Dependent Tests
Geostatistics Distance Based Models, Continuous Surfaces Semi-variograms of different types Theoretical Empirical Kriging for Surface Extrapolation Kriging Models (Ordinary, Simple, Universal, Co-Kriging, Disjunctive) for Prediction
Spatial Econometrics Regression Models with One or More Spatial Parameters Development of Spatial Association Matrices Parameter Estimation and Testing Spatial Filtering Study of Model Assumptions Creation of Spatial Models
Software Developments New Packages Arrive Often GIS (ESRI: ARCGIS 9.1, 9.2, 9.3) Anselin s GeoDa (Free) Rey s STARS (Free) LeSage s Spatial Econometrics Tool Kit Geostatistics package (ESRI s Geospatial Analyst), GeoLib Aldstadt, Chen, and Getis PPA (Free) Jacquez ClusterSeer, for health applications Kulldorff s Scan Statistics Bivand s R Package Fotheringham, Brunsdon, and Charlton s GWR The Big Stat Packages (SPSS, SAS, S-Plus, etc.) include some spatial data manipulators.
Problems of Spatial Analysis Problems Help to Define the Field Scale Zoning Sizing Dependence Spatial Sampling Heterogeneity Boundaries Missing Data Large Data Sets
Modifiable Areal Unit Problem (MAUP): Scale Changes in scale change results How do changes in scale change results? What is the appropriate scale? Aggregation and the ecological fallacy Multi-scale analyses
Scale
MAUP: Zoning Changes in district boundaries change results. How do changes in zoning change results? The political redistricting problem Appropriate zoning Multiple zonings
Sizing Problem How do we deal with heterogeneous spatial units? Spatial units of varying sizes Shape may be a problem Should each spatial unit be weighted equally?
Pattern of Provincial PCGDP in 1978 Source: Long Gen Ying, dissertation
Pattern of Provincial PCGDP in 1994 Source: Long Gen Ying, dissertation
The Dependence Problem One must account for spatial dependency. Tobler s Law The problem of nearness The value of an observation problem Too many observations Spillovers/bisection Traditional statistics and independence Overcoming the problem
The Heterogeneity Problem One must make appropriate assumptions about the underlying spatial distribution. Uneven distributions at the global scale How does heterogeneity affect our results? Stationarity Drift and its effect on analysis Some suggested solutions
Original Data
The Boundaries Problem Variables and relationships are often different near boundaries. What effect do boundaries have on results? How do we take them into account? Sampling problems Awareness and care
Boundary Problem Violent crime is a problem in the city of Wilmington, NC.
The Missing Data Problem Empty Areas do not exist Census restrictions, privacy Imputation Algorithms and common sense solutions TINs, Kriging, etc.
The Large Data Sets Problem Steps need be taken to handle large data sets. Censuses Remotely sensed data Dependence and heterogeneity Data mining, partitioning and filtering, principal components analysis
Solutions Associated with Spatial Pattern Analysis Scale (statistics that allow d to vary (LISA, G, K), ESDA, multiple scales) Zoning (use smallest units and then aggregate upward; use statistics that vary d; ESDA, multiple zonings) Sizing (weighting of observations) Dependence (Global, Local, Variogram, Spa. Econ.) Spatial Sampling ( independent samples) Heterogeneity (models that allow parameters to vary, GWR, Spa. Econ., partitioning) Boundaries (NN, K function) Missing Data (Kriging) Large Data Sets (nearly all of the above, partitioning)
Current Hot Topics in Spatial Analysis Spatial Filtering Spatial Autoregressive Modeling The W Matrix Space-Time Modeling Hierarchical Modeling, Multilevel Modeling Bayesian Geostatistics and Spatial Modeling Spatial Clustering False Discovery Rates in Spatial Tests