Spatial Data Analysis Why Geography is important..
-
Upload
randolf-bailey -
Category
Documents
-
view
230 -
download
0
Transcript of Spatial Data Analysis Why Geography is important..
![Page 1: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/1.jpg)
Spatial Data Analysis
Why Geography is important.
![Page 2: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/2.jpg)
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
locations of the objects under study changes» median center, clusters, spatial autocorrelation
– where matters• In an absolute sense (coordinates)• In a relative sense (spatial arrangement, distance)
![Page 3: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/3.jpg)
Components of Spatial Analysis
• Visualization– Showing interesting patterns
• Exploratory Spatial Data Analysis (ESDA)– Finding interesting patterns
• Spatial Modeling, Regression– Explaining interesting patterns
![Page 4: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/4.jpg)
Implementation of Spatial Analysis
• Beyond GIS– Analytical functionality not part of typical commercial
GIS» Analytical extensions
– Exploration requires interactive approach» Training requirements» Software requirements
– Spatial modeling requires specialized statistical methods
» Explicit treatment of spatial autocorrelation» Space-time is not space + time
• ESDA and Spatial Econometrics
![Page 5: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/5.jpg)
What Is Special About Spatial Data?
• Location, Location, Location– “where” matters
• Dependence is the rule– spatial interaction, contagion, externalities,
spill-overs, copycatting– First Law of Geography (Tobler)
• everything depends on everything else, but closer things more so
![Page 6: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/6.jpg)
• Spatial heterogeneity– Lack of stationarity in first-order statistics
• Pertains to the spatial or regional differentiation observed in the value of a variable– Spatial drift (e.g., a trend surface)– Spatial association
![Page 7: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/7.jpg)
Nature of Spatial Data
• Spatially 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, transmission lines
– polygons: series of connected arcs» provinces, cities, census tracts
![Page 8: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/8.jpg)
GIS Data Model
• Discretization 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)
• Data model implies spatial sampling and spatial errors
![Page 9: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/9.jpg)
3 Classes of Spatial Data
• Geostatistical 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 with regular or irregular areal units
![Page 10: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/10.jpg)
• Point Patterns– points on a map (occurrences of events at
locations in space)• Observations of a variable are made at location X• Assumption that the spatial arrangement is directly
related to the interaction between units of observation
![Page 11: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/11.jpg)
![Page 12: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/12.jpg)
Visualization and ESDA
• Objective– highlighting and detecting pattern
• Visualization– mapping spatial distributions– outlier detection– smoothing rates
• ESDA– dynamically linked windows– linking and brushing
![Page 13: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/13.jpg)
Mapping patterns
http://www.cdc.gov/nchs/data/gis/atmapfh.pdf
![Page 14: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/14.jpg)
ESDAhttp://www.public.iastate.edu/~arcview-xgobi/
![Page 15: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/15.jpg)
Spatial Process
• Spatial Random Field– { Z(s): s ∈ D }
» s R∈ d : generic data location (vector of coordinates)
» D R⊂ d : index set(subset of potential locations)
» Z(s) random variable at s, with realization z(s)
– Examples• s are x, y coordinates of house sales, Z sales price
at s• s are counties, Z is crime rate in s
![Page 16: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/16.jpg)
Point Pattern Analysis
• Objective– assessing spatial randomness
• Interest in location itself– complete spatial randomness– clustering, dispersion
• Distance-based statistics– nearest neighbors– number of events within given radius
![Page 17: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/17.jpg)
Point Patterns
• Spatial process– index set D is point process, s is random
• Data– mapped pattern
» examples: location of disease, gang shootings
• Research question– interest focuses on detecting absence of
spatial randomness (cluster statistics)– clustered points vs dispersed points
![Page 18: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/18.jpg)
![Page 19: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/19.jpg)
Geostatistical Data
• Spatial Process– index set D is fixed subset of Rd (continuous)
• Data– sample points from underlying continuous surface
» examples: mining, air quality, house sales price
• Research Question– interest focuses on modeling continuous spatial
variation– spatial interpolation (kriging)
![Page 20: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/20.jpg)
Variogram Modeling (Geostatistics)
• Objective– modeling continuous variation across space
• Variogram– estimating how spatial dependence varies
with distance– modeling distance decay
• Kriging– optimal spatial prediction
![Page 21: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/21.jpg)
![Page 22: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/22.jpg)
![Page 23: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/23.jpg)
Lattice or Regional Data
• Spatial process– index set D is fixed collection of countably many
points in Rd
– finite, discrete spatial units
• Data– fixed points or discrete locations (regions)
» examples: county tax rates, state unemployment
• Research question– interest focuses on statistical inference– estimation, specification tests
![Page 24: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/24.jpg)
Spatial Autocorrelation
• Objective– hypothesis test on spatial randomness of
attributes = value and location
• Global and local autocorrelation statistics: Moran’s I, Geary’s c, G(d), LISA
• Visualization of spatial autocorrelation– Moran scatterplot– LISA maps
![Page 25: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/25.jpg)
![Page 26: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/26.jpg)
![Page 27: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/27.jpg)
Spatial process models
• How is the spatial association generated?– Spatial autoregressive process (SAR)
• Y = ρWY + ε
– Spatial moving average process (SMA)• Y = (I + ρW) ε
– ε – vector of independent errors
– W = distance weights matrix
– In SAR, correlation is fairly persistent with increasing distance, whereas with SMA is decays to zero fairly quickly.
![Page 28: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/28.jpg)
• Spatial process—the rule governing the trajectory of the system as a chain of changes in state.
• Spatial pattern—the 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 s.a. in the residuals using Moran’s I or Geary’s c or G(d).
![Page 29: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/29.jpg)
Perspectives on spatial process models
• Finding out how the variable Y relates to its value in surrounding locations (the spatial lag) while controlling for the influence of other explanatory variables.
• When the interest is in the relation between the explanatory variables X and the dependent variable, after the spatial effect has been controlled for (this is referred to as spatial filtering or spatial screening).
![Page 30: Spatial Data Analysis Why Geography is important..](https://reader031.fdocuments.net/reader031/viewer/2022032310/56649d825503460f94a685d6/html5/thumbnails/30.jpg)
• The expected value of the dependent variable at each location is a function not only of explanatory variables at that location, but of the explanatory variables at all other locations as well.