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ArcGIS Spatial Analyst Statistical Modeling. Kevin Johnston Ryan DeBruyn. Outline. Statistical models – general concepts Descriptive models Predictive models Demonstration Response Models Classification Models Demonstration. Data Types. Polygons Lines Points Rasters Tins

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outline
Outline
  • Statistical models – general concepts
  • Descriptive models
  • Predictive models
  • Demonstration
  • Response Models
  • Classification Models
  • Demonstration

UC2009 Technical Workshop

data types
Data Types
  • Polygons
  • Lines
  • Points
  • Rasters
  • Tins
  • UnSampled and Sampled
    • Continuous
    • Incident

UC2009 Technical Workshop

outline4
Outline
  • Statistical models – general concepts
  • Descriptive models
  • Predictive models
  • Demonstration
  • Response Models
  • Classification Models
  • Demonstration

UC2009 Technical Workshop

descriptive models
Descriptive Models
  • Plots or output rasters
    • Histograms
  • Single band raster
    • Moving window (Focal)
    • Block
    • Zones
  • Multiple band raster
    • Min, Max, Mean, etc.

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predictive statistical models
Predictive Statistical Models
  • Points
  • Sampled continuous
    • Density
    • Interpolation

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prediction statistical models cont density
Prediction Statistical Models (cont.)Density
  • General concepts
    • Take a known commodity and spreads it over a landscape.
    • Point and lines
  • Kernel
    • A smooth curved surface is fitted over each point.
    • The value is highest at the location of the point, and diminishes with increasing distance from the point.
    • The volume under the surface equals the identified field value for the point.
  • Point
    • A neighborhood is defined around each raster cell center, and the number of features that fall within the neighborhood is totaled and divided by the area of the neighborhood.

UC2009 Technical Workshop

prediction statistical models cont interpolation
Prediction Statistical Models (cont.)Interpolation
  • From sample points

UC2009 Technical Workshop

prediction statistical models cont interpolation10
Prediction Statistical Models (cont.)Interpolation
  • Create a continuous surface

UC2009 Technical Workshop

prediction statistical models cont interpolation11
Prediction Statistical Models (cont.)Interpolation
  • General concepts
  • Inverse Distance Weighted (IDW)
  • Spline
  • Trend
  • Nearest Neighbor
  • Topo to Raster
  • Kriging

UC2009 Technical Workshop

prediction statistical models cont interpolation12
Prediction Statistical Models (cont.)Interpolation
  • All based to a certain degree on a basic principle of geography
  • Things that are closer together are more alike
  • Deterministic and Geostatistical
  • Assumptions

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prediction statistical models interpolation idw cont
Prediction Statistical ModelsInterpolation - IDW (cont.)
  • Explicit Use of the Nearby Sample Points

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prediction statistical models interpolation global polynomial cont
Prediction Statistical ModelsInterpolation – Global Polynomial (cont.)
  • Fitting a rubber membrane

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prediction statistical models interpolation kriging cont
Prediction Statistical ModelsInterpolation - Kriging (cont.)
  • Two Main Steps
    • Variography: Quantifies the Spatial Autocorrelation of the Sample Points
      • Value
      • Relative Position
    • Define the Processing Neighborhood
      • Number of Neighbors
      • Shape of Neighborhood
      • Angle of Neighborhood

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outline16
Outline
  • Statistical models – general concepts
  • Descriptive models
  • Predictive models
  • Demonstration
  • Response Models
  • Classification Models
  • Demonstration

UC2009 Technical Workshop

response statistical model regression analysis
Response Statistical Model Regression Analysis
  • Regression Analysis
    • Logistic
    • Linear
  • Spatial Autocorrelation
  • Sampling
  • Spatial Regression

UC2009 Technical Workshop

regression analysis problem one
Regression Analysis: Problem One
  • There are actual sightings of deer within a study site
  • We wish to determine what features deer prefer and which they avoid
  • We want to evaluate the correlations in the features in known deer sites with those in areas they are not
  • We desire to create a probability surface of the likelihood of locating deer at a site (creating a deer preference map)

UC2009 Technical Workshop

regression analysis problem two
Regression Analysis: Problem Two
  • Sample data exists for the percent damage resulting from spruce budworm on the vegetation in the study area
  • We would like to predict the potential spruce budworm damage on other locations based on the features

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what is really being modeled
What Is Really Being Modeled?

Image from Colorado State University

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regression analysis in gis
Regression Analysis in GIS
  • Establishes the relationship of many features and values
  • Presents the relationship of these features in a concise manner
  • Allows for further exploration of the data

UC2009 Technical Workshop

regression analysis in gis22
Regression Analysis in GIS
  • The analysis output format is conducive to the GIS environment
  • Can make assumptions from samples that can be applied to the entire population (or every location in the raster)

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character of regression
Character of Regression
  • Dependent variable
    • Biomass
    • Tree growth
    • Probability of deer
  • Independent variable
    • Slope
    • Soils
    • Vegetative type
  • Logistic regression
    • Presence or absence
  • Linear regression (methods, stepwise, etc)
    • Continuous data

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spatial autocorrelation
Spatial Autocorrelation
  • What is it?
  • The effects of it on the output from the regression analysis
  • Testing for spatial autocorrelation
    • Spatial correlation indices
  • Sample points
    • Correlation (take every 5 cell out of 6 row)
    • Random sampling
  • In the statistical algorithm
    • Spatial Regression

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using a statistical package
Using a Statistical Package
  • Synergistic use of a statistical package with Spatial Analyst
  • Why do we need the statistical package?
  • Basic assumption–independent observations
  • Utilizing the results from the models in the GIS

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creating the probability surface
Creating the Probability Surface
  • Run regression with the significant factors
  • Obtain the coefficients for each value within each raster
  • Use the coefficients in a map algebra expression to create a probability surface

UC2009 Technical Workshop

creating the probability surface27
Creating the Probability Surface
  • Linear Regression
  • Logistic Regression

Z = a0 + x1a1 + x2a2 + x3a3 … xnan

Z = 1 / 1 + exp (- S ai xi)

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creating the probability surface28
Creating the Probability Surface
  • Output from a regression

Coef# Coef

-------------------------------------

0 1.250

1 -0.029

2 0.263

UC2009 Technical Workshop

creating the probability surface29
Creating the Probability Surface

Outgrid = 1.25 + (-0.029* elevation) + (0.263 * distancetoroads)

UC2009 Technical Workshop

spatial regression
Spatial Regression
  • Still must determine significant independent variables
  • Spatial regression accounts and uses spatial autocorrelation
  • Use the results to create a probability surface
  • Where the regression capability exist:
    • Classical statistical packages
      • SAS, SPSS, R
    • ArcGIS Spatial Statistics toolbox
      • Ordinary Least Squares
      • Geographically Weighted Regression

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outline31
Outline
  • Statistical models – general concepts
  • Descriptive models
  • Predictive models
  • Demonstration
  • Response Models
  • Classification Models
  • Demonstration

UC2009 Technical Workshop

classification and clustering analysis problem one unsupervised
Classification and Clustering Analysis: Problem One – (Unsupervised)
  • We wish to map the study area into habitat preference classes of high, medium, and low for Black Bears
  • We have many layers of data relevant to Black Bears for our study site
  • We want to explore the relationships between the layers that are not readily apparent to us

UC2009 Technical Workshop

classification and clustering analysis problem two supervised
Classification and Clustering Analysis: Problem Two – (Supervised)
  • We know the actual land use for several locations within a study site and have multiple layers of data for a study area
  • We wish to classify the areas not yet known into the known land uses (as closely as possible)

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multivariate analysis the multiband raster or stack
Multivariate Analysis: The MultiBand Raster or Stack

Multiple bands or rasters that are grouped for a reason

The intersection

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multivariate analysis the process
Multivariate Analysis:The Process
  • Create samples or clusters
  • Evaluate signature files
  • Classify
  • Interpret the results

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creating classes and clusters
Creating classes and clusters
  • Supervised – define the classes by training samples
  • Unsupervised – identify the number of clusters

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performing the classification
Performing the classification

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multivariate analysis review
Multivariate Analysis Review

Create stack

Create signature file

Supervised: Training set

Unsupervised: Clustering

Edit the signatures

Analyze signatures

Classification

Interpret results

UC2009 Technical Workshop

arcgis arcview sas and splus
ArcGIS, ArcView, SAS, and SPlus
  • ArcInfo Grid
  • Spatial Analyst 8+
  • Spatial Analyst 9.2 and 9.3
  • Spatial Statistics Toolbox
  • Visual Basic and COM Objects
  • SAS Bridge
  • SPlus linking to ArcView
  • Where to go from here

UC2009 Technical Workshop

available spatial analyst sessions
Available Spatial Analyst sessions

Technical Workshops

  • ArcGIS Spatial Analyst – An Introduction
    • Tuesday, July 14th. 8:30 – 9:45. Rm 1A/B
    • Wednesday, July 15th. 1:30 – 2:45. Rm 1A/B
  • ArcGIS Spatial Analyst – Suitability Modeling
    • Tuesday, July 14th. 1:30 – 2:45. Rm 1A/B
    • Thursday, July 16th. 8:30 – 9:45. Rm 1A/B
  • ArcGIS Spatial Analyst – Statistical Modeling
    • Tuesday, July 14th. 3:15 – 4:30. Rm 1A/B
    • Thursday, July 16th. 10:15 – 11:30. Rm 1A/B
  • ArcGIS Spatial Analyst – Hydrologic Modeling
    • Wednesday, July 15th. 10:15 – 11:30. Rm 5A/B
    • Thursday, July 16th. 3:15 – 4:30. Rm 5A/B
  • An Introduction to Dynamic Simulation Modeling
    • Wednesday,July 15th. 8:30 – 9:45. Rm 5A/B
    • Thursday, July 16th . 1:30 – 2:45. Rm 5A/B

Demo Theater Presentations

  • Site selection and suitability modeling
    • Tuesday, July 14th. 5:00 – 6:00. Exhibit Hall C
  • Water resource applications using Spatial Analyst and NetCDF data
    • Wednesday, July 15th. 12:00 – 1:00. Exhibit Hall C
  • Solar radiation modeling
    • Wednesday, July 15th.4:00 – 5:00. Exhibit Hall C
  • Working with surface interpolation tools
    • Thursday, July 16th. 10:00 – 11:00. Exhibit Hall C
questions answers
Questions & Answers

UC2009 Technical Workshop