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ArcGIS Spatial Analyst Statistical Modeling

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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ArcGIS Spatial Analyst Statistical Modeling

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  1. ArcGIS Spatial Analyst Statistical Modeling Kevin Johnston Ryan DeBruyn

  2. Outline • Statistical models – general concepts • Descriptive models • Predictive models • Demonstration • Response Models • Classification Models • Demonstration UC2009 Technical Workshop

  3. Data Types • Polygons • Lines • Points • Rasters • Tins • UnSampled and Sampled • Continuous • Incident UC2009 Technical Workshop

  4. Outline • Statistical models – general concepts • Descriptive models • Predictive models • Demonstration • Response Models • Classification Models • Demonstration UC2009 Technical Workshop

  5. Descriptive Models • Plots or output rasters • Histograms • Single band raster • Moving window (Focal) • Block • Zones • Multiple band raster • Min, Max, Mean, etc. UC2009 Technical Workshop

  6. Predictive Statistical Models • Points • Sampled continuous • Density • Interpolation UC2009 Technical Workshop

  7. 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

  8. Prediction Statistical Models (cont.)Density UC2009 Technical Workshop

  9. Prediction Statistical Models (cont.)Interpolation • From sample points UC2009 Technical Workshop

  10. Prediction Statistical Models (cont.)Interpolation • Create a continuous surface UC2009 Technical Workshop

  11. Prediction Statistical Models (cont.)Interpolation • General concepts • Inverse Distance Weighted (IDW) • Spline • Trend • Nearest Neighbor • Topo to Raster • Kriging UC2009 Technical Workshop

  12. 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 UC2009 Technical Workshop

  13. Prediction Statistical ModelsInterpolation - IDW (cont.) • Explicit Use of the Nearby Sample Points UC2009 Technical Workshop

  14. Prediction Statistical ModelsInterpolation – Global Polynomial (cont.) • Fitting a rubber membrane UC2009 Technical Workshop

  15. 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 UC2009 Technical Workshop

  16. Outline • Statistical models – general concepts • Descriptive models • Predictive models • Demonstration • Response Models • Classification Models • Demonstration UC2009 Technical Workshop

  17. Response Statistical Model Regression Analysis • Regression Analysis • Logistic • Linear • Spatial Autocorrelation • Sampling • Spatial Regression UC2009 Technical Workshop

  18. 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

  19. 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 UC2009 Technical Workshop

  20. What Is Really Being Modeled? Image from Colorado State University UC2009 Technical Workshop

  21. 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

  22. 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) UC2009 Technical Workshop

  23. 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 UC2009 Technical Workshop

  24. 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 UC2009 Technical Workshop

  25. 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 UC2009 Technical Workshop

  26. 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

  27. Creating the Probability Surface • Linear Regression • Logistic Regression Z = a0 + x1a1 + x2a2 + x3a3 … xnan Z = 1 / 1 + exp (- S ai xi) UC2009 Technical Workshop

  28. Creating the Probability Surface • Output from a regression Coef# Coef ------------------------------------- 0 1.250 1 -0.029 2 0.263 UC2009 Technical Workshop

  29. Creating the Probability Surface Outgrid = 1.25 + (-0.029* elevation) + (0.263 * distancetoroads) UC2009 Technical Workshop

  30. 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 UC2009 Technical Workshop

  31. Outline • Statistical models – general concepts • Descriptive models • Predictive models • Demonstration • Response Models • Classification Models • Demonstration UC2009 Technical Workshop

  32. 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

  33. 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) UC2009 Technical Workshop

  34. Multivariate Analysis: The MultiBand Raster or Stack Multiple bands or rasters that are grouped for a reason The intersection UC2009 Technical Workshop

  35. Multivariate Analysis:The Process • Create samples or clusters • Evaluate signature files • Classify • Interpret the results UC2009 Technical Workshop

  36. Creating classes and clusters • Supervised – define the classes by training samples • Unsupervised – identify the number of clusters UC2009 Technical Workshop

  37. Performing the classification UC2009 Technical Workshop

  38. Multivariate Analysis Review Create stack Create signature file Supervised: Training set Unsupervised: Clustering Edit the signatures Analyze signatures Classification Interpret results UC2009 Technical Workshop

  39. 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

  40. 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

  41. Questions & Answers UC2009 Technical Workshop

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