Modeling Count-based Raster Data with ArcGIS and R

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This presentation outlines the conceptual framework for building regression models of event counts where the unit of analysis is small. It explains how ArcGIS for Desktop can be used to build raster data sets that are modeled as generalized linear models within the open source R package.

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Modeling Count-based Raster Data with ArcGIS and R

  1. 1. Modeling Count-based Raster Data Using R with ArcGIS Desktop Jeremy Heffner HunchLab Product Manager jheffner@azavea.com
  2. 2. We have events that occur in space (i.e. crimes)
  3. 3. ? ? ? But why do they occur where they do? Do events correlate with geographic features?Can we predict the rate of events at particular locations?
  4. 4. Let’s create a raster covering formed of square cells
  5. 5. And bring in features of the geography that may explain the pattern
  6. 6. For some geographic features we may use a proximity measure of spatial influence
  7. 7. For some geographic features we may use a proximity measure of spatial influence
  8. 8. For some geographic features we may use a proximity measure of spatial influence
  9. 9. For other geographic features we may look at the concentration of the features (density)
  10. 10. For each raster cell we have values for these explanatory variables
  11. 11. So can’t we use ArcGIS’s built-in regression models?
  12. 12. They all assume a normal distribution for the response variable } y = b0 + b1x1 + b2x2 + …
  13. 13. Our cells have 0 or more events and are not a normal distribution
  14. 14. Poisson ProcessThis is a process which counts independentevents happening in a given interval (time,space).Poisson DistributionThis process leads to a Poisson distribution ofcounts. Source: WikipediaGeneralized Linear Model y = exp(b0 + b1x1 + b2x2 + …)A GLM can represent this distribution in aregression model.
  15. 15. Our counts fit aPoisson distribution much better
  16. 16. We can process our geographic data sets in ArcGIS and then export the cells to R for modeling Raster Calculate Export to Convert to Build Model Processing Predictions ASCII CSV (R) (ArcGIS) (ArcGIS)
  17. 17. Here is sample output from fitting a Poisson model in R:
  18. 18. We can take the fitted coefficients from R and plug theminto the equation within ArcGIS using the ‘raster calculator’ y = exp(b0 + b1x1 + b2x2 + …)
  19. 19. Here’s an example of the outputwhich explains the expectationof shootings based uponthe location ofdrug arrests andbus stops.
  20. 20. This example is derived from a collaborative project between Azavea and the Rutgers Center on Public Security For more information: Jeremy Heffner HunchLab Product Manager jheffner@azavea.com

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