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.

1. Modeling Count-based Raster Data
Using R with ArcGIS Desktop
Jeremy Heffner
HunchLab Product Manager
jheffner@azavea.com

2. We have events that occur in space (i.e. crimes)

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. Let’s create a raster covering formed of square cells

5. And bring in features of the geography
that may explain the pattern

6. For some geographic features we may use a proximity
measure of spatial influence

7. For some geographic features we may use a proximity
measure of spatial influence

8. For some geographic features we may use a proximity
measure of spatial influence

9. For other geographic features we may look at the
concentration of the features (density)

10. For each raster cell we have values for these
explanatory variables

11. So can’t we use ArcGIS’s built-in
regression models?

12. They all assume a normal distribution
for the response variable
}
y = b0 + b1x1 + b2x2 + …

13. Our cells have 0 or more events and are not a
normal distribution

14. Poisson Process
This is a process which counts independent
events happening in a given interval (time,
space).
Poisson Distribution
This process leads to a Poisson distribution of
counts.
Source: Wikipedia
Generalized Linear Model y = exp(b0 + b1x1 + b2x2 + …)
A GLM can represent this distribution in a
regression model.

15. Our counts fit a
Poisson distribution
much better

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. Here is sample output from fitting a Poisson model in R:

18. We can take the fitted coefficients from R and plug them
into the equation within ArcGIS using the ‘raster calculator’
y = exp(b0 + b1x1 + b2x2 + …)

19. Here’s an example of the output
which explains the expectation
of shootings based upon
the location of
drug arrests and
bus stops.

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