Ordinary Least Squares Point Aggregation

Question

I want to run an ordinary least squares regression in ArcGIS Pro on my dataset which is composed of about 400 fire occurrences (point data) and demographic variables (100x100m polygons of income, education, etc). I plan to use the fire occurrences for my dependent variable and the demographics for my explanatory variables.

The problem I have is with aggregating my fire incident point data. Essentially, I don't want to aggregate my incidents into larger polygons (larger fishnet, census districts, postal districts, etc) and lose the accuracy of my 100x100m demographic variables (which when spatially joined with the point layer only yield maximum 3 join count).

I have tried the Integrate/Collect Events method of aggregation suggested in the help documentation (and ESRI seminar videos), however because I do not have so many coincident points I am finding myself with a low ICOUNT as a result (again maximum of 3 events aggregated). I know that the dependent variable input for OLS requires more variation in the weighted value.

Does anyone know of a method that I can both aggregate my points properly and preserve the high detail of my 100x100m demographics for my regression?

Answer 1

So first, I'd perform some kind of density analysis like Kernel Density. This will create a raster that you can use later to calculate this fire density in your polygons.

To calculate these stats inside each polygon you can use the Zonal Satistics as Table tool. This will give you the average, sum and other stats you can use as your new dependent variable.

From here you can proceed to perform the OLS analysis after joining this new data.

Answer 2

After lots of valuable input, I've found that a binary logistic regression (using Generalized Linear Regression) rather than OLS is the best match for my data. This works well because the dependent variable operates with 1 if a fire is present in the grid and 0 if absent, thus eliminating the need to aggregate the points altogether.