I want to use the Geographically Weighted Regression (GWR) to model local relationships between my dependent variable and a set of independent variables.
When running GWR in ArcGIS, the coefficients with the parameter estimates can be mapped, which is also recommended. But I am not sure, how to interpret these values correctly.
The following graphic shows a sample (!) how a result could look like. Assuming the dependent variable is auto theft and the visualized independent variable are parking lots. I want to understand how to interpret the parameter estimates.
I do not understand the connection between the parameter estimate values and what they mean in regard to the correlation, meaning if for higher values it can be said that "many parking lots lead to many auto thefts" and for lower values "few parking lot lead to many/few auto thefts".
How can this result be interpreted correctly?
The aim is to find out the local regions, where parking lots correlate with auto thefts.
Best Answer
The parameter estimates are essentially the slopes of regression lines that fit your data averaged at that location. So if the parameter is positive then there are more auto thefts in places with more parking lots, and if the parameter is negative then there are fewer thefts where there are more parking lots.
However, without looking at the uncertainty in those parameters, you can't say if the parameter is significantly different from zero. Since GWR works on a moving window system (and hence there's a tuning parameter for window size) your outputs will be autocorrelated, so its likely to look smooth. You can't make valid statements about any trend across the space without taking this into account.
Also, conclusions from GWR seem a bit pointless. You might be able to say "over here, we get more thefts with more parking lots, and over here we get fewer". All that tells you is that the number of parking lots is not the determining factor in the theft rate! Some factor not covered by the variables in your model must be responsible for the change in behaviour of car thieves from one area to the other. Its not the number of parking lots!
Spatial modelling should be the process of working towards removing all unknown spatial structure in your model, until what you are left with are known modelled terms and uncorrelated noise residuals. GWR doesn't really take you there.