Are there multiple models to consider?
One of the main reasons that we get so excited about GWR is the fact that it allows the relationships in our model to vary across space. While it is a very powerful tool that can help us understand our data and improve our models, we cannot stress enough the importance of first finding a good model using OLS. One of the main reasons that this is important is the fact that OLS gives us all sorts of great diagnostics to help us figure out if our explanatory variables are significant, if our residuals are normally distributed, and ultimately if we have a good model.
Sometimes, however, it�??s difficult to find a good (properly specified) OLS model because a single global model doesn�??t fit the entire study area. It may be that one set of variables provides a great model in one part of your study area, and another set of variables provide a great model in another part of your study area. To see if this is the case, you can pick several small sample areas within your broader study area and then see if the explanatory variables for each subarea change. Pick sample areas where you think the processes associated with what you are trying to model might be different (high vs. low income areas, old vs. new housing, etc.). Alternatively map the Local R2 results from GWR and select areas where GWR performed well and where it performed badly. These might be areas with different sets of explanatory variables. It can be very useful to look at these areas individually using OLS.
If you do find good OLS models in several small study areas, then you can conclude that you�??ve found the proper variables (overall), but just aren�??t getting a good global model because of regional variation. You can move to GWR with the FULL set of variables from the combined smaller study area analyses, because GWR will adjust the coefficients to reflect that regional variation. If you don�??t get a good OLS model in any of the smaller areas, it may be that the key explanatory variables are too complex to represent as a simple series of numeric measurements, and you will need to look for other analytical methods.
Okay, so all of this is a bit of work, I know, but it really is a great exercise in exploratory data analysis, and will help you understand your data better, find new variables to use, and could even help you find a great model!
Lauren Rosenshein
Geoprocessing Product Engineer
ESRI | Redlands, CA