Which regression model to use- GWR confusion

[FraserM]

Hello,

I'm still learning about spatial statistics so this may be basic, but I would like some guidance 🙂

I have some count data (electric vehicle chargers). I'm trying to model its relationship with % of cars that are electric within an area. They have significant correlation linearly.

Normally I would use Poisson model because it is count data. However, both the dependent and independent variables show very strong spatial autocorrelation. From my understanding, normal linear regression won't work because of this so I need to use Geographically-weighted regression-  this measures regression locally, giving different models for each area.

My question is, if autocorrelation is present, is there no way to have an overall regression model for the whole area I'm looking at? I'm unsure what conclusions I can draw from GWR other than regression varies significantly across the whole area- isn't this basically saying there is no relationship between the data unless we significantly narrow down? What's the point of having such a non-general model? I could be being ignorant but I'm at a bit of a loss.

[EdwardGause]

GWR is going to let you see which coefficients of your explanatory variables has more impact locally as you look around the map, so that you can make policy decisions that are different in those areas where that one variable might have more impact. At least for me, that was the one thing that I thought was very useful about GWR.  You can look at ESRI's https://spatialstats-analysis-1.hub.arcgis.com/ link to get a lot of great resources on this topic.  Your original linear regression gives you the global results you are looking for, however you need to verify other statistics if you want to trust the global model you created. That URL has resources on how to interpret the other statistics to verify you model is not bias, along with other things you need to verify. Sorry, I am keeping this short, but ESRI has great resources in that link.  Its some of the best documentation ESRI creates in my opinion.

[dslamb2022]

"However, both the dependent and independent variables show very strong spatial autocorrelation"

Typically, the concern is if the residuals show some spatial autocorrelation or indicate they are not independent, violating one of the assumptions of linear regression. So you could run your Poisson model, then test the residuals for spatial autocorrelation to see if you really need to use GWR or a Spatial Regression Model.

I don't know if Esri supports the Poisson variation of GWR, but you can do this in R: https://zia207.github.io/geospatial-r-github.io/geographically-weighted-poisson-regression.html

Otherwise, you will be looking for different Spatial Regression Models (https://link.springer.com/referenceworkentry/10.1007/978-0-387-35973-1_1294#:~:text=Three%20spatial%...

Something like the spatial lag model will let you account for spatial autocorrelation and would be a model for the whole area. There are linear and non-linear equivalents for this type of model. Again, you would need to probably do this in R. https://apwheele.github.io/Class_CrimeMapping/08_Tutorial_R_SpatRegression.html