Consistency of bandwidth (GWR) between methods

[EugenioJairEscobarSánchez]

Using ArcGis 10.8 
Whe using arcpy.GeographicallyWeightedRegression_stats() or arcpy.stats.GeographicallyWeightedRegression(), the bandwidth obtained is different than those equivalents obtained trough R software (spgwr AND GWmodel), which are consistent between them

Reproducible example: 
using  columbus dataset (library spData) i can get the same bandwidth using GWmodel::bw.gwr() and spwgr::gwr.sel() using same arguments as adapt, approach and method. In the other hand, using arcpy I get very different bandwidth selection 

[EricKrause]

Hi @EugenioJairEscobarSánchez,

There are a few things to keep in mind.  First, the GWR tool that you are using in ArcMap is not that same one that is only available in ArcGIS Pro. The newer GWR was designed to match the implementation of the GWR4 software (as it was at the time), and has been tested to give matching results.

Second, there is not one single "correct" bandwidth, and there are a variety of methods to estimate it that agree/disagree with each other to varying extents.  I am not certain the method that ArcMap's GWR tool uses to optimize the bandwidth, but I can verify that Fatheringham (the "father" of GWR) approved of the methodology and created at least one tutorial using the ArcMap tool:

https://gwr.maynoothuniversity.ie/wp-content/uploads/2016/01/GWR_Tutorial.pdf