GWR and Morans i

[LaurenSmith]

Hi,

I am new(ish) to ArcGIS and haven't done Stat's in a few years so sorry if this seems very simple.

I am attempting to explore relationships between respiratory diseases and 3/4 environmental variables over a large area. I have been advised to use GWR and I've read around the subject and it seems appropriate. However, it talks about spatial autocorrelation as well. I am wondering if I am meant to run Moran's i on the original data or on the residual results from GWR? Also, I have been advised I want the Morans i result to be around zero, is this correct?

Thank you,

Lauren

[LaurenSmith]

OK, so I've read some more and realise now I need to map the residuals. However the ESRI help doesn't specify if it is the std residuals or just the residuals. The image they show is of the std residuals and then talks about running spatial autocorrelation on the regression residuals - I assume it means on those std residuals??

[LaurenScott]

Hi Lauren,
You will get the same results from the Spatial Autocorrelation tool using either the residuals or the standardized residuals, so use either.
Regression does sound like a good strategy for your analysis.  Please check out our resources page which includes a free 1 hour web seminar on regression and also tutorials that will walk you through an analysis start to finish.  The tutorial will take you about an hour to finish.  We also have a sample script called Exploratory Regression that can help you find a properly specified model.  It works with ArcGIS 10.0 (but it will be core functionality with ArcGIS 10.1... which will likely release this summer).  Exploratory Regression works similar to Stepwise Regression, but instead of just looking for models with high Adj R2, it looks for models that meet all of the requirements of the OLS method (including checking for spatial autocorrelation in your model residuals).  Unfortunately, GWR does not have the strong diagnostics to tell you if you have a properly specified model or not... and if you are missing key explanatory variables, you can't really trust model coefficients.  Consequently, we always recommend that you start with OLS, find a properly specified model, then move to GWR.  This is all explained in the tutorial and also in the documentation that comes with the Exploratory Regression tool.  To download Exploratory Regression, the free video seminar, the tutorial and other resources, please check out: www.esriurl.com/spatialstats 
(for Exploratory Regression look for "Supplementary Spatial Statistics").  I hope this helps!
Best wishes,
Lauren

Lauren M Scott, PhD
Esri
Geoprocessing, Spatial Statistics