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I'm trying to do regression analysis using a shapefile which contains dependent variable (NDVI) and explanatory variable (prec) in ArcGIS.

First, I run GWR analysis and then run spatial autocorrelation Moran I on residual of GWR result.

Finally, I wanted to see summary statistics on result window in ArcGIS but it just gives me 3 warnings related with analysis.

Do you have any ideas about why these warnings appear?

The shapefile has already been projected into Geographical lat/long which makes me wonder whether the result of regression is correct or not.

result of GWR shown in result window

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2 Answers 2

up vote 11 down vote accepted

The ESRI Spatial Statistics tools do not calculate great circle distance if the data is in a geographic coordinate system (Lat/Long). As such, distance based spatial analysis is incorrect. The tools require that your projection units be in feet or meters. The "ZONE_OF_INDIFFERENCE" is a term made up by ESRI that basically means that within a local neighborhood the values one or both sides of the equation are exhibiting identical values. You cannot fit a regression on a single value!

I feel obligated to point out that you should use GWR with great caution. There are several papers that have identified serious flaws with this method. You should also be aware of the original intent of GWR. It is specifically designed to address data that exhibits nonstationarity. This is a second order (local) autocorrelation effect whereas the Moran's-I statistic represents 1st order effects (global). If your data does not have any 2nd order effects the results of GWR will be quite incorrect. You can test this using one of the local autocorrelation tools (under Mapping Clusters). If you have spatial outliers with significant p values then GWR is appropriate, given its limitations. Spatial exploratory analysis is a critical step before applying a given regression approach.

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Jeffrey, would you be able to supply references to a few of those papers that identify flaws with GWR? This is not to challenge your assertion, but only so that I can follow up and learn more about those flaws. –  whuber Dec 13 '13 at 23:09
1  
@whuber, two papers that come to mind are: Páez A, S. Farber, D. Wheeler (2011) (envplan.com/abstract.cgi?id=a44111) and Wheeler & Tiefelsdorf (2005) (dces.wisc.edu/documents/articles/curtis/cesoc977-11/…). –  Jeffrey Evans Dec 18 '13 at 17:37

Whenever you are doing an analysis that involves distance measurements you should project your data (at present the spatial statistics tools in ArcGIS do not calculate geodesic distances, unfortunately). This link will tell you more about projected coordinate systems:

The ZONE OF INDIFFERENCE conceptualizations is not appropriate when your data is measured in degrees because the smallest unit you can specify with this method is 1, and 1 degree is very large and represents different distances at various locations on the earth. This is discussed in the Spatial Autocorrelation tool help.

If you haven't already done so, you may want to take a little time to work through a regression tutorial. My guess is that it might answer some of your questions: www.esriurl.com/spatialstats (scroll down to the regression tutorials).

I hope this helps!Best wishes.

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