Geographically Weighted Regression Local R2 Values

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05-13-2021 02:11 PM
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NatalieRobbins
New Contributor III

I am running a GWR in ArcGIS Pro for the first time. I appreciate the new abilities to choose the model type based on the type of response variable you have. However, in ArcMap when running a GWR, the output always used to give you local r2 values that could then be used to render a thematic map. In ArcGIS Pro, when I ran a Poisson GWR, there are no local r2 values calculated in the attribute table. Is this because of the type of model that is being run? Would appreciate some clarification about why we always got local r2 values in ArcMap but now don't have them in ArcGIS Pro. 

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LynneBuie
Esri Contributor

Hi @NatalieRobbins,

 

You can use the field Local Percent Deviance, which is a value between 0 and 1, to map as a substitute for r2. This metric is a goodness of fit metric, so plays the same role in the poisson (and logistic) model as r2 does for the gaussian model. R2 is not used because the R2 equation does not hold in the poisson model.  The Outputs section of the tool documentation explains in more detail what the percent deviance metric means.

 

Lynne

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DanPatterson
MVP Honored Contributor

GWR changed in Pro 2.3 and I doubt that ArcMap is using the same code base.

Have you reviewed the support documents?

This is for the deprecated version

Geographically Weighted Regression (GWR) (Spatial Statistics)—ArcGIS Pro | Documentation

and these are for the new incarnation

Geographically Weighted Regression (GWR) (Spatial Statistics)—ArcGIS Pro | Documentation

How Geographically Weighted Regression (GWR) works—ArcGIS Pro | Documentation


... sort of retired...
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NatalieRobbins
New Contributor III

I have reviewed the documentation extensively. I notice in the new algorithm when running a Gaussian model I get local r2 values but not with Poisson. Based on this, my assumption is that the old algorithm used a Gaussian model to fit every time. My main question is why do we not get the r2 values for Poisson model GWRs (what's the statistical reasoning behind that) and what kind of thematic map could I render that would substitute for the generally accepted local r2 thematic map. 

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LynneBuie
Esri Contributor

Hi @NatalieRobbins,

 

You can use the field Local Percent Deviance, which is a value between 0 and 1, to map as a substitute for r2. This metric is a goodness of fit metric, so plays the same role in the poisson (and logistic) model as r2 does for the gaussian model. R2 is not used because the R2 equation does not hold in the poisson model.  The Outputs section of the tool documentation explains in more detail what the percent deviance metric means.

 

Lynne

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