GEOG 566






         Advanced spatial statistics and GIScience

May 24, 2017

Tutorial 2: Identifying clustering with a geographically weighted regression

Question You Asked

How much spatial clustering is present in the regression model of vegetation response to canopy cover? I am interested in determining if a single equation can predict the way that the two variables interact within east-side ponderosa pine forests, or if multiple equations are necessary.

Name of Tool or Approach You Used

To answer this question, I used the Geographically Weighted Regression tool in ArcMap.

Brief description of steps you followed to complete the analysis

In the GWR tool, I used vegetation cover as the dependent variable, and canopy cover as the explanatory variable. Because my points are somewhat clustered across the landscape, I used an adaptive kernel with an AICc bandwidth method.

Brief description of results you obtained

The map of coefficients did reveal certain clusters of high coefficients and low coefficients across the landscape. However, judging by the GWR table below, this clustering may not be statistically significant. One anomaly of this assessment was the negative adjusted R2 value. A negative R2 means that the equation did not include a constant term.


Map of clustered plots

VARNAME VARIABLE DEFINITION
Neighbors 46
ResidualSquares 14750.95231
EffectiveNumber 3.80525057
Sigma 18.69738296
AICc 405.3014401
R2 0.048524493
R2Adjusted -0.01473284
Dependent Field 0 Total_cvr
Explanatory Field 1 Canopy_Cov

Table of original GWR results

To remedy the negative adjusted R2, I tried adding in another explanatory variable (elevation). This appeared to help the model, reducing the residual squares and bringing the adjusted R2 value back above 0.

VARNAME VARIABLE DEFINITION
Neighbors 46
ResidualSquares 13904.07263
EffectiveNumber 5.22764912
Sigma 18.46665082
AICc 405.8795404
R2 0.103150476
R2Adjusted 0.01015694
Dependent Field 0 Total_cvr
Explanatory Field 1 Canopy_Cov
Explanatory Field 2 Elevation

Table of remedied GWR

Critique of the method – what was useful, what was not?

This method was useful in that I could process the data in ArcMap, which is where I was already analyzing my points. It was also very helpful to visualize the coefficients in the map below. However, I am still a little unsure why the coefficient map shows such strong clustering while the output table does not show any significance.

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