# GEOG 566

May 24, 2017

### Tutorial 2: Identifying clustering with a geographically weighted regression

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.