Interpreting results of GWR - what do the values mean?

Question

I used R to run a Geographically Weighted Regression (GWR) model.

The resulting model comes with a bunch of values that are given in a table. These are:

• sum.w
• X.Intercept, X.Intercept_se (standard error), X.Intercept_se_EDF
• variable1, variable1_se, variable1_se_EDF
• variable2, variable2_se, variable2_se_EDF,
• variableX, ...
• gwr.e
• pred, pred_se, pred_se_1
• localR2

Could you provide a short summary of what the calculated values mean?

• Variable coefficient: I know that for each variable a coefficient is given, which shows the strength of the correlation. But are these values normalized and can be compared between variables? As an example: if variable1 has a coefficient of 5 in a certain area, does a coefficient for variable2 of 10 in the same area mean that its correlation is twice as high?

• Standard error, EDF: What does the standard error tell? And what is the value EDF?

• Sum, gwr.e, Intercept: I am also not sure what sum.w, gwr.e and the Intercept are for.

• Prediction: The prediction values show what y-value is expected through the model.

• Local R2: The local R2 shows the model performance at a local scale.

Answer 1

I had the same doubt myself, and contrary to what some other people suggested you to do in the answers above, from the source code it is not straightforward what all those concepts mean. However, according to the answer from rafa.pereira here, gwr.e are the residuals.

Regarding EDF, Roger Bivand and Danlin Yu, who are the developers of the package, indicate that: "Follow Leung et al. EPA 2000 page 15, the estimate of sigma square can be obtained through rss and delta1 (which is actually edf)." Hence, EDF is actually the estimate of sigma square.

The full source code of the gwr function, and the source of the quote are in this link.

For clarification of the rest of the concepts, maybe contacting the authors is a good idea.