What is the difference between Geographically Weighted Regression (GWR) and Empirical Bayesian Kriging Prediction and Regression (EBKR)?

[Elijah]

I need to investigate the relationship between Air Qaulity parameter (Co2) and certain meteorological and traffic-related variables such temperature, number of vehicles, road width, elevation, etc. I know both GWR and EBKR can do it while accounting for possible spatial non-stationarity in the variables' relationship. 

But what could be the difference between these tools in an analysis like this where EBKR will produce a prediction map based on a combination the variables and the GWR will produce intercept and variable coefficient rasters showing the magnitude and direction of the relationship between the predicted and the predictor variables.

Again, is 19 sample points too small for GWR

Thanks

[DrVSSKiran · Accepted solution]

GWR should be applied to datasets with several hundred features for best results. It is not an appropriate method for small datasets. The tool does not work with multipoint data.

[EricKrause]

Hi Elijah,

This is a deceptively complicated question.  The general idea is that when predicting to a new location, GWR uses a single model, thus creating a single set of coefficients for the location. EBKRP, however, uses many (potentially very different) models when predicting to a new location, and it isn't reliable or meaningful to try to disentangle how each explanatory variable contributed to the final prediction.

In EBKRP, predictions are performed using weighted combination of regression-kriging results from defined subsets of points, each using principle components of the original variables within each subset.  This is where the problem comes in.  While it is fine to use weighted combinations of PCA-regression for prediction, the individual coefficient values could be very misleading when expressed in terms of the original variables.  EBKRP, in essence, averages only the predicted value of various local models, and while it is safe to average the final prediction, it doesn't follow that it is safe to average the individual components of each model, which you would have to do in order to give a single estimate of the coefficients at the prediction location.  

Hope that made some sense.

-Eric

[Elijah]

Dear Eric,

I am happy you chose to answer my question. I have enthusiastically watched your videos on EBK both in 2D and 3D. If I did understand your explanation, among others, it follows that if I need to disentangle the coefficients in EBK as can be done in GWR, it is both impossible and reliable. So, there is really no way of knowing what variables are playing what magnitude of roles in the prediction of the new value. GWR would of course let me know the variables and their magnitude that are relevant in a particular local area according to the chosen bandwidth.

Let me seize this opportunity to ask you if there is EBKRP in 3D capable of utilizing multiple variable rasters in predicting a new value, like it's done in 2D? That would be fantastic anyway. Or any related tool?

Maybe I will need to add in 'ArcGIS ideas' that multivariate EBK 3D should have more than EBK algorithm for interpolation. I think EBK alone is too restrictive.

Thanks a lot.

Regards,

[EricKrause]

Hi again, thank you for the kind words!

To kind of rephrase, the issue is more that GWR provides a single answer, so it makes sense to present that answer.  EBKRP, on the other hand, provides many answers, and while the final predictions are comparable, the components of the different models can vary significantly and appear to contradict each other.  Simply asking, "How does this explanatory variable affect the dependent variable at this location," it is very possible that EBKRP could say "positively, negatively, and no effect." 

Personally, I see no contradiction in using GWR to explain relationships, then using EBKRP to actually make predictions.  I do it frequently myself.

And, yes, EBK in 3D does not support explanatory variables (aside from vertical detrending).  If this is a feature you think would help solve your problems, posting it in ArcGIS Ideas is the best course of action.

-Eric