[R-sig-Geo] gstat::krige() - regression kriging vs. kriging with external drift

[Edzer Pebesma]

On 14/11/15 17:32, Bede-Fazekas Ákos wrote:
> Dear List, dear Edzer,
> is it correct if I use the term "regression kriging" when I run this
> function?:
> kriged_value <- gstat::krige(z ~ x + y, [...])@data$var1.pred
> 
> Or should I call it "kriging with external drift" (or "universal kriging" if
> x and y are coordinates), and use the term "regression kriging" only in the
> case of running this?:
> linear_model <- lm(z ~ x + y, [...])
> residuals <- linear_model$residuals
> kriged_residuals <- gstat::krige(residuals ~ 1, [...])@data$var1.pred
> kriged_value <- linear_model$fitted.values + kriged_residuals
> 

For what it's worth, my opinion:

I would call it universal kriging, in line with the software you're
using (which I wrote):

> x = krige(zinc~x+y, meuse, meuse.grid, m)
[using universal kriging]

Most of the (older) literature associates external drift kriging with a
single external drift variable (e.g. Goovaerts), and universal kriging
with using coordinates as covariates.

The statistician might call everything best linear unbiased prediction
under the the general linear model y = X beta + e, with a spatial
covariance function describing the covariance of e, and in that
perspective both methods are equivalent.

I'm not the person to tell what regression kriging is and what it is
not, but it might include the above models as well as those where trend
fitting and residuals are done in different steps, and potentially under
different assumptions for e.

-- 
Edzer Pebesma
Institute for Geoinformatics (ifgi),  University of Münster,
Heisenbergstraße 2, 48149 Münster, Germany; +49 251 83 33081
Journal of Statistical Software:   http://www.jstatsoft.org/
Computers & Geosciences:   http://elsevier.com/locate/cageo/
Spatial Statistics Society http://www.spatialstatistics.info

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