Antonio Manuel Moreno Ródenas wrote:

> Thanks a lot Edzer,

>

> I'm not sure that would work.

> In that way I would transfer to the kriging function the averaged value

> of the covariate in the block. I'm not sure that would make the kriging

> behave correctly.

>

> All the points calculated with the prediction inside the block (and

> later averaged to give the block kriging prediction) will have as

> "drift" the average of the covariate in the block. Instead of getting

> the correct spatial variability inside the block (given by the

> covariate). At first sight it doesn't seems correct to me. Am I wrong?

I think so, when the operations (computing the drift, and block

averaging) are both linear, it does not matter in which order they are

carried out: f(g(x)) = g(f(x)).

It would be easy to verify by computing the universal point kriging

values and aggregating those. Try

> library(sp)

> demo(meuse, ask = FALSE, echo = FALSE)

> library(gstat)

>

> v = vgm(.5, "Sph", 900, .1)

> kr1 = krige(log(zinc)~dist, meuse, meuse.grid, v)

[using universal kriging]

>

> meuse.area$dist = aggregate(meuse.grid["dist"], meuse.area)[[1]]

> kr2 = krige(log(zinc)~dist, meuse, meuse.area, v)

[using universal kriging]

> kr2$kr1 = aggregate(kr1["var1.pred"], meuse.area)[[1]]

>

> kr2$var1.pred

[1] 5.687753

> kr2$kr1

[1] 5.685026

>

> kr2$var1.pred / kr2$kr1

[1] 1.00048

>

My guess is that the difference can be attributed to how the area is

discretized (see ?predict.gstat)

>

> kind regards

>

> Antonio Manuel Moreno Rodenas

>

> /Marie Curie Early Stage Researcher/

> /PhD Candidate/

>

> *T**U **Delft / Section Sanitary Engineering, office 4.64*____

>

> *Civil Engineering and Geoscience Faculty *

>

> T +31 15 278 14 62

>

>

> On 13 January 2016 at 14:43, Edzer Pebesma

> <[hidden email] <mailto:[hidden email]>>

> wrote:

>

>

>

> On 13/01/16 14:16, Antonio Manuel Moreno Ródenas wrote:

> > Hello, I would like to rise a question on the use of predict {gstat},

> >

> > I'm trying to perform the estimation of a spatially distributed variable at

> > the support scale of a particular area (Block kriging). I have access to an

> > additional variable, it is known that the variable of interest is

> > correlated to the new variable. So I would be interested on updating my

> > estimation by the use of this new information. This could be done by the

> > use of a kriging with external drift (KED), but with a block support

> > (Universal Block kriging). Theoretically this is included in the gstat

> > library as mentioned in the documentation.

> >

> > The issue comes when I try to perform the prediction:

> >

> > blockprediction <- predict(gstat(formula=Variabletopredict~additionalVariable,

> > data=Observed, model=vgm), newdata = shapefile)

> >

> > The newdata argument should contain the prediction location. In a normal

> > KED we would include a dataframe with a grid (coordinates in which to

> > predict) and the values of the covariate (additionalVariable). As I'm

> > trying to use a universal block kriging, I understood the newdata should be

> > the region in which I'm interested to know the prediction, hence a polygon.

> > How could I include in newdata the values of the covariate if its

> > resolution is finer than my block?

> >

> > As far as I know, what block kriging does is to predict point values inside

> > the region (which I could specified with the argument sps.args

> > discretization), and later average them. But I don't know how to attach the

> > covariate values to the block of interest (shapefile).

>

> maybe by

>

> shapefile = aggregate(additionalVariable, shapefile, mean)

>

> >

> > Thanks in advance,

> > I hope I could explain it properly, but I will give more details if

> > necessary.

> > Kind regards,

> > Antonio

> >

> > [[alternative HTML version deleted]]

> >

> > _______________________________________________

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> > [hidden email] <mailto:[hidden email]>

> >

https://stat.ethz.ch/mailman/listinfo/r-sig-geo> >

>

> --

> Edzer Pebesma

> Institute for Geoinformatics (ifgi), University of Münster

> Heisenbergstraße 2, 48149 Münster, Germany; +49 251 83 33081

> <tel:%2B49%20251%2083%2033081>

> Journal of Statistical Software:

http://www.jstatsoft.org/> Computers & Geosciences:

http://elsevier.com/locate/cageo/> Spatial Statistics Society

http://www.spatialstatistics.info>

>

I believe the residual variogram should then be computed using the covariate data at block support.

Sytze de Bruin

Wageningen University

Laboratory of Geo-Information Science and Remote Sensing

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