
I agree with Paulo - gstat can work with any linear model including the transforms of the original predictors e.g.:

Z ~ X + X^2 + Y + Y^2    etc.

The problem is that gstat implements the so-called Kriging-with-external-trend algorithm to make predictions (see section 2.1 of my lecture notes), which is mathematically more elegant, but then it accepts only a family of linear models (and not GLMs, regreesion-trees etc.). I have been promoting the concept of regression-kriging (deterministic and stochastic predictions seperated), but we still did not implement it in any package so far.

You can at any time separate the predictions (e.g. krige only the residuals), but then gstat will not give you the regression-kriging variance, and you can not run geostatistical simulations.

see also:
https://stat.ethz.ch/pipermail/r-sig-geo/2008-February/003174.html


All the best,

Tom Hengl
http://spatial-analyst.net

Hengl, T., 2007. A Practical Guide to Geostatistical Mapping of
Environmental Variables. EUR 22904 EN Scientific and Technical Research
series, Office for Official Publications of the European Communities,
Luxemburg, 143 pp.
http://bookshop.europa.eu/uri?target=EUB:NOTICE:LBNA22904:EN:HTML


-----Original Message-----
From: r-sig-geo-bounces@stat.math.ethz.ch on behalf of Dave Depew
Sent: Mon 6/16/2008 10:54 PM
To: Paulo Justiniano Ribeiro Jr
Cc: r-sig-geo@stat.math.ethz.ch
Subject: Re: [R-sig-Geo] kriging
 
Ok,
What about higher order polynomials? I have fitted one using a gam to 
the data which which helps to normalize the residuals, and reduce the 
variance of the residuals.
Is it simply a matter of plugging in the function into the gstat command 
line? Or is it simpler to krig the residuals and then add the trend back 
to the interpolated residual grid?


Paulo Justiniano Ribeiro Jr wrote:
> Dave,
>
> what is necessary for UK is a relation expressed by a linear model, not
> necessaraly a linear relation between the variables.
> e.g. you could have a second degree polinomial and still work within the
> scope of universal kriging.
>
>
> On Mon, 16 Jun 2008, Dave Depew wrote:
>
>   
>> Hi all,
>> I have a data set that I would like to krige to interpolate between
>> transects. There is a non-linear trend between two of the variables...my
>> impression from reading the gstat help file is that there must be a
>> linear relationship between the data to use universal kriging?
>> Second, would a method of non-linear regression followed by modelling of
>> the residuals with a semivariogram be an appropriate solution?
>>
>> Thanks,
>>
>> Dave
>>
>> _______________________________________________
>> R-sig-Geo mailing list
>> R-sig-Geo@stat.math.ethz.ch
>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>>
>>     
>
> Paulo Justiniano Ribeiro Jr
> LEG (Laboratorio de Estatistica e Geoinformacao)
> Universidade Federal do Parana
> Caixa Postal 19.081
> CEP 81.531-990
> Curitiba, PR  -  Brasil
> Tel: (+55) 41 3361 3573
> Fax: (+55) 41 3361 3141
> e-mail: paulojus AT  ufpr  br
> http://www.leg.ufpr.br/~paulojus
>
>
>
>

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