Hengl, T. wrote: > 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. > And I can see why, as there are quite a few problems still to solve (afaik) ahead of you. When you cut the problem in two, do the regression estimation and residual prediction in two separate processes (often under different assumptions, e.g. wrt spatial correlation) you ignore the correlation between the two. Finding a prediction variance by naively adding the variances of the two components e.g. does not yield zero variance at observation locations, because a non-zero correlation is ignored. At other locations, this correlation is also non-zero. Furthermore, if you cut the problem in two for e.g. binomial or Poisson distributed cases, in this approach you likely end up with negative predictions or predictions above one for the binomial case.
Does the paper you refer to (by yourself) give solutions to these two problems? > 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. > No, of course not, for the reasons mentioned above. The gstat approach is: if you want to make a mess, please take responsibility for it by yourself (and don't blame me--through the package). There is a paper I did it with count data, though, which is E.J. Pebesma, R.N.M. Duin, P.A. Burrough, 2005. Mapping Sea Bird Densities over the North Sea: Spatially Aggregated Estimates and Temporal Changes. Environmetrics 16 <http://www3.interscience.wiley.com/cgi-bin/jissue/110577560>, (6), p 573-587 <http://dx.doi.org/10.1002/env.723>. and (part of) the analysis is found in library(gstat) demo(fulmar) I'm also confused by this term "regression kriging". Would you claim that the universal kriging/kriging with (one or more) external drifts implemented by gstat is not regression kriging? Are you actually working on a package that does do regression kriging as you define it? -- Edzer > 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: [EMAIL PROTECTED] 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 >> >> >> >> >> > > _______________________________________________ > R-sig-Geo mailing list > R-sig-Geo@stat.math.ethz.ch > https://stat.ethz.ch/mailman/listinfo/r-sig-geo > > > > [[alternative HTML version deleted]] > > _______________________________________________ > R-sig-Geo mailing list > R-sig-Geo@stat.math.ethz.ch > https://stat.ethz.ch/mailman/listinfo/r-sig-geo > -- Edzer Pebesma Institute for Geoinformatics (IfGI) University of Münster http://ifgi.uni-muenster.de/ [[alternative HTML version deleted]]
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