[R-sig-Geo] Summary: Fitting nested variograms to empirical variograms

Mon Oct 18 18:38:17 CEST 2004

Eliot

Despite of the very interesting debate and exchange of ideias on
validity/merit etc
here it is example on how to overimpose  variograms variogram models
using nested models in geoR.
It's is a try and error exercise with lines.variomodel:
> data(s100)
> v <- variog(s100, max.d=1)
> plot(v)
# a single structure variogram
> lines.variomodel(seq(0,1,l=100), cov.model="exp", cov.pars=c(1, .25),
nug=0)
# a nested variogram model
> lines.variomodel(seq(0,1,l=100), cov.model="exp", cov.pars=rbind(c(.5,
.1), c(.5,.3)), nug=0, col=2)

Besides there is an tcl/tk based function with a menu and sliding bars.
The function is eyefit() and is based on lines.variomodel.
However it does not cope with nested models, but can be modifyed to do so

Best
P.J.

On Mon, 18 Oct 2004, Eliot McIntire wrote:

> Thank you for your comments Edzer, Ole and Paulo,
>
> Edzer:
> > Also, be aware that the linear model with range is not a valid variogram
> > model for data in more than one dimension.
>
> Yes, for some reason, I copied the code for the Linear models.  I believe
> I had been trying nesting two exponentials or spherical and exponential,
> which was resulting in the error.  I tried to simplify the model by
> putting in the linear models and had the same problem.
>
> Ole and Edzer:
>
> > * Nested variogram models. My objection to them is based on what I have
> > sometimes seen : a very elaborate fitting to empirical variograms, where
> > a lot of effort is going into fitting the variogram away from the
> > origin, and where the number of variogram models used in the nested
> > structure seems to decided by this fitting to the empirical variogram in
> > mind.
> > A nested model for the variogram really says that the phenomenon we are
> > modelling is Y(x) = Y_1(x) + Y_2(x) + Y_3(x) + Y_4(x) etc. , where the
> > different components have different spatial structure.
> > Rather than letting the empirical variogram decide the number of
> > components, then shouldn't we start thinking about at the data
> > generating mechanisms instead ?
> > When having more than one spatial component Y_i(x), shouldn't we attempt
> > interpreting the different components ?
> > How about the implicit additivity assumption of the components when
> > using a nested model ? [The data generating mechanism may suggest
> > otherwise ... ].
> > A blind use of nested variogram models seems silly to me.
>
> I am an ecologist, and it is actually the mechanisms I am interested in,
> which is arguably more than "modeling what's out there".  The data that I
> am fitting using WLS fitted to empirical variograms or ML fit to the data
> are only just numbers.  They do, however, represent the outcome of
> potentially several underlying ecological mechanisms.  The context for
> this study is identifying competition among trees in plantations in
> Chile.  The expected variogram shape reflecting underlying environmental
> variation would be a traditional increasing function, like an exponential:
> closer points are more alike.  The expected variogram shape reflecting
> competition among trees (which is expected to be assymetrical, i.e., the
> larger tree negatively affects the smaller tree, the not the inverse) is
> more like a wave function: neighbouring trees are expected to have MORE
> variation than the average variation across the forest stand.  To test
> this mechanistic hypothesis, I have tree ring growth data from 7 different
> forests, so I have growth increment each year for every tree.  To test for
> competition, I would like to fit a wave function; to test for
> environmental variation, I would like to fit an exponential function; to
> test for the two, I would like to test a nested function.  I will be
> comparing the relative fits of these three models using AIC (since the
> nested model now has more parameters, an information criterion like AIC
> becomes appropriate).
>
> I the end, I have decided to model my own variograms and fit them using
> weighted non-linear least squares, unrelated to the "built in" functions
> in geoR or gstat because I couldn't get them to work.  I am having success
> fitting the models in this way (i.e., coding my own functions).
>
> Ole:
> I am glad you do not bunk fitting empirical variograms, as you point out,
> there seems to be useful places for either approach.  And it seems to me
> that there are fewer distributional assumptions in fitting an empirical
> variogram using WLS, and that it does "a pretty good job" most of the time.
>
> I still have not had a conclusive statement that I can model nested
> variograms in any of these R functions.  I will write the authors.
>
> Thank you for your comments,
> Eliot
>
>
> On Sat, 16 Oct 2004 10:49:17 +0200, Edzer J. Pebesma
> <e.pebesma at geog.uu.nl> wrote:
>
> >
> >
> > Eliot McIntire wrote:
> >
> >>
> >> gstat: I can run nested models using
> >> F2.BA1.fit = fit.variogram (F2.BA1.variogram, vgm(psill=33,"Lin",6,
> >> add.to  = vgm(psill=33,"Lin",6, nugget=20) )
> >>                 , print.SSE=T, fit.sills=T, fit.ranges=T )
> >>
> >>
> >> but I never seem to get a good fit, i.e., it always fails to fit the
> >> empirical variogram.
> >>
> >> If anyone has a solution, I also need to calculate the Residual Sums
> >> of  Squares to test for the relative fit.
> >
> > The problem is your starting values for the ranges. Use the values that
> > you
> > fit `by eye' from the sample variogram; they should be sufficiently
> > distinct
> > (and present in the sample variogram) for gstat to fit them with success.
> >
> >
> > Best regards,
> > --
> > Edzer
>
>
>
> --
> Eliot McIntire
> NSERC Post Doctoral Fellow
> Department of Ecosystems and Conservation Science
> College of Forestry and Conservation
> University of Montana, Missoula, MT 59812
> 406-243-5239
> fax: 406-243-4557
> emcintire at forestry.umt.edu
>
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>
>

Paulo Justiniano Ribeiro Jr
Departamento de Estatística
Universidade Federal do Paraná
Caixa Postal 19.081
CEP 81.531-990
Curitiba, PR  -  Brasil
Tel: (+55) 41 361 3573
Fax: (+55) 41 361 3141
e-mail: paulojus at est.ufpr.br
http://www.est.ufpr.br/~paulojus

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