[R-sig-Geo] variogram question

[Paulo Justiniano Ribeiro Jr]

A possible extension of Edzer thoughts on this is to consider a initial
search for the non-linear range parameters.

For instance, take a grid of (20 say) values for this parameters within a
reasonable range for the given problem, e.g. between 0 and the maximum
distance.
Evaluate the objective funcion (least squares, wighted least squares etc)
for such values. Use the best one as the initial value for the fitting
algorithm.

This is what variofit() does in geoR whan initial values are not provided,
but the same ideia holds for other variogram fitting functions
using other packages such as gstat and therefore can be made automatic.

P.J.


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



On Mon, 18 Aug 2008, Edzer Pebesma wrote:

> In general: no, in special cases: yes.
>
> Fitting variograms involves non-linear regression for most models (Sph,
> Exp, Gau, ...) for the range parameter, so you need starting values.
> Given the initial range, linear regression is sufficient to find the
>
nugget/sill component(s), as they are linear. In principle, gstat could
> be made simpler in that respect, I'd say.
>
> For an initial range, you could use some heuristics (20% of the longest
> distance in your data?), but it is often not so hard to think of cases
> where this would fail.
>
> Another issue is automatic values for the width and cutoff.
>
> You could have a look at package automap, by Paul Hiemstra, which tries
> to do some of these heuristics--good or bad, who will tell.
> --
> Edzer
>
> Wesley Roberts wrote:
> > Dear r-sig-geo users,
> >
> > I am currently analyzing some Lidar data we have collected over our study area. I am interested in identifying the range of the semi-variogram as this value will determine the width of pseudo-flight lines I intend to use to sample the lidar data. Our point density is upwards of 5 points per square meter captured over even-aged managed Eucalyptus plantations with an espacement of 2 meters between trees and 3 meters between rows.
> >
> > I have imported an x,y,z data set containing canopy height and coordinates and successfully run the experimental variogram using the "variogram" module in gstat.
> >
> > cpy.pts2 <- variogram(dbl_5 ~ 1, cutoff=50, width=2, D)
> >
> > I have also managed to fit several models using the
> >
> > cpy.pts2.fit <- fit.variogram(cpy.pts2, model = vgm(2, "Sph", 4, 5))
> >
> > command as suggested by the gstat manual.
> I would like to fit the various models "Sph, Exp..." etc without having
to specify the nugget psill and range. Essentially I would like an objective method to measure and record these values as I will be running several hundred variograms. Is it possible to perform this type of analysis using gstat?
> >
> > Many thanks for all your help and suggestions
> > Wesley
> >
> > Wesley Roberts MSc.
> > Researcher
> > Earth Observation (Ecosystems)
> > Natural Resources and the Environment
> > CSIR
> > Tel: +27 (21) 888-2490
> > Fax: +27 (21) 888-2490
> >
> > "To know the road ahead, ask those coming back."
> > - Chinese proverb
> >
> >
>
> --
> Edzer Pebesma
> Institute for Geoinformatics (ifgi), University of Münster,
> Weseler Straße 253, 48151 Münster, Germany.  Phone: +49 251
> 8333081, Fax: +49 251 8339763  http://ifgi.uni-muenster.de/
>
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