[R-sig-Geo] goodness of fit for anisotropic model in 4 directions

[Edzer Pebesma]

the SSErr attribute is the (weighted) sum of squared errors minimized by
the procedure called for. So if weights are Nh, then SSErr is

sum_i Nh_i (gammaModel_i - gammaSample_i)^2

or see the second equation on page 66 of the longer reference manual for
gstat, http://gstat.org/gstat.pdf for a properly formatted version.

This implies, that this SSErr depends on the weights chosen, and cannot
be compared accross different weighting schemes.

For comparing the quality of a particular variogram, I would use cross
validation (krige.cv) on kriging predictions to compare various
variogram models. The aestetics of the fit is usually seen as less
important compared to how well the variogram worked for spatial prediction.

On 08/27/2010 04:22 PM, Kerry Ritter wrote:
> HI I am looking for a goodness of fit measure in the case of an
> anisotropic variogram model fit in 4 directions.  I want to be able to
> compare between different fitting algorithms, so a measure that is
> independent of the fitting method is key.  I also want to compare
> between different models (ie. anisotropic with linear trend vs
> anisotropic).  Does anyone know if such a measure exists in one of the R
> libraries?  Three seems to be a measure "SSErr" in gstat using
> fit.variogram that may work when all parameters are fixed, but I do not
> know how the statistic is calculated.  Can someone provide me with a
> formula for this computation in the case of fitting a variogram in 4
> directions? Alternatively can you help me with a different goodness of
> fit formula that I could program myself in R?
> Thanks,
> Kerry
> 

-- 
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
http://www.52north.org/geostatistics      e.pebesma at wwu.de