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goodness of fit for anisotropic model in 4 directions

2 messages · Kerry Ritter, Edzer Pebesma

Original
Kerry Ritter
# 
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
1 day later
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: