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goodness of fit for anisotropic model in 4 directions

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