Problems estimating anisotropy parameters for a spatial model I am looking for someone with experience in how to handle the anisotropy-parameters in the likfit() function which is part of the GeoR package in R.
I am using likfit() to generate the obj.m-parameter for the function krige.conv(). The data I use consists of scattered points (5 to 30) on a ~50*50 grid.
In likfit(), I want the parameters psiA and psiR to be estimated from the available data. This works fine by stating:
fix.psiA = FALSE, fix.psiR = FALSE

However, the estimated values show quite a huge range for psiR, given that the datasets I used are not fundamentaly different from each other. (It is a set of soil moisture measurements with values from 0 to ~45.)
psiR ranges from 1 to about 8000... can that be right? Most of the values are in a range from 1 to 10, but I can not tell why some datasets produce these very large values for psiR.
I was unable to find further information on what this parameter exactly does. I do understand that this parameter regulates the dependency of an estimated value according to it's location relative to the ambient measured values. But I do not know in which way this is accomplished.
I am sorry for not posting my code, but it is quite long and I felt that it is not necessary in behalf of my question.
Thank you very much for your interest. I will post additional details, if required.
 A: In short, identifying anisotropy is hopeless with these sparse data.
The two parameters in question, psiA and psiR, describe anisotropy (the angle and ratio, respectively, of a "geometric anisotropy": consult GSLIB or Journel & Huijbregts for details, because the geoR documentation in Diggle & Ribeiro Jr is indeed inadequate concerning anisotropy). With relatively few datapoints it is quite possible--indeed, with soils data (which can be notoriously variable) it is quite likely--that in some directions almost no spatial correlation is detected while in other directions there appears to be some correlation. This can result in near-infinite ratios.  Also, if there is a trend in just one direction and it is not removed, this trend will create a strong anisotropy.
Your problem is that five points are way too few for any kind of parameter estimation and $30$ are still too few to identify anisotropy reliably. Rules of thumb in the literature suggest you need at a minimum between $30$ and $100$ points just to get started with estimating the parameters and computing the predictions (that is, kriging).  (All rules of thumb have exceptions, but it sounds like these data are not nice enough to qualify.)  If you do not assume an isotropic model, you need to explore directional variograms in at least four cardinal directions, whence each such variogram would be based on approximately $5$ to $10$ points each, which again is too small.  To identify anisotropy, figure on needing about $100$ points.
The cure is to impose isotropic variograms (or determine anisotropy from considerations independent of the data) and hope for the best.  Expect the prediction errors to be large.
