GEOSTATS: Cross validation vs. semivariogram comparison?
- Andrew and others,
We are interested in this issue as well in the context of
subsampling from a GIS coverage to conduct semivariogram
analysis. My colleagues are concerned by the idea that we
would be throwing away data and want to compare semivariograms
from the whole set with those estimated from samples (I'm
suggesting sampling with a mixed design of regular and more
closely spaced nearest neighbors).
In the past, I've assumed that the best way to test the
adequacy of the semivariogram is to do cross-validation --
krig based on the estimated semivariogram(s) leaving out
one point at a time, sum the squared errors (predicted Z - actual)
and compare with the kriging variance estimate (which is based
on the semivariogram and the spacing of data). This ensures
that the distances that will actually be used most are given
the correct weight. For example, if the data are all fairly
closely spaced, it doesn't matter if the semivariogram is way
off at large distances. If comparing semivariograms is the
issue, then I'd just be inclined to pick the one that does
a better job of producing accurate kriging variances.
I'd be interested in dissenting or confirming opinions, since
we are dealing with the same controversy.
At 11:16 AM 9/30/98 -0400, you wrote:
>I read an interesting article about constructing confidence intervals for
>variograms in order to assess the validity of grouping several sample sites
>together to estimate one composite variogram. (Kabrick et al. 1997.
>spatial patterns of carbon and texture .....Soil Science Society of America
>I would like to do a similar thing: to see if it's valid to group
>variograms calculated from data from each of several smaller, non
>contiguous plots in a forest into one composite variogram. Basically, the
>Kabrick article points out that assessing confidence interval overlap is
>not really a statistical test of similarity of two regression lines, so
>they give a z test to further support a conclusion of similarity or
>dissimilarity; I was, however, confused by this.
>I was a little unclear on their approach and was wondering if anybody had
>any more straightforward approach to comparing variograms. It seems like
>one could estimate confidence intervals by calculating the standard errors
>of all of the (xi-xi+h)^2/2n's, and multiply this std error by t (1.96 for
>large n) to define the limits of the CI. Is this overly simplistic? I'm
>sort of an intermediate geostatistics (and classical statistics for that
>Thanks for any advice.
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