Dear S-news group,
I recently began using S-plus. I am running version 4.0 for Windows with
the SpatialStats module attached. I am currently trying to use geostatistics
to characterize the spatial patterns of continuous data that I collected on a
regular grid in several forest plots. I have several questions and comments
stemming from these attempts.
1. In order to remove any large scale trends from the data, I employed the
median polishing method using the twoway.formula function. Included in the
call to this function is the formula z ~ x * y. Although the help file states
that x represents the row variable and y represents the column variable, they
appear to be reversed in the output. Is this the only problem with this
function?
2. I used the residuals generated by median polishing to construct empirical
variograms to which I fit theoretical variogram models. I then generated
kriging predictions at unsampled locations (all of this was accomplished using
SpatialStats functions). I used the results of the theoretical variogram
fitting to define the covariance function used in the kriging. Predictions
generated in this way did not match those generated by the surf.gls/prmat
functions of the spatial library provided by Venables and Ripley (MASS, ver:
5.3; patchlevel 1999/01/10) or those generated by another kriging software
package. It appears that the effect of a nugget was not incorporated into the
SpatialStats function. As a partial fix, I wrote a new covariance function to
pass to the SpatialStats krige function based on the one found in the V&R
spatial library. This appeared to bring these two functions into agreement,
except for a few points for which SpatialStats generated anomalous extreme
predictions (cases in which the predicted point fell very close to a
measurement point).
Will changing the covariance function serve as a general method for
incorporating a nugget effect into the SpatialStats function or are there cases
in which this will lead to errors?
Why are the anomalous extreme predictions being generated by the SpatialStats
functions?
Is there a way to correct this problem?
For either function, what would the covariance function be for a linear
variogram model that incorporates a nugget effect (both error variance and
microscale variance)?
3. Finally, in order to correct for skewness, I log transformed my data prior
to doing any of the above analyses. In order to back-transform the values I
obtained from kriging, I am following the formula presented by N. A. C. Cressie
in Statistics for Spatial Data (1993) on p.g. 135 that includes a value for the
Lagrange multiplier.
Is there a way to extract this Lagrange multiplier value from the results of
the SpatialStats krige or the V&R spatial surf.gls functions?
Do I need to make any similar corrections for bias in the back-transformation
of the values predicted from the results of median polishing or can they be
back-transformed simply before being added to the kriging predictions?
In closing, I would appreciate hearing about other possible problems I may run
into as I continue these analyses or other possible approaches I might explore.
Thanks,
Mike Tobin
Graduate Student
Forest Resources Dept.
University of Minnesota
e-mail: tobi0009@tc.umn.edu
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