Hi Lorenz,
I'm glad you are finding the Patternplus approach useful. I was unable to
send this response to you directlyit looks like your server rejects mail
from the .gov domain, which may be why it won't send mail here
either? Some responses to your questions below.
Questions:
1. When calculating multiple linear regression (pattern)model i did
not include xycoordinates of the sample sites as aditional predictor
variables allthough there is considerable correlation between coordinates
and heavy metal contents (but there is no trend in variograms!). is that ok?
Sure, the covariates that you included in your model probably explain
geographic drift in a more mechanistic and meaningful way.
2. (backtransformed) semivariograms of the patternmodels still have a
"good shape" suggesting a spatial/random variability. shouldn't they behave
like "white noise"?
I'm assuming you mean residual semivariograms still show autocorrelation
structure (i.e., nugget << sill)? I would interpret this to mean that the
deterministic model did not explain all spatial variation or remove all
autocorrelation. That's ok  I think its reasonable to expect small
scale autocorrelation that is not due to in situ conditions because of
local transport processes and other variables that were not included.
The good news is that kriging can help add predictive power (pattern+).
Remember to use a different subset of data to estimate the semivariogram
model.
3. how do i get backtransformed residuals from lntransfortmed data ?
when i backtransform lnresiduals of the regression/patternmodels negative
lnvalues are just interpreted as positive values below 1,0. is it possible
to get residuals by substracting (backtransformed) predicted values
(=exp(regression model)) from the original (= untransformed) values?
Yes, I think the latter idea is a good one. In general I'd stay out of
logworld when possible. Especially if the variances are going to be needed.
4. simultanous estimation of drift and semivariogram with a single
realization is rigorously not possible. Are there some (simple)
aproximations for the semivariogram? What about the iterative solution for
the simultaneaous inference of drift and semivariogram, how does it work in
detail?
I wrote a FORTRAN program to do the iterative estimation, but that was
quite a while ago and I think it needs some work (maybe only to find the
right machine constants). I was last adding the capability to vary the sill
by stratum, and still hope to get back to it someday. If you are facile
with statistical coding and want to try it, you are welcome but I wouldn't
be able to offer support. It uses Linpack routines for the generalized
least squares regression and Minpack routines to estimate parameters of the
semivariogram using iteratively reweighted nonlinear least squares. I
think Gstat could probably be used to implement it now, although it
wouldn't be an automated stepwise procedure with visual feedback on
anisotropy etc.. The idea of the iterative analysis derives from:
S.P. Neuman and E.A. Jacobsen. 1984. Analysis of nonintrinsic spatial
variability by residual kriging with application to regional groundwater
levels, Math Geology 16(5): 499519.
If anyone else interested in this, there is a pdf file on my website,
which is listed below, entitled "Spatial Modeling of Landscape Pattern".
Good luck,
Yetta


Yetta Jager
Environmental Sciences Division
Oak Ridge National Laboratory
P.O. Box 2008, MS 6036
Oak Ridge, TN 378316036
U.S.A.
For packages, please replace "P.O. Box 2008" with
"Bethel Valley Road" in the address above.
OFFICE: 865/5748143
FAX: 865/5768543
Work email:
jagerhi@...
Home email:
hjager@...
WEBpage:
http://www.esd.ornl.gov/~zij/
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"How like fish we are: ready, nay eager, to seize upon whatever new thing
some wind of circumstance shakes down upon the river of time! And how we
rue our haste, finding the gilded morsel to contain a hook."
Aldo Leopold, 1949
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