Thank you for your perspective. I should state that I intend to use the
variogram model, not for prediction, but for understanding the spatial
variability. My end goal is to create the best sample spacing for a new
design based on the variogram. In the anisotropic case I would create a
rectangular grid with stations in one direction closer than in the
other. In the other "trend" case I would create a square grid. This is
the question I am trying to answer. Do you have any advice in this context?
Thanks,
Kerry
Ashton Shortridge wrote:
On 2010-08-20, Kerry Ritter, wrote:
Hi. I was wondering which model you would tend to choose given similar
cross validation results.
1. An isotropic model with linear trend
2. An anisotropic model
Assume linear trend is ~x + y + I(x*y), where x,y are spatial coordinates.
I have read papers that argue that unless you know how to interpret the
linear trend (from a phyiscal/geographical/biological point of view) it
is better NOT to detrend the data prior to fitting a variogram. On the
other hand, one must ultimately assume stationarity. So I am not sure
which way to go. How do you decide?
Thanks,
Kerry
Hi Kerry,
If your goal with this model is to develop predictions within the extents of
your existing data (that is, not extrapolating), then either approach probably
produces about the same result. These alternatives do employ very different
conceptual models of the process you are trying to capture, so from that
perspective it might be best to go with the model that best fits your
understanding, but from a utilitarian perspective, either will work.
I find it is often difficult in practice to fit an anisotropic model well - the
lack of sufficient data in different directions can make the variograms noisy.
Low-order trends like yours are simple to fit. Using OLS to fit a trend surface
to spatially autocorrelated observations can be problematic, but universal
kriging is a more robust alternative (though this frequently seems to make
little difference in practice).
Of course, you can use both to develop predictions, or prediction surfaces,
and take the difference of the two to see how much your choice matters. In the
end, perhaps employ the method that you find simplest to explain!
Yours,
Ashton
-----
Ashton Shortridge
Associate Professor ash...@msu.edu
Dept of Geography http://www.msu.edu/~ashton
235 Geography Building ph (517) 432-3561
Michigan State University fx (517) 432-1671
--
**********************
Kerry Ritter, Ph.D.
statistician
Southern California Coastal Water Research Project
3535 Harbor Blvd., Suite 110
work: 714-755-3210
cell: 714-420-3346
fax: 714-755-3299
email: ker...@sccwrp.org
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