[R-sig-Geo] anisotropic models vs. detrending

[Ashton Shortridge]

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			ashton at msu.edu
Dept of Geography			http://www.msu.edu/~ashton
235 Geography Building		ph (517) 432-3561
Michigan State University		fx (517) 432-1671