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

[Kerry Ritter]

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			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
>
>   


-- 
**********************
Kerry Ritter, Ph.D.
statistician
Southern California Coastal Water Research Project
3535 Harbor Blvd., Suite 110

work: 714-755-3210
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email: kerryr at sccwrp.org