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 _______________________________________________ R-sig-Geo mailing list R-sig-Geo@stat.math.ethz.ch https://stat.ethz.ch/mailman/listinfo/r-sig-geo
