[R-sig-Geo] Summary: Fitting nested variograms to empirical variograms

[Eliot McIntire]

Thank you for your comments Edzer, Ole and Paulo,

Edzer:
> Also, be aware that the linear model with range is not a valid variogram
> model for data in more than one dimension.

Yes, for some reason, I copied the code for the Linear models.  I believe  
I had been trying nesting two exponentials or spherical and exponential,  
which was resulting in the error.  I tried to simplify the model by  
putting in the linear models and had the same problem.

Ole and Edzer:

> * Nested variogram models. My objection to them is based on what I have  
> sometimes seen : a very elaborate fitting to empirical variograms, where  
> a lot of effort is going into fitting the variogram away from the  
> origin, and where the number of variogram models used in the nested  
> structure seems to decided by this fitting to the empirical variogram in  
> mind.
> A nested model for the variogram really says that the phenomenon we are  
> modelling is Y(x) = Y_1(x) + Y_2(x) + Y_3(x) + Y_4(x) etc. , where the  
> different components have different spatial structure.
> Rather than letting the empirical variogram decide the number of  
> components, then shouldn't we start thinking about at the data  
> generating mechanisms instead ?
> When having more than one spatial component Y_i(x), shouldn't we attempt  
> interpreting the different components ?
> How about the implicit additivity assumption of the components when  
> using a nested model ? [The data generating mechanism may suggest  
> otherwise ... ].
> A blind use of nested variogram models seems silly to me.

I am an ecologist, and it is actually the mechanisms I am interested in,  
which is arguably more than "modeling what's out there".  The data that I  
am fitting using WLS fitted to empirical variograms or ML fit to the data  
are only just numbers.  They do, however, represent the outcome of  
potentially several underlying ecological mechanisms.  The context for  
this study is identifying competition among trees in plantations in  
Chile.  The expected variogram shape reflecting underlying environmental  
variation would be a traditional increasing function, like an exponential:  
closer points are more alike.  The expected variogram shape reflecting  
competition among trees (which is expected to be assymetrical, i.e., the  
larger tree negatively affects the smaller tree, the not the inverse) is  
more like a wave function: neighbouring trees are expected to have MORE  
variation than the average variation across the forest stand.  To test  
this mechanistic hypothesis, I have tree ring growth data from 7 different  
forests, so I have growth increment each year for every tree.  To test for  
competition, I would like to fit a wave function; to test for  
environmental variation, I would like to fit an exponential function; to  
test for the two, I would like to test a nested function.  I will be  
comparing the relative fits of these three models using AIC (since the  
nested model now has more parameters, an information criterion like AIC  
becomes appropriate).

I the end, I have decided to model my own variograms and fit them using  
weighted non-linear least squares, unrelated to the "built in" functions  
in geoR or gstat because I couldn't get them to work.  I am having success  
fitting the models in this way (i.e., coding my own functions).

Ole:
I am glad you do not bunk fitting empirical variograms, as you point out,  
there seems to be useful places for either approach.  And it seems to me  
that there are fewer distributional assumptions in fitting an empirical  
variogram using WLS, and that it does "a pretty good job" most of the time.

I still have not had a conclusive statement that I can model nested  
variograms in any of these R functions.  I will write the authors.

Thank you for your comments,
Eliot


On Sat, 16 Oct 2004 10:49:17 +0200, Edzer J. Pebesma  
<e.pebesma at geog.uu.nl> wrote:

>
>
> Eliot McIntire wrote:
>
>>
>> gstat: I can run nested models using
>> F2.BA1.fit = fit.variogram (F2.BA1.variogram, vgm(psill=33,"Lin",6,  
>> add.to  = vgm(psill=33,"Lin",6, nugget=20) )
>>                 , print.SSE=T, fit.sills=T, fit.ranges=T )
>>
>>
>> but I never seem to get a good fit, i.e., it always fails to fit the   
>> empirical variogram.
>>
>> If anyone has a solution, I also need to calculate the Residual Sums  
>> of  Squares to test for the relative fit.
>
> The problem is your starting values for the ranges. Use the values that  
> you
> fit `by eye' from the sample variogram; they should be sufficiently  
> distinct
> (and present in the sample variogram) for gstat to fit them with success.
>
>
> Best regards,
> --
> Edzer



-- 
Eliot McIntire
NSERC Post Doctoral Fellow
Department of Ecosystems and Conservation Science
College of Forestry and Conservation
University of Montana, Missoula, MT 59812
406-243-5239
fax: 406-243-4557
emcintire at forestry.umt.edu