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

[Ole F. Christensen]

Dear Elliot

I am glad that there is an interpretation behind the the nested modellig 
you are doing.
Given that the likelihood approach to the nested variogram models is not 
implemented I would also do what do, fit by eye a variogram-model to the 
empirical variogram. [I just noticed that Paulo replied about how to do 
such things using his software]
Just a thought : Could there be some information in the locations of the 
trees, i.e. in the neighbourhood of a large three there would probably 
be no other trees at all ?
Marked point processes may (at least in principle) provide a framework 
for a type of modelling (but don't ask me, I don't know much about such 
models).

> 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.


Well, I actually wrote that I do not bunk  the "empirical variogram". 
I don't really like the "fitting to empirical variograms".
Note the distinction here : I very am happy with the empirical 
variograms in themselfves but less happy with the fitting to them. When 
you use the likelihood function, you are fitting a model to the data, 
instead of fitting to a summary of the data [which emprirical variograms 
are]
I disagree with "there are fewer distributional assumptions in fitting 
an empirical variogram". When the distributional assumptions are not 
true, say Gaussian, you may still use that specific likelihood function 
estimate your parameters.
Neither the likelihood approach nor the fitting to empirical variograms 
have a theoretical justification when the model is wrong. The difference 
is that likelihood approach has a justification when the model is true.
In practice, where one should be worried, is when the distribution of 
the data is skewed. Here you should really transform the data [and it 
does not matter which approach you are using to estimate parameters].
The fitting to empirical variograms may do "a pretty good job" in 
practice, but actually you need to fit by likelihood before you can 
confirm this :-)


I have probably already written too much about likelihood ...... We seem 
to agree on modelling which is the important part.

Ole