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

[Edzer J. Pebesma]

Ole F. Christensen wrote:

>
> I have no experience fitting nested variogram models myself, but my 
> general opinion is that nested variograms aren't really useful, since 
> what matters the most is
> to make a good fit of the empirical variogram near the origin. And if 
> one really wants to make a very careful fit of a variogram-model to 
> the data, then the likelihood function should be used rather than 
> fitting to the empirical variogram.

This reasoning has been put forward in the 1999 book by Michael Stein which
contains besides this one a few very provocative statements, such as 
"forget about
sample variograms, only look at likelyhood profiles". Although I like 
the book,
the problem I have with it is that it contains hardly any analysis of 
real data. The
argument therefore is based on theory; mathematicians do that, and they 
may prove
right.

However, nested variograms have been very useful in the past, especially for
describing spatial variability in larger data sets. There are 
theoretical arguments
for using them, think e.g. of the nugget effect: it consists of 
measurement error
(a "true" nugget effect) and spatially correlated microvariation: a 
nested variogram
model with a range so small that it's usually not detected by the data; see
Cressie (1993) for more on this. Given it's not in the data, ML or REML 
will never pick
it up, it's only something you can (and should) impose when you know for
instance the true measurement error from other sources than the observed 
data.

I would like to see papers where both approaches (ML without nested vs.
nested models, traditionally fit) were compared with large data sets; I find
it hard to embrace theoretical ideas without having them seen work in 
practice.

Geostatistics is about modelling what's out there.
--
Edzer