R help - Dec 2009 - nonlinear (especially logistic) regression accounting for spatially correlated errors

Hello,

Sorry to be a bit longwinded, but I've struggled quite a bit with the
following over the last few days.  I've read all entries related to spatial
autocorrelation in R help and haven't found what I'm after.  If it's
okay, I'm going to first describe my general understanding of the process by
which a mixed model can account for correlated errors.  If possible, please
briefly point out any misunderstanding I have to help my work overall (the
literature I've found on this area does not go into extensive explanation).

I'm aware that mixed models are currently in use to fit fixed effects while
controlling for correlation among residuals.  I believe this is often done by
specifying a theoretical variogram that one believes describes the spatial
structure of the error correlation and which is then used to modify the
variance-covariance error matrix that is used in model fitting (which I think in
this case would be block diagonal with distance input into chosen variogram
model determining matrix element value).  So, as the fixed effects are adjusted
algorithmically to maximize likelihood, simultaneously the parameters of the
theoretical variogram (which enter as a random effect) are similarly adjusted
which in turn influences the variance-covariance error matrix.  The combined
goal of these two parallel adjustments (I believe) would be to maximize overall
model likelihood.

I have been looking for an example of R code that uses a nonlinear mixed model
in this way.  I've only found this so far.

http://www.ats.ucla.edu/stat/r/faq/spatial_regression.htm

It seems that in the example given in this link, the incorporated correlation
structure is not specifically on the error term but instead on the reponse
itself.  Therefore, it seems that the effect of the explanatory variable is
diluted by this approach.  For instance, if you had a 'true' model where
temperature was only a function of elevation but elevation was strongly
autocorrelated, the approach in the link would likely leave elevation as a
nonsignificant part of the model.  Versus, if the correlation structure was
assigned to model error this would not happen.  Is this true or am I speaking of
6 of one and half dozen of the other (that in practice it makes no difference to
results)?

If the above example is not an example of modeling the correlation among model
errors, is there a good example of R code somewhere that does this that I can
reference?

Thanks, Seth Myers

PS I plan to read all the excellent books suggested in other threads, but ask
this now to help me digest this material more quickly.

	[[alternative HTML version deleted]]