Dear mixed model experts and interested others,

I would like to ask some advice regarding the fitting of a linear mixed 
effect model using the nlme library in R.

I am fitting a linear mixed effect model to data of repeated 
measurements on individuals which are themselves nested within populations.
 
Preliminary diagnostics of classical linear models indicate that the 
residual errors are heteroscedastic across combinations of measurement 
occasions and populations and correlated within individuals but with a 
different covariance matrix for each population, resulting in a 
correlation matrix of residuals varying across populations.

Although I could easily find a way to allow for varying residual error 
variance across combinations of measurement occasions and populations 
using the VarIdent class in the weight argument with occasion*population 
as a stratification variable
weight = VarIdent(form = ~ 1 | occasion*population),
I  could not find a way to model an unstructured correlation matrix that 
would vary according to the stratification variable population.

In other words, I tried to use the corSymm class in the correlation 
argument,
correlation = corSymm(form = ~ 1  | population/individual),
which indeed gave me an unstructured correction matrix across residuals 
but I could not find a way to let it vary according to the 
stratification variable population.
In other words, is there a way, similar to what can be done for residual 
variance, to model correlation functions for within-group errors that 
are heterogeneous according a stratification variable?

A corollary to this question is how to interpret the current model I 
fitted i.e. how to interpret a constant correlation matrix across 
population while the variance of residual errors is varying across the 
populations: it means that somehow the covariance matrix of the 
residuals vary so as to compensate variability in variance to obtain a 
constant correlation matrix but I am not sure whether this is right 
since I do not know exactly how the correlation matrix is treated in the 
(restricted) maximum likelihood estimation.

You help will be most appreciated.
I thank you very much in advance.

Best regards,
Bruno Ernande.

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Bruno Ernande
Laboratoire Ressources Halieutiques
IFREMER
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email : Bruno.Ernande@ifremer.fr
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