[R-sig-ME] No need to handle between-group correlation structure in glmm in general?

[Junyan Luo]

Hi,
Recently I have been working with a data set that contains individual
samples from a set of connected geographical areal units. While I plan
to use glmm to model the data with individuals as the 1st level units
and the areal units as the 2nd level units, I am concerned with the
potential spatial autocorrelation among the geographical areal units
(i.e., at the second level). It is reasonable to think that the random
effects at the second level will be spatial autocorrelated. I know
nlme has the option to specify "within-group" correlation structure,
but I couldn't figure out a way to specify "between-group"
correlations structure for the geographical areal units.

However, one of my colleagues told me it was totally unnecessary to
specify a correlation structure at the second level. This is because
the two assumptions of multi-level models are (1) the individual error
term is independent; (2) the individual error term is uncorrelated
with the random effects. It does NOT assume that the random effects
should be independent. So unless (2) is violated, generally we don't
need to worry about autocorrelation in the random effects. That's
probably why nlme only has the option for specifying "within-group"
correlation structure. I feel the assessment is reasonable, but I am
unsure if that is correct. Can anybody help me clarify this? Thanks!