Hi all,

I am working with mixed models and have the following general model
structure:

model<-lmer(X~Y*Z+(A|B), where Y is a continuous mean centered
environmental variable, Z is Year (2012 or 2013).

Part of my interest in my study is to explore variation in plasticity
between individuals, not just population level plasticity.  When settling
on a final model, I first check for significance of random effects and then
I worry about the fixed effects structure.  For the random effects
structure, even in there is not significant variation between individuals
in their slope, I leave this term in the model because it is a primary
interest of mine.  My question is, if I am leaving random slopes in all of
final models along with random intercepts, should I also allow for the
correlation of the random effects, i.e. (A|B) or should I not allow for
this, i.e. (A+0|B) if there is no significant correlation when checked LRT
fitted by REML?

I initially thought that I would remove the ability for correlated random
effects if there was no significant correlation, but then I read the
following: "In models with both individual-speciﬁc elevations and slopes we
allowed for the potential correlation between these, to ensure that BLUP
estimates produced by the models were not affected by the method used to
centre covariates." from 'Phenotypic plasticity in a maternal trait in red
deer" by Nussey et al. 2005.  Do you understand their reasoning?

Thank you for your help.

Jacob

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