[R] Hierarchical Terms in RE models?

[vito muggeo]

Hi all,
this is a question (really, not necessarly related to R) that I was not able
to find in standard textbooks (at last those I've read, of course: Bates and
Pinero, Lindsey). I'm fitting a linear mixed model with fixed part: X+A+X:A
Just the interaction term X:A is significant suggesting an effect of X only
in one group (suppose X is continuous and A is a binary variable, although
this should be not important in a general context ). The main effects X and
A are requested of course in order to fit hierarchical model.
My doubt concerns the random part where the interest lies on X:A .
Which should be the right one?
a) 1+X
b) 1+X:A
c) 1+X+X:A
d) 1+X+A+X:A
A Hierarchical (RE) model implies d) or I can invoke some likelihood-based
criterion (e.g. AIC), but because only X:A is significant in the fixed part,
I would suggest using the b). Infact because the random coefficients mean
significant deviations from the fixed one, what is the sense in modelling
significant deviations from a non-significant term?
I'd like to hear some comment from some "RE-expert"

Hope to have been clear,
thanks for your time,
vito
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