[R-sig-ME] Group-mean centering in linear mixed models

[Maarten Jung]

Dear list,

My current understanding is that in order to get unbiased estimates of 
the within-group1 effects of the continuous predictors A, B, and the 
interaction effect A:B on the dependent variable Y in model m1, one has 
to mean-center A and B within each level of the random grouping factor 
group1 ("group-mean centering"). Is this correct?

Let's now consider a model m2 that describes a design with an additional 
random grouping factor group2 and assume that the by-group1 random 
effects and by-group2 random effects are crossed.
Is mean-centering A and B within each level of the random grouping 
factor group1 still valid to obtain unbiased estimates of the 
within-group1 effects in this case?

If A and B are categorical predictors (factors), is group-mean centering 
still useful? E.g., if A and B are 2-level factors, then group-mean 
centering in a balanced design would basically be the same as 
sum-contrast coding (up to a multiplicative constant); however, in case 
of missing data/an unbalanced design, group-mean centering and 
sum-contrast coding would differ.

m1: Y ~ 1 + A*B + (1 + A*B|group1)
m2: Y ~ 1 + A*B + (1 + A*B|group1) + (1 + A*B|group2)

Best,
Maarten