[R-sig-ME] Group-mean centering in linear mixed models
Maarten Jung
jungm@@rten @end|ng |rom gm@||@com
Wed Mar 24 21:49:03 CET 2021
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
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