How does group mean centering affect the interpretation of coefficients in a hierarchical model? I've dived deeply into the literature, but still don't understand if it's necessary to group-mean center my predictors if I'm entering them into a hierarchical model. Surely, if they're being entered into a hierarchical model, group-mean centering is redundant? I'll be partialling out my level-2 variance anyway.
Preparing myself for having massively misunderstood group-mean centering and wasted hours of my time.

When we have a variable which varies both within, and between, groups, then by mean-centering it, fitting the centred variable, and also the group means then this splits the estimate into within and between, which can be very useful to a resercher (depending on their research question(s) of course !).
In some areas of applied research (eg social sciences) this is known as "contextual effects"
