Hi. I am currently working on a multilevel analysis and have decided to use the grand mean (and grand mean centering) instead of the group mean (centering). I wonder though whether I have to add the group means (not the centered variables, just the group means) to the model to test for contextual effects or how else I can justify a multilevel approach (only using the grand means).
PS: plain explanations are welcome, I am not too familar with mlm yet :)
Thank you!
I believe you'd want to enter a group x level1 variable interaction term to test fornxontextual effects. Otherwise, the grand mean is reducing some of your cross-level variance.
Hope this helps
Matt
Grand mean centering is an useful re-scaling that helps with the interpretation of the terms associated with the intercept, be it the fixed mean, or the associated variances at any level; it does not fundamentally change the model.
Group mean centering is designed to isolate the within effect of a predictor variable measured at level 1 , and it makes a lot of sense to include the group means as a higher level variable to estimate this between effect. (The group means can be usefully be additionally grand centred to aid interpretation of the intercept.) It is also possible not to group mean centre the lower level variable but to just include the group means in the model specification (Mundlak model).
This article explains the different specifications and why it is so important to estimate the group mean effect, and to isolate the within effect:
Article Understanding and misunderstanding Group mean centering: a c...
The chapter on Contextual effects in this book show how to do it in practice.
Book Developing multilevel models for analysing contextuality, he...
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