While analyzing multi level model, which option should be used while including predictor variables from uncentered variable, group centered or grand mean centered?
Also guide about the implications of these three?
This paper may be helpful:
Hofmann, D. A., & Gavin, M. B. (1998). Centering decisions in hierarchical linear models: Implications for research in organizations. Journal of Management, 24(5), 623-641.
Enders, C. K., & Tofighi, D. (2007). Centering predictor variables in cross-sectional multilevel models: A new look at an old issue. Psychological Methods, 12(2), 121-138.
The Enders and Tofighi reference is a good starting point. If you want to separate out effects at level 1 and level 2 it can make sense to use the group centred predictor at level 1 and the group means as level two predictors. The total effect is the sum of these two effects. This sort of separation is not always interpretable, but can be revealing if it is (e.g., level 1 and level 2 effects can be different in magnitude or sign).
I have put a long answer including slides to this question
https://www.researchgate.net/post/What_is_and_what_is_not_a_contextual_variable_in_hierarchical_linear_models
Some of this material has now been worked up into
https://www.researchgate.net/publication/299604336_Fixed_and_Random_effects_making_an_informed_choice
Article Fixed and Random effects models: making an informed choice
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