Centering Predictor Variables in Cross-Sectional Multilevel Models: A New Look at an Old Issue

Appropriately centering Level 1 predictors is vital to the interpretation of intercept and slope parameters in multilevel models (MLMs). The issue of centering has been discussed in the literature, but it is still widely misunderstood. The purpose of this article is to provide a detailed overview of grand mean centering and group mean centering in the context of 2-level MLMs. The authors begin with a basic overview of centering and explore the differences between grand and group mean centering in the context of some prototypical research questions. Empirical analyses of artifical data sets are used to illustrat key points thoughout. The artical provide a number of practical recommendations designed to facilitate centering decisions in MLM applications.
http://www-bcf.usc.edu/~sping/PM-515/references/Enders%202007%20centering%20in%20multilevel%20analysis.pdf

Occup Health Psychol. 2000 Jan;5(1):182-90.

A multilevel analysis of the demands--control model: is stress at work determined by factors at the group level or the individual level?

Van Yperen NW, Snijders TA.

Abstract
This study explored the extent to which negative health-related outcomes are associated with differences between work groups and with differences between individuals within work groups using R.A. Karasek's (1979) demands-control model. The sample consisted of 260 employees in 31 working groups of a national bank in the Netherlands. Results suggest that job demands and job control should be conceptualized as having both group- and individual-level foundations. Support for Karasek's demands-control model was found only when these variables were split into the 2 parts, reflecting shared perceptions and employees' subjective assessment, respectively. One of the most appealing practical implications is that absence rates among homogeneous work groups can be reduced by enhancing actual control on the job.

group-mean centering 和grand-mean centering 到底有什么区别，该怎么区分使用呢