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Hi all

There isn't much literature out there on centring in models with 3 or more levels. My model is continuous Y on level 1, with fixed effects predictors at all 4 levels (no random effects in my study). My main interest is a predictor on level 2. Levels are students -> classes -> schools -> countries (there is sufficient variance on each level to justify a 4-level model). There is no multicollinearity issues (r>.8) in the model, no interaction terms or non-linear terms and no convergence issues experienced. However, I have class means as predictors. Enders & Tofighi (2007) suggest grand-mean centering of level 1 control variables in a two-level model when the main interest is a level-2 predictor, but the paper does not mention multiple levels. Furthermore, some of my control variables, like the level-1 student motivation, can be considered culture-specific (some cultures have higher or lower standards and complain more frequently). In that regard all the variables in a cross-national study would be better to be country-centred, but I haven't come across anything suggesting that.

The centring doesn't seem to influence the significance level, but since I have space-limitations I would prefer to follow a guideline (there's so much else to discuss!). Any suggestions, preferably with a reference or justification?

Professor Kelvyn Jones has asked me to pass on the following:

The use of grand mean centring of continuous has two useful properties. First it makes the intercept term more meaningful as it then gives the predicted mean value of the response when when the predictors are at their mean value. You are not then predicting beyond the range of the data. Second, the use of grand mean centring can help with estimation and convergence. It all depends on the extent to which a value of zero is a meaningful value for a variable.

Grand mean centring can be applied to continuous variables measured at all levels. This will not change the deviance nor the slope estimates nor the overall variance function but does give a more interpretable intercept.

On group mean centring you may wish to have a look at the following article which discusses these issues in relation to within and between models.

Andrew Bell and Kelvyn Jones (2014) Explaining Fixed Effects: Random Effects modelling of Time-Series Cross-Sectional and Panel Data Political Science Research and Methods 05/2014; online. DOI: 10.1017/psrm.2014.7 . This is downloable from https://www.researchgate.net/publicatio ... Panel_Data