I have a cross-sectional panel dataset with observations that are country-years (12 years for 25 countries, so 300 observations). I'm running a multilevel model that includes a random intercept for countries, but has fixed slopes for all countries. Importantly, all my covariates vary across countries and years too, so they can all be regarded as level-1 variables. I fit the model and then compare predicted outcomes against actually observed outcomes.
Curiously, uncertainty around effect estimates is smaller if I center my predictors around their grand means, but the predictions are much more accurate (compared to my observed outcomes) when I center predictors by groups (subtract group means) instead.
- In a random intercept, fixed slope model where all predictors vary within and across groups, is it necessary to center around the group-mean? The interpretation of coefficients feels unnatural, as it is dependent on the group-mean but overall effects are the same for different groups.
- Why would grand-mean centering lead to better estimates, but group-mean centering result in better predictions?
I apologize for the lack of replication materials, but I am unable to provide them.