There are two reasons to center predictor variables in any type of regression analysis–linear, logistic, multilevel, etc.
1. To lessen the correlation between a multiplicative term (interaction or polynomial term) and its component variables (the ones that were multiplied).
2. To make interpretation of parameter estimates easier.
I was recently asked when is centering NOT a good idea?
Well, basically when it doesn’t help.
For reason #1, it will only help if you have multiplicative terms in a model. If you don’t have any multiplicative terms–no interactions or polynomials–centering isn’t going to help.
For reason #2, centering especially helps interpretation of parameter estimates (coefficients) when:
a) you have an interaction in the model
b) particularly if that interaction includes a continuous and a dummy coded categorical variable and
c) if the continuous variable does not contain a meaningful value of 0
d) even if 0 is a real value, if there is another more meaningful value such as a threshold point. (For example, if you’re doing a study on the amount of time parents work, with a predictor of Age of Youngest Child, an Age of 0 is meaningful and will be in the data set, but centering at 5, when kids enter school, might be more meaningful).
So when NOT to center:
1. If all continuous predictors have a meaningful value of 0.
2. If you have no interaction terms involving that predictor.
3. And if there are no values that are particularly meaningful.