Centering with cross-level interaction

[Eran Itskovich]

Hi all,

I'm currently working on research in which I conduct a multilevel analysis. More specifically, my main interest is a cross-level interaction between two dichotomous categorical variables.
My question is about centering. I understand that it's useful on certain occasions, but from previous answers on this forum, I learned that it is mainly useful in terms of easier interpretation.
In my research, I illustrate the results of my cross-level interaction with a graph, so it should be clear to the readers what the results mean. Do I get this right? Are there any other reasons to center that I missed?

And following this:
1. In case I should center, do I center all my independent variables or just those of the cross-level interaction?
2. Does Stata have an automatic way to center variables, or should I create centered variables myself first?

Thanks!
Eran

[Erik Ruzek]

Dichotomous categorical variables, provided that they are coded 0/1, are already centered. Centering is useful in general because it helps to create a meaningful 0 value (in 0/1 binary variables, this is the reference group) but also specifically for multilevel models because centering can be useful for estimation and can help distinguish within- and between-group associations. For your purpose, I would focus on the interpretability angle and not center these variables. With an interaction involving two binary categorical variables, you can map them onto four distinct groups in your data, those cases representing the following values for binary variable 1 and 2: 0-0, 0-1, 1-0, and 1-1.

1. In case I should center, do I center all my independent variables or just those of the cross-level interaction?

This is up to you. If you center all variables, then the intercept is meaningful - it is the mean of the outcome when all other variables take on a value of 0.

2. Does Stata have an automatic way to center variables, or should I create centered variables myself first?

There is a user-written command from SSC called mcenter that you can use, but make sure that it does the centering you want. You can also do it yourself in code.

[Eran Itskovich]

Thank you very much, Erik. Your answer really helps.

I just came across a recent article ("Centering Categorical Predictors in Multilevel Models: Best Practices and interpretation", Yaremych et al., 2021) in which the authors say that categorical variables should be centered. For example, they state that "...we have demonstrated that centering guidelines for continuous predictors should be applied analogously to categorical predictors" (p. 8).

Am I missing something?