Centering discrete variables (1,2,3,to 100) in interaction terms

[Fimi Karimi]

Hi everyone,

It's often recommended to center continuous variables in interaction terms to make them more interpretable. However, I’m wondering: if I have a discrete variable that represents the ranking of countries (e.g., 1, 2, 3, ..., 100), does it make sense to center it?

Thanks.

[Maarten Buis]

yes, especially if 0 is not part of that variable. Remember that centering does not mean (pun intended) that you have to center at the mean. It just means (pun intended) that you choose some meaningful (pun intended) value for 0. Actually the mean is often a bad choice: it will change from dataset to dataset. For example, your variable is age and the mean age is meaningful (OK, I have pushed this pun far enough now). But real science is also about being able to replicate your study. So if someone tries to replicate your study using another dataset, than that person will get other results just because the mean age will differ. However, if you chose to center at some meaningful number within the range of the data, say 30, than you would have removed this source of randomness and it becomes easier to compare your results with the replication. It is also easier to communicate with your audience: we all have an idea about a 30 year old, but do we know the average age in your dataset?

So, back to your question. Yes center at some meaningful value in your variable. What that meaningful value is depends: could be 1 if you think the "best" country is the benchmark with which you want to compare all other countries, or N if you want to compare everybody to the worst country, or 10 if you want to compare everybody to a "good" country but not the "best" (you are in that case worried about outliers), or N/2 if you want to compare everybody to the middle country, or you can choose a country you are particularly interested in and use that countries rank, or ....

[Fimi Karimi]

Thank you so much for your detailed and helpful response. I really appreciate it, Maarten!