# choice of mean for mean centering

I am doing statistical analysis of empirical data using a a generalized ordered regression model.

I would like to test for interaction terms.

I have a 3-level categorical IV (coded as 2 dummy variables), which divides my subjects (observations) into groups, and a few contineous IVs.

I am interested in testing interactions between my categorical IV and each of the contineous IVs.

I want to mean-center my contineous IVs for that, to avoid multicolinearity issues.

What mean should I use for that? The overall mean for all observations? Or should I mean-center my variables for each group separately?

(means for my contineous variables are different in different groups)

Which approach is more correct?

• Richard Williams of University of Notre Dame writes: "If you do center, be consistent throughout, i.e. different sample selections could produce different means, so comparing results produced by different centerings could be deceptive.", which I guess is my answer? (source: www3.nd.edu/~rwilliam/stats2/l53.pdf) – Mandarc Apr 3 '18 at 13:17

Richard Williams of University of Notre Dame writes:

"If you do center, be consistent throughout, i.e. different sample selections could produce different means, so comparing results produced by different centerings could be deceptive.", which I guess is my answer.

(source: www3.nd.edu/~rwilliam/stats2/l53.pdf)

It's perfectly fine to have different means for different groups. What's not fine is to calculate those means having your test set included. As you say, you are trying to test a hypothesis on your data. That test should be done on a set aside test set, which should not be taken into account when you estimate your means.

Mean-center the predictor variables. Generating polynomial terms (i.e., for $x_{1}, x_{1}^{2}, x_{1}^{3}$, etc.) or interaction terms (i.e., $x_{1}\times x_{2}$, etc.) can cause some multicollinearity if the variable in question has a limited range (e.g., [2,4]). Mean-centering will eliminate this special kind of multicollinearity. However, in general, this has no effect. It can be useful in overcoming problems arising from rounding and other computational steps if a carefully designed computer program is not used.