Centering control variables in an interaction regression model -

[em lowthian]

Hi forum members,

Building on my last post about interaction interpretation - I'm looking to run a multitude of interaction models.

My interaction models will include the main effects of X (independent variable) and M (moderator) along with them being multiplied i.e. #.# or * . For some models there will be a need to centre (subtract the mean) as some are highly correlated - I am not looking to discuss this as I have adequately justified this elsewhere, but looking for guidance on my next step.

I also am including control variables - like Hayes and Matthes (2009) and Linneman (2014). Is it neccessary to center all control and main effects variables? Or is it just neccessary to center the variables which form the interaction for interpretation?

Many thanks

E

[Richard Williams]

You don't need to center, but it may make interpretation a little easier. The intercept is the predicted value of Y when all Xs = 0. Zero may be an impossible value. But if you center all Xs, then the intercept is the predicted value for a person who has average values on all the Xs.

You don't center categorical IV. So, a value of 0 on female may mean male. Then, the intercept is the predicted score for a male who has average values on all the other Xs.

Also you don't have to center at the mean. In the US, you might subtract 12 from years of education. Then the intercept is the score for a high school graduate with average values on the other Xs.

Again, you don't have to center. There are other ways to get the same information, like by using margins. This is just one way to facilitate interpretation.

For more see

https://www3.nd.edu/~rwilliam/stats2/l53.pdf

[em lowthian]

Hi Richard,

Thanks again for spending time on this issue for me.

Ok, thank you. I think after our post on standardisation, centering will definitely aid my interpretation. Yes I am aware that categorical variables are not centered - thank you.
I will likely centre by the mean as it is easier for me to interpret and reference in my project.

My main question here was the control variables that are not going to be interpreted but they will be controlling the main effects/moderation analysis and whether along with the main effects, do control variables i.e. sex, age etc. need to be centered too? I am assuming yes so the model uses meaningful 0's at each coefficient.

In addition to this - on an unrelated point, can I run continous*continous regressions using the #.# you specified yesterday?

E

[Richard Williams]

Centering the control variables will make the intercept easier to interpret, if that is something you want to do.

The main issue with mean centering is that the mean will differ across different samples. If you are only using one data set mean centering may be fine.

For continuous by continuous interactions, just do something like

reg y x1 x2 c.x1#c.x2

Remember c., since the default with the # and ## operators is to assume the variables are categorical.

[em lowthian]

I am not wanting to interpret the control variables, they are theorised to have an effect on Y - so, I am wondering if I only need to centre the main effects for the interaction? However, if a regression has the main effects centered and then 3 control variables uncentered could this be problematic in terms of the model?

I am only using one dataset.

Yes indeed to clarify c. is continous and i. is categorical?

Emily

[Richard Williams]

Yes indeed to clarify c. is continous and i. is categorical?

Yes.

I am not wanting to interpret the control variables, they are theorised to have an effect on Y - so, I am wondering if I only need to centre the main effects for the interaction? However, if a regression has the main effects centered and then 3 control variables uncentered could this be problematic in terms of the model?

There is no need to center the controls UNLESS you want to easily interpret the intercept as well. Centering the controls will also affect the value of the intercept. Further, centering won't change the coefficients for the controls, it will only change the intercept.

If in doubt, just go ahead and try it with and without centering and see what happens.

[em lowthian]

Many thanks Richard. I will post on our last thread the results shortly.