interpretation and inclusion of interaction terms in regression model

[csetzkorn]

I have a 3-way interaction model as follows:

Y = A + B + C + A*B + A*C + B*C + A*B*C

A is a dummy and B and C are centred continuous variables.

I am mainly interested in the parameters for BC and B. The interpretation of these parameters depends on the inclusion of AB*C and all 2-way interactions. I am using SAS and PROC GLMSELECT with selection=none, thus (IMHO) forcing the interactions to be included? 

For some data the p-values for the aforementioned interactions are above 0.05. Does that mean they are not ‘included’ and thus the interpretation of the aforementioned parameters changes?

Any feedback would be very much appreciated.

[Norman21]

I'm not quite sure what your are trying to do.

If you must have "AB*C and all 2-way interactions" in the model, then it sound like you must include everything in the model.

The P values are only indicating where you might like to make changes to the model.

Remember, if you include higher terms then you should include the lower terms (e.g. include A and B if you are going to keep A*B).

[PaigeMiller · Accepted solution]

For some data the p-values for the aforementioned interactions are above 0.05. Does that mean they are not ‘included’ and thus the interpretation of the aforementioned parameters changes?

You will find statisticians who advise removing terms from the model where the p-values are above 0.05. You will find statisticians who advise the opposite. I find myself in the group who advises you to not remove these terms from the model.

Removing terms from the model requires you to re-fit the model, and yes then not only the interpretation of the model changes but the coefficients change as well.

As the other commenter said, if you include B*C in the model, then you need to make sure B and C individually are included.