DOE analysis: should I include an individual effect because I included the interaction?

Question

Hi everyone,

I have a very basic question regarding the fitting of a multivariate model using DoE data.
Suppose I have done a DoE (for example, using DSD) that allows me to consider 2-way interactions. I have now created a multivariate linear regression model for my response and verified that the interaction between A and B are significant but the individual factors themselves are not.
Should I include the individual factors A and B in my model because I have included the interaction between them (A*B) or that will only create a unnecessarily complex model?

Thank you!

statman · Answer

Mark is, of course correct.  I will just add some logic.  How could you change the interaction effect without changing the factors that are involved in the interaction?  You can't.  You must move the factors and that will result in the interaction effect.  Also realize that having the insignificant factors in the model will negatively affect the delta between R-square and R-square adjusted and insignificant p-values.  Not a problem, but some folks get hung up on those statistics.

Mark_Bailey · Answer

Yes.

This is called 'model hierarchy.' The A term and the B term are 'contained' within the A*B term, creating the hierarchy. JMP will warn you if you try to remove A or B when A*B remains in the model. You are allowed to remove either A or B but we recommend that you don't.