Interaction terms


New Member
Dear all, I would like to hear your thoughts/ideas/comments on this.

Brambor et al. (2006) write the following on interaction terms:
"The analyst cannot even infer whether X has a meaningful conditional effect on Y from the magnitude and significance of the coefficient on the interaction term either. As we showed earlier, it is perfectly possible for the marginal effect of X on Y to be significant for substantively relevant values of the modifying variable Z even if the coefficient on the interaction term is insignificant. Note what this means. It means that one cannot determine whether a model should include an interaction term simply by looking at the significance of the coefficient on the interaction term. Numerous articles ignore this point and drop interaction terms if this coefficient is insignificant. In doing so, they potentially miss important conditional relationships between their variables."

Yet, as one can read in Hayes' book moderation - and which is obvious when trying it in praxis - the interaction term's p-level is the p-level one gets for testing the increase in the R2 of an OLS upon adding the interaction term. Hence, if the interaction term is not significant, neither is the increase in R2.

So here's my question:
Suppose I, following Brambor et al., can show that for certain regions the marginal effect of the interaction indeed is significant different from zero, could one then not respond: So be it, but you should stick to the parsimonious model without the interaction term as the increase in R2 is not significant since the interaction term is not?

Brambor, Thomas, William Roberts Clark, and Matt Golder. 2006. “Understanding Interaction Models: Improving Empirical Analyses.” Political Analysis 14(1): 63–82.