Should the two variables in an interaction term both be included as regressors?

[Arren Zhou]

Hi everyone!

My question is that I'm trying to include an interaction term, say, AxB in a regression model. As for this case, should I also include both variables (A and B) as regressors in the same model? What would happen if I only have the interaction term AxB as the regressor but neither A nor B? Or, what would happen if I only have either A or B in the regression model along with the interaction term AxB?

situation 1: only AxB
situation2: AxB and A
situation3: AxB and B

Thank you!

[Jared Greathouse]

Just do

reg y a##b

You need both of them to interpret the interaction correctly

[Joro Kolev]

Yes, when you include interactions, you should include all the lower order terms. In your example if you have AXB, you should also have A and B as regressors.

This is known as the principle of marginality, I talk a bit more about it in the paper below, and you can also find the references to regression textbooks in the paper below.

Gender differences in cheating: Loss vs. gain framing
Lara Ezquerra, Gueorgui I. Kolev, Ismael Rodriguez-Lara,
Economics Letters 2018.

[Arren Zhou]

Dear Greathouse and Kolev,

Thank you for your help! I really appreciate it.

[Jared Greathouse]

Yeah and just know, you'll never need to manually include them. The syntax I used includes them by default