# How do you call multiple linear regression when it has an interaction term?

I'm writing a report and need to be precise but concise in the abstract. Currently I called it 'multiplicative multiple linear regression'. But when I Googled it, not much came up. In the same vein, I called multiple linear regression without the interaction term, additive multiple linear regression. But what is the official way to call it and be concise about it?

Technically, it is still called 'multiple linear regression' (assuming you do, in fact, have multiple predictors). I have at times seen the term 'multiple polynomial linear regression' when polynomial terms are added, but this is not that common; I've never seen 'multiplicative multiple linear regression'. In your abstract, you might consider simply noting that you included interaction terms. Better yet, if your field allows it, reference 'eq. 1', whereby in text, the full, expanded model with all terms are spelled out.

• Unfortunately, that is not possible. Something along the lines of "multiple linear regression with an interaction term", but man so many words lost :P Aug 27, 2015 at 18:51
• Few words are lost if you must explicitly reference both "multiple linear regression" and "interaction." Those with an acute need for brevity, though, might be content with saying they "controlled for interaction" or "included an interaction" (in the analysis), especially if the use of linear regression were either clear from the context or expected by the community of specialists who might read the abstract. ("Interaction" and "regression" together will imply "multiple regression" anyway).
– whuber
Aug 27, 2015 at 18:56
• Ah, now I get it. Aug 27, 2015 at 19:09
• (+1) I have joined your fan club.
– Carl
Mar 19, 2018 at 23:12

It is not a multiplicative model, which would be of the form $$y=\beta_0\beta_1^{x_1}\beta_2^{x_2}\epsilon.$$ Technically it is still a multiple regression model with an interaction term. (I think leaving out the "linear" is excusable in an abstract.)

You can use the term moderation. For example, let's say your dependent variable is some sort of self-esteem measure and you want to see whether the effect of some intervention on self-esteem is moderated by (depends on) gender, then your regression model has self-esteem as the dependent variable, and intervention group, gender, and the intervention*gender interaction term as predictors.

• Hmm this does give me some ideas :) but maybe I should elaborate. I have two multiple linear regressions that are very alike, basically one has an interaction term while the other doesn't. So in the case of these variables I have: (1) self-esteem = gender + intervention (2) self-esteem = intervention + gender + intervention * gender. The thing is I need to distinguish from them in the abstract. My hypothesis is about (1), but I need to perform (2) to prove that the predictors are indeed independent of each other. My supervisor demands it. So I'm looking for a concise term to describe them. Aug 27, 2015 at 18:54