Why add Interaction effects in MMM and How many interaction terms to add?

Last week I got a very interesting comment “How many interaction terms to include in MMM”.

This is a very pertinent question.

But lets step back for a minute and understand why add interaction effects?

📌 Why Add Interaction Effects?

We have been asked this questions in our courses and seminars too. “Why add the interaction effect in MMM? Wouldn’t the variables already in the model suffice?”

Y = β1X1+ β2X2 + e

The above is a simplistic representation of Multi linear regression or MMM (pls assume adstock transformed).

In this, your X’s are independent variables. Think of them as CTV and Meta for example.

Now what the above equation says is Meta always gives the same marginal return. CTV always gives the same marginal return. No matter what else is happening. The word ‘Marginal’ here means ‘on its own’ or’ ‘effect only due to it’

But we all know the reality is different.

In the real world:

TV builds awareness -> improves digital conversion
Search captures demand -> works better when brand is high affinity

So the real effect is: “The impact of CTV depends on Meta or vice versa”.

Interaction effects allows us to relax the rigid assumption that media / marketing variables operate independently without any effect on each other.

You might think:

“If both Meta and CTV are in the model, shouldn’t that capture everything?” No, Because:

– Individual terms capture direct effects
– Interaction captures joint effects

If you ignore interactions You get biased attribution:

– One channel may get too much credit and another could get too little
– or both look weaker than reality !!

How Many Interaction Effects to Add?

Sorry, but there is not magical number as such. But but there is a practical rule:

Include only the interactions you can defend.

In MMM, that usually means 2–5 interaction terms in most real world models

📌 What should drive inclusion?

Definitely not “let’s try all combinations” or a “stepwise regression”.

Include interactions only when you have a clear domain knowledge validated mechanism and historical proof of such effects.

For Example

TV × Digital -> awareness to conversion synergy
Search × Brand -> capture effect

If you can’t explain why the interaction exists, you shouldn’t include it.

There are statistical tests for this, will cover them in next post.

📌 What goes wrong if you include too many interactions?

One major problem is Multicollinearity.

Interaction terms are mathematically tied to their original variable. Inclusion of both the original variables and interaction effects could inflate multicollinearity. There is also risk of overfitting the model.

There is also risk of double counting if there is no real interaction effect.

High multicollinearity can lead to : unstable coefficients, Sign flipping and Nonsensical contributions.

In summary: Domain knowledge and statistics are your guard rails for adding Interaction effects.