Adstock & transformations

[ASevastkms]

Hello! As I understand it, Robin first transforms media variables by adding ADstock, and then saturation. Why this particular order? The only source I found is an article by Jin, Y., Wang, Y., Sun, Y., Chan, D. & Koehler, J. (2017). Bayesian methods for media mix modeling with carryover and shape effects, which actually provides a very concise rationale for choosing a sequence of transformations. Has anyone faced this issue? After all, these transformations are not commutative and the order of their application will change the result.

[gufengzhou]

This is a good question. We do have a reason behind the order of first adstock second saturation. For an always-on channel as an example, if you shut it down for a day, it probably will still convert on that day due to adstock. This means adstock is part of the saturation curve. Or to be precise, adstock is on the bottom of saturation curve, while actual spend sits on the higher part of the curve on top of adstock. This is exactly how robyn calculates the immediate & carryover effect for media channels.

[ASevastkms]

Thanks, but I don't quite understand your logic. If transforms were applied first and then adstock, then this "shutdown day" would also have a non-zero contribution from the media. So what's the difference?

[gufengzhou]

No it's adstock first, saturation second. They're both data transformation.
Maybe this: we believe adstock can also saturate, same behaviour as raw spend. That's why we do adstock first, so that it gets the diminishing behaviour afterwards.