Hi @Nir4,

Thank you for contacting us.

As you would be familiar, as spending on a given media channel within any given time period increases, you eventually see diminishing marginal returns, for example, saturation. Meridian models this saturation effect through the Hill function.

In order to combine the carryover effect with the shape effect, there are two possible approaches that specifically forms your query.

We could first apply the adstock transformation to the time series of media spend, and then apply
the shape transformation. An alternative way would be to reverse the order. If media spend in
each time period is relatively small compared to the cumulative spend across multiple time periods,
the shape effect in each time period is less obvious compared to that of cumulative media spend.
In this case, we would prefer to apply the shape transformation after the adstock transformation.
However, if the media spend is heavily concentrated in some single time periods with an on-and-off
pattern, the latter choice might be preferable. [Cited from section 2.3 of the paper on Bayesian methods for MMM with Carryover and Shape Effect.]

I would like to inform you that in Meridian, the Hill function can be applied either before or after the Adstock transformation, depending on the boolean hill_before_adstock argument of the ModelSpec. The default setting is hill_before_adstock = False, which makes the media effect of channel m within geo g and time period t equal to:

$\beta_{g,m}Hill(Adstock(x_t,x_{t-1},\cdots,x_{t-L}; \alpha_m);e_{cm},slope_m)$ [See here].

In addition, please note that the choice has less to do with implications to the causal inference and has more to do with the model-data fit and model identifiability.

Feel free to reach out if you have any questions or suggestions regarding Meridian.

Thank you,

Google Meridian Support Team