Set max delay on adstock and scale it back to actual spend

[cynthia10wang]

When running with geometric adstock, and assume the theta is 0.4, Robyn would transform adstocked media to be 10000 for week 1, 4000 for week 2, 1600 for week 3 etc. and this would continue till the end of the model period, which makes the total of adstocked media to be 10000/(1-0.4) = 16667...

When running with weibull (although more flexibility on shape), it would do similar and can scale up the adstocked spend extremely bigger (10x or 20x) when shape and scale ranges are large.

This is creating confusion as the response curves and budget allocator are ran based on adstocked spend. In real data we're running, there are two channels with very similar CPA, but one channel has large shape/scale hyperparameters causing the total of adstocked spend to be 16x larger than raw spend. thus skewing both the response curves and mean responses and then the buget reallocation.

Is there any plan to set a max on # of weeks of delaying effect and also scale it back? One of the idea is here in another MMM approach: https://github.com/leopoldavezac/BayesianMMM. Also see the comparison below: