Ambiguitiy in `optimal_allocation_per_time_unit` argument of `plot_response_curve`

[openerror]

I think I finally figured it out with trial-and-error, but confirmation from people in the know would be great. Then if appropriate/feasible, I can contribute documentation.

The question is: after obtaining an optimized budget, how should I calculate optimal_allocation_per_timeunit for plot_response_curve? It is important to specify this argument, so that we get an intuitive, visual idea of how budgets should be shifted.

Following exactly the example notebook in this repo,

• I am allocating across 20 time periods and 7 media channels;
• optimal_budget_allocation is an array generated from optimization routines; it is of length 7 i.e. the number of media channels, and it sums up to about the budget I specified for the optimizer.
• optimal_allocation_per_timeunit is therefore media_scaler.transform(optimal_budget_allocation) / 20, where media_scaler is the CustomScaler object I trained to transform media variables.

^Is what I did correct? I tried several other things before, such as giving the plotting function optimal_budget_allocation directly, dividing that by 20 etc. It is simply not clear that I am supposed (?) to use media_scaler.

FYI, the documentation currently says the following about optimal_allocation_per_timeunit.

If ‘ optimal_allocation_per_timeunit is given it uses it to add markers based on historic average spend and the given optimal one on each of the individual subplots.

optimal_allocation_per_timeunit – Optimal allocation per time unit per media channel. This can be obtained by running the optimization provided by LightweightMMM.

[michevan]

I think you want optimal_allocation_per_timeunit to be media_scaler.transform(optimal_budget_allocation)/n_time_periods, but I agree this is unclear and we'll try to improve this workflow. Thanks for flagging this!