Estimating daily effect with adstock/saturation transformation

[tjadipeeters]

Thanks for this great library (please let me know if I should move this to discussions). Not 100% sure whether this is related to this issue, please let me know if it is.

I am wondering what the best way is to get an estimated effect per day accounting for the lagged effects of adstock. Often it is quite nice to be able to retrieve the effect to the specific day the impressions/ spend happened (i.e. when you want to integrate these numbers with other datasets).

For example, if I have an array of impressions: [1,0,0], the data after an adstock transformation could be something along the lines of [1, 0.2, 0.04] with contribution values of: [10, 2, 0.4]. In this example it is quite obvious that the effect of the impression at index 0 is 10 + 2 + 0.4 = 12.4, but when you have daily impressions this becomes a bit more complex. In the past I did calculate these values for non-Bayesian models, but am wondering how to approach it using this library/ with Bayesian models. The saturation effect will play a role also I suppose. If anyone more familiar with the specifics of the library can give some pointers, I could do some analysis into it and whether it is possible.

I used the code below to test whether the compute_mean_contributions_over_time function already produces these results, but it seems to me that it produces the values only for the day the increase/decrease in the target variable occurred.

dataset = pd.DataFrame(
  {
    'channel' : [1, 0, 0, 0], 
    'result' : [1, 0.2, 0.04, 0], 
    'date' : ['2023-01-31 00:00:00', '2023-02-01 00:00:00', '2023-02-02 00:00:00', '2023-02-03 00:00:00']
    })

mmm = DelayedSaturatedMMM(
    data=dataset,
    target_column="channel",
    date_column="date",
    channel_columns=["channel"],
    adstock_max_lag=3
)
mmm.fit(target_accept=0.95, chains=2, random_seed=2)

get_mean_contributions_over_time_df = mmm.compute_mean_contributions_over_time(original_scale=True)
get_mean_contributions_over_time_df