Time-Shift Curves

[steven-struglia]

Hello! I want to make plots associated with my model that detail how much time has elapsed to realize the full impact of spend on a media channel. I want to plot on x: days elapsed since spend, and y: the cumulative effect of the original spend over the days. It would look quite similar to a saturation/response curve that we have already, but would offer a different insight like "how many days will it be until we see the full impact of Facebook spending". I was thinking I could just use the lag_weight parameter to calculate this, since it represents how much impact the spend on day t carries into day t+1. I pasted the code that I believe is the correct way to do this, but please let me know if my understanding of this parameter is wrong.

n_days = 40
lag_weights = mmm.trace['lag_weight'].T
shift_curves = pd.DataFrame()
for x,col in list(zip(lag_weights, mdsp_cols)):
    x = x.mean()
    # Since lag_weight is the fraction we carry into the next day, 1-lag_weight gives us the realized spend
    #      day 0                  day 1                               day 2                                          day 3
    # (1-lag_weight) + (lag_weight)(1-lag_weight)  + (lag_weight)(lag_weight)(1-lag_weight) + (lag_weight)(lag_weight)(lag_weight)(1-lag_weight)
    lag_weight = x
    realized = 1-x
    shift_vals = [realized]
    for i in range(1,n_days):
        shift_vals.append(shift_vals[-1] + realized*(lag_weight**i))
    shift_curves[col] = shift_vals

for x in shift_curves.columns:
    plt.plot(shift_curves[x])
    plt.title(x)
    plt.show()