Carryover vs Immediate Effects

[nupur-greenhouse]

Hi! I've been trying to figure out how you get % breakdown for Carryover vs Immediate effect come from in the one-pagers. I've seen the code in the main/R/R/model.R file. I am able to recreate the total decomposition based on the saturatedMedia * coef, but I can't get the breakdown of Immediate vs Carryover to match the output.

I am following that carryover = x_decay - rawMedia in Line 1. But I'm not sure what is going in Line 2 and Line 3. Can you help me understand this? Thank you very much.

Line 1: m_carryover <- m_adstocked - m
Line 2: m[m_carryover < 0] <- m_adstocked[m_carryover < 0] # adapt for weibull_pdf with lags
Line 3: m_carryover[m_carryover < 0] <- 0 # adapt for weibull_pdf with lags
Line 4: mediaImmediate[[v]] <- m
Line 5: mediaCarryover[[v]] <- m_carryover

[RachelMcNeely]

@nupur-greenhouse I'm also struggling to make the breakdown match the output in the pdf. I'm assuming I have a flaw in logic - but my xDecomp vectors match the decompMedia in pareto_media_transform_matrix.csv. The model is showing a 54% carryover response while I'm getting 99%. Any guidance on overall logic (or including the xDecompVector in an output file) would be helpful. I used Robyn 3.9 so maybe there is an update in 3.10.

Robyn_202303021027_init.zip

import numpy as np
import json

def saturation_fxn(adstocked_channel_spend, alpa, gamma):
    gammaTrans = round(np.quantile(np.linspace(min(adstocked_channel_spend), max(adstocked_channel_spend), 100), gamma), 4)
    x_scurve = adstocked_channel_spend ** alpha / (adstocked_channel_spend ** alpha + gammaTrans ** alpha)
    return x_scurve


'''
LOAD NECESSARY PARAMS AND DATA FROM OUTPUT CSV FILES
'''
parent_path = './Robyn_202303021027_init/'
solution = "4_75_6"

# Load hyperparams and media coefficients
hyperparams = pd.read_csv(parent_path + "pareto_hyperparameters.csv", index_col=0)
hyperparams = hyperparams[hyperparams['solID'] == solution]

coeff = pd.read_csv(parent_path + "pareto_aggregated.csv", index_col=0)
coeff = coeff[coeff['solID'] == solution]

media_transform = pd.read_csv(parent_path + "pareto_media_transform_matrix.csv", index_col=0)
media_transform = media_transform[media_transform['solID'] == solution]

# Select 1 channel for demonstration & get associated hyperparams
CHANNEL = 'tv_S'
alpha = hyperparams[f'{CHANNEL}_alphas'].iloc[0]
gamma = hyperparams[f'{CHANNEL}_gammas'].iloc[0]
theta = hyperparams[f'{CHANNEL}_thetas'].iloc[0]
channel_coefficient = coeff[coeff['rn'] == CHANNEL]['coef'].iloc[0]



'''
SEPARATE IMMEDIATE VS CARRYOVER MEDIA
https://github.com/facebookexperimental/Robyn/blob/1fc8cab41793250d6e817bc3b1f995edb3d364fb/R/R/model.R#L607-L6202
'''
raw_spend = media_transform[media_transform['type'] == 'rawMedia'][CHANNEL].values
adstocked_spend = media_transform[media_transform['type'] == 'adstockedMedia'][CHANNEL].values

spend_df = pd.DataFrame({'ds': media_transform[media_transform['type'] == 'rawMedia']['ds'].values,
                         'm': raw_spend,
                         'm_adstocked': adstocked_spend,
                         'm_carryover': adstocked_spend - raw_spend})

# m[m_carryover < 0] <- m_adstocked[m_carryover < 0] # adapt for weibull_pdf with lags
spend_df['m'] = np.where(spend_df['m_carryover'] < 0, spend_df['m_adstocked'], spend_df['m'])

# m_carryover[m_carryover < 0] <- 0 # adapt for weibull_pdf with lags
spend_df['m_carryover'] = np.where(spend_df['m_carryover'] < 0, 0, spend_df['m_carryover'])



'''
CALCULATE SATURATED MEDIA (I have confirmed saturation function is correct.)
https://github.com/facebookexperimental/Robyn/blob/1fc8cab41793250d6e817bc3b1f995edb3d364fb/R/R/model.R#L607-L6202
'''

rollWind_df = spend_df[spend_df['ds'].between("2016-01-01","2018-12-31")]
mediaSaturated = saturation_fxn(rollWind_df['m_adstocked'].values, alpha, gamma)
mediaSaturatedCarryover = saturation_fxn(rollWind_df['m_carryover'].values, alpha, gamma)
mediaSaturatedImmediate = mediaSaturated - mediaSaturatedCarryover



'''
CALCULATE RESPONSE (decomMedia). Essentially multiply saturated media by coefficient. 
https://github.com/facebookexperimental/Robyn/blob/1fc8cab41793250d6e817bc3b1f995edb3d364fb/R/R/model.R#L1025-L1049
'''
xDecomp = mediaSaturated * channel_coefficient
mediaDecompImmediate = mediaSaturatedImmediate * channel_coefficient
mediaDecompCarryover = mediaSaturatedCarryover * channel_coefficient

# Assert immediate + carryover response is equal to total response
assert round(mediaDecompImmediate.sum() + mediaDecompCarryover.sum(), 2) == round(xDecomp.sum(), 2)



'''
Calculate carryover percent of total response.
https://github.com/facebookexperimental/Robyn/blob/1fc8cab41793250d6e817bc3b1f995edb3d364fb/R/R/pareto.R#L477-L494
'''
df_caov = mediaDecompCarryover.sum()
df_total = xDecomp.sum()
[Robyn_202303021027_init.zip](https://github.com/facebookexperimental/Robyn/files/10874971/Robyn_202303021027_init.zip)

print(f'Carryover pct: {round(df_caov / df_total, 3)}') ```