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data_generator.py
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851 lines (694 loc) · 32.1 KB
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import numpy as np
import pandas as pd
import pytensor.tensor as pt
from pymc_marketing.mmm.transformers import geometric_adstock, logistic_saturation
from datetime import datetime, timedelta
import xarray as xr
import matplotlib.pyplot as plt
class MMMDataGenerator:
def __init__(self, seed=42):
self.rng = np.random.default_rng(seed)
def generate_global_parameters(self):
"""Generate global parameters with more realistic variations"""
return {
# Channel-specific base parameters with more overlap
'alpha_channel_base': {
'TV': 0.8,
'Radio': 0.25,
'OOH': 0.35,
'Digital': 0.28
},
'alpha_country_sigma': 0.15,
'lambda_channel_base': {
'TV': 1.5,
'Radio': 2,
'OOH': 1,
'Digital': 6
},
'lambda_country_sigma': 0.4,
'effect_channel_base': {
'TV': 10,
'Radio': 6.0,
'OOH': 4.7,
'Digital': 8
},
'effect_country_sigma': 0.35,
'promo_mu': 1.3,
'promo_sigma': 0.2,
'base_mu': 2,
'base_sigma': 0.5
}
def generate_launch_dates(self, n_dates, countries):
"""Generate launch dates for each country"""
launch_dates = {}
# First country always starts from beginning
launch_dates[countries[0]] = 0
# Other countries start at random weeks
for country in countries[1:]:
# Random start between week 0 and week n_dates/2
launch_dates[country] = self.rng.integers(0, n_dates//2)
return launch_dates
def generate_country_parameters(self, global_params, countries, channels, launch_dates):
"""Generate country parameters with launch dates"""
country_params = {}
# Generate country sizes
country_sizes = self.rng.lognormal(0, 1, size=len(countries))
country_sizes = country_sizes / np.max(country_sizes)
# Generate shared effects
traditional_effect = abs(self.rng.normal(0, 0.3))
digital_effect = abs(self.rng.normal(0, 0.3))
for i, country in enumerate(countries):
country_effect = 0
country_params[country] = {
'size': country_sizes[i],
'launch_date': launch_dates[country],
'alphas': {
ch: np.clip(
global_params['alpha_channel_base'][ch] *
(1 + abs(self.rng.normal(country_effect, global_params['alpha_country_sigma']))),
0.1, 0.9
) for ch in channels
},
'lambdas': {
ch: max(0.1,
global_params['lambda_channel_base'][ch] *
(1 + abs(self.rng.normal(country_effect, global_params['lambda_country_sigma'])))
) for ch in channels
},
'effects': {
ch: global_params['effect_channel_base'][ch]*
(1 + abs(self.rng.normal(country_effect, global_params['effect_country_sigma'])))
# * (1 + traditional_effect)
# if ch != "Digital" else global_params['effect_channel_base'][ch] * (1 + digital_effect)
for ch in channels
},
'promo_multiplier': np.exp(
self.rng.normal(
np.log(global_params['promo_mu']),
global_params['promo_sigma'])
),
'base_sales': np.exp(
self.rng.normal(
np.log(global_params['base_mu']),
global_params['base_sigma'])
)
}
return country_params
def generate_media_data(self, n_dates, channels, country_size):
"""Generate media data with varying sparsity based on country size"""
spends = {}
# Adjust sparsity based on country size
base_prob = 0.2 * country_size # Smaller countries have sparser data
for channel in channels:
if channel == 'Digital':
# Generate more consistent digital spending
base_spend = self.rng.uniform(0, 1, size=n_dates)
spend = np.where(base_spend > (1 - base_prob),
base_spend * 0.75,
base_spend )
else:
# Generate sparser traditional media spending
base_spend = self.rng.binomial(1, base_prob, size=n_dates) # Generate
noise = np.where(base_spend>0, self.rng.normal(0, 0.2, size=n_dates),0)
spend = base_spend + noise
spend = np.clip(spend, 0, 2)
spends[channel] = spend
return spends
def generate_launch_dates(self, n_dates, countries, staggered_starts=False):
"""
Generate launch dates for each country
Parameters:
-----------
n_dates : int
Number of dates in the dataset
countries : list
List of countries
staggered_starts : bool
If True, countries start at different times with first country at 0
If False, all countries start at time 0
"""
launch_dates = {}
if staggered_starts:
# First country always starts from beginning
launch_dates[countries[0]] = 0
# Other countries start at random weeks
for country in countries[1:]:
# Random start between week 0 and week n_dates/2
launch_dates[country] = self.rng.integers(0, n_dates//2)
else:
# All countries start at time 0
for country in countries:
launch_dates[country] = 0
return launch_dates
def generate_dataset(self, n_dates, countries, channels, staggered_starts=False, noise_std=0.4):
"""
Generate dataset with optional staggered launches
Parameters:
-----------
n_dates : int
Number of dates
countries : list
List of countries
channels : list
List of channels
staggered_starts : bool
If True, uses staggered launch dates
If False, all countries start at time 0
noise_std : float
Standard deviation for noise
"""
global_params = self.generate_global_parameters()
launch_dates = self.generate_launch_dates(n_dates, countries, staggered_starts)
country_params = self.generate_country_parameters(global_params, countries, channels, launch_dates)
# Initialize arrays for all components
all_targets = np.zeros((len(countries), n_dates))
all_spends = np.zeros((len(countries), n_dates, len(channels)))
all_promos = np.zeros((len(countries), n_dates))
all_base_sales = np.zeros((len(countries), n_dates))
all_trends = np.zeros((len(countries), n_dates))
all_seasonality = np.zeros((len(countries), n_dates))
all_media_response = np.zeros((len(countries), n_dates, len(channels)))
all_noise = np.zeros((len(countries), n_dates))
all_promo_effects = np.zeros((len(countries), n_dates))
t = np.arange(n_dates)
trend_slope = 0.15
seasonal_amplitude = 10
amplitude = 10
overall_trend = trend_slope * t
overall_seasonal = seasonal_amplitude * np.sin(2 * np.pi * t / 52)
for i, country in enumerate(countries):
launch_date = country_params[country]['launch_date']
country_size = country_params[country]['size']
# Generate data only for post-launch period
active_dates = n_dates - launch_date
spends = self.generate_media_data(active_dates, channels, country_size)
promos = self.rng.binomial(1, 0.2 * country_size, size=active_dates)
# Place data after launch date
for j, channel in enumerate(channels):
all_spends[i, launch_date:, j] = spends[channel]
all_promos[i, launch_date:] = promos
# Store base sales
all_base_sales[i, launch_date:] = country_params[country]['base_sales']
# Store trend and seasonality
all_trends[i, launch_date:] = overall_trend[launch_date:]/10
all_seasonality[i, launch_date:] = overall_seasonal[launch_date:]/10
# Calculate and store media response
for j, channel in enumerate(channels):
if launch_date < n_dates:
spend = all_spends[i, :, j]
adstocked = geometric_adstock(
spend,
country_params[country]['alphas'][channel],
l_max=8,
normalize=True
).eval()
saturated = logistic_saturation(
adstocked,
country_params[country]['lambdas'][channel]
).eval()
all_media_response[i, :, j] = saturated * country_params[country]['effects'][channel]
# Store noise component
# noise_scale = noise_std * (1 + (1 - country_size))
noise_scale = 0.75
epsilon = np.zeros(n_dates)
epsilon[launch_date:] = self.rng.normal(0, noise_scale, size=active_dates)
all_noise[i, launch_date:] = epsilon[launch_date:]
# Calculate base response before promotional effect
base_response = (
all_base_sales[i, :] +
all_trends[i, :] +
all_seasonality[i, :] +
np.sum(all_media_response[i, :, :], axis=1) + # Sum across channels
all_noise[i, :]
)
# Calculate and store promotional effect
promo_effect = 0 #base_response * (all_promos[i, :] * (country_params[country]['promo_multiplier'] - 1))
all_promo_effects[i, :] = promo_effect
# Calculate final response
all_targets[i, :] = amplitude * (base_response + promo_effect)
dates = [datetime(2023, 1, 1) + timedelta(weeks=i) for i in range(n_dates)]
# Create an array of launch dates (one per country)
launch_date_arr = np.array([country_params[c]['launch_date'] for c in countries])
# Create dataset with all components
ds = xr.Dataset({
'target': xr.DataArray(all_targets, coords=[countries, dates], dims=['country', 'date']),
'spends': xr.DataArray(all_spends, coords=[countries, dates, channels], dims=['country', 'date', 'channel']),
'promotions': xr.DataArray(all_promos, coords=[countries, dates], dims=['country', 'date']),
'base_sales': xr.DataArray(all_base_sales, coords=[countries, dates], dims=['country', 'date']),
'trend': xr.DataArray(all_trends, coords=[countries, dates], dims=['country', 'date']),
'seasonality': xr.DataArray(all_seasonality, coords=[countries, dates], dims=['country', 'date']),
'media_response': xr.DataArray(all_media_response, coords=[countries, dates, channels],
dims=['country', 'date', 'channel']),
'noise': xr.DataArray(all_noise, coords=[countries, dates], dims=['country', 'date']),
'promo_effects': xr.DataArray(all_promo_effects, coords=[countries, dates], dims=['country', 'date']),
'launch_date': xr.DataArray(launch_date_arr, coords=[countries], dims=['country'])
})
return ds, global_params, country_params
def generate_dataset_with_dynamics(self, n_dates, countries, channels, staggered_starts=False,
apply_dynamic_effects=True, noise_std=0.4):
"""
Generate dataset with optional staggered launches and exponential decay effectiveness
Parameters:
-----------
n_dates : int
Number of dates
countries : list
List of countries
channels : list
List of channels
staggered_starts : bool, default=False
If True, uses staggered launch dates
If False, all countries start at time 0
apply_dynamic_effects: bool, default=True
If True, applies exponential decay to media effects over time
noise_std : float, default=0.4
Standard deviation for noise
"""
global_params = self.generate_global_parameters()
launch_dates = self.generate_launch_dates(n_dates, countries, staggered_starts)
country_params = self.generate_country_parameters(global_params, countries, channels, launch_dates)
# If applying dynamic effects, generate exponential decay effectiveness patterns
dynamic_effectiveness = {}
if apply_dynamic_effects:
for country in countries:
dynamic_effectiveness[country] = {}
# Parameters for exponential decay
initial_value = 1.0 # Start at full effectiveness
decay_rate = self.rng.uniform(0.012, 0.018) # Digital decays slightly faster
# Asymptote (floor) varies slightly by channel
asymptote = self.rng.uniform(0.25, 0.35)
# Create time indices
t = np.arange(n_dates)
# Generate smooth exponential decay curve
# Formula: y = asymptote + (initial_value - asymptote) * exp(-decay_rate * t)
effectiveness = asymptote + (initial_value - asymptote) * np.exp(-decay_rate * t)
# Store this effectiveness pattern
dynamic_effectiveness[country] = effectiveness
# Initialize arrays for all components
all_targets = np.zeros((len(countries), n_dates))
all_spends = np.zeros((len(countries), n_dates, len(channels)))
all_promos = np.zeros((len(countries), n_dates))
all_base_sales = np.zeros((len(countries), n_dates))
all_trends = np.zeros((len(countries), n_dates))
all_seasonality = np.zeros((len(countries), n_dates))
all_media_response = np.zeros((len(countries), n_dates, len(channels)))
all_noise = np.zeros((len(countries), n_dates))
all_promo_effects = np.zeros((len(countries), n_dates))
# Store dynamic effects if used
if apply_dynamic_effects:
all_dynamic_effects = np.zeros((len(countries), n_dates, len(channels)))
t = np.arange(n_dates)
trend_slope = 0.15
seasonal_amplitude = 10
amplitude = 10
overall_trend = trend_slope * t
overall_seasonal = seasonal_amplitude * np.sin(2 * np.pi * t / 52)
for i, country in enumerate(countries):
launch_date = country_params[country]['launch_date']
country_size = country_params[country]['size']
# Generate data only for post-launch period
active_dates = n_dates - launch_date
spends = self.generate_media_data(active_dates, channels, country_size)
promos = self.rng.binomial(1, 0.2 * country_size, size=active_dates)
# Place data after launch date
for j, channel in enumerate(channels):
all_spends[i, launch_date:, j] = spends[channel]
all_promos[i, launch_date:] = promos
# Store base sales
all_base_sales[i, launch_date:] = country_params[country]['base_sales']
# Store trend and seasonality
all_trends[i, launch_date:] = overall_trend[launch_date:]/10
all_seasonality[i, launch_date:] = overall_seasonal[launch_date:]/10
# Calculate and store media response
media_response = np.zeros(n_dates)
for j, channel in enumerate(channels):
if launch_date < n_dates:
spend = all_spends[i, :, j]
adstocked = geometric_adstock(
spend,
country_params[country]['alphas'][channel],
l_max=8,
normalize=True
).eval()
saturated = logistic_saturation(
adstocked,
country_params[country]['lambdas'][channel]
).eval()
# Apply dynamic effectiveness if enabled
if apply_dynamic_effects:
# Apply the effectiveness pattern for this country and channel
effectiveness = dynamic_effectiveness[country]
# Store for analysis
all_dynamic_effects[i, :, j] = effectiveness
# Apply to the media response
media_effect = saturated * country_params[country]['effects'][channel] * effectiveness
else:
media_effect = saturated * country_params[country]['effects'][channel]
all_media_response[i, :, j] = media_effect
# Store noise component
noise_scale = 0.75
epsilon = np.zeros(n_dates)
epsilon[launch_date:] = self.rng.normal(0, noise_scale, size=active_dates)
all_noise[i, launch_date:] = epsilon[launch_date:]
# Calculate base response before promotional effect
base_response = (
all_base_sales[i, :] +
all_trends[i, :] +
all_seasonality[i, :] +
np.sum(all_media_response[i, :, :], axis=1) + # Sum across channels
all_noise[i, :]
)
# Calculate and store promotional effect
promo_effect = 0 # Disabled in this version
all_promo_effects[i, :] = promo_effect
# Calculate final response
all_targets[i, :] = amplitude * (base_response + promo_effect)
dates = [datetime(2023, 1, 1) + timedelta(weeks=i) for i in range(n_dates)]
# Create an array of launch dates (one per country)
launch_date_arr = np.array([country_params[c]['launch_date'] for c in countries])
# Create dataset with all components
ds_components = {
'target': xr.DataArray(all_targets, coords=[countries, dates], dims=['country', 'date']),
'spends': xr.DataArray(all_spends, coords=[countries, dates, channels], dims=['country', 'date', 'channel']),
'promotions': xr.DataArray(all_promos, coords=[countries, dates], dims=['country', 'date']),
'base_sales': xr.DataArray(all_base_sales, coords=[countries, dates], dims=['country', 'date']),
'trend': xr.DataArray(all_trends, coords=[countries, dates], dims=['country', 'date']),
'seasonality': xr.DataArray(all_seasonality, coords=[countries, dates], dims=['country', 'date']),
'media_response': xr.DataArray(all_media_response, coords=[countries, dates, channels],
dims=['country', 'date', 'channel']),
'noise': xr.DataArray(all_noise, coords=[countries, dates], dims=['country', 'date']),
'promo_effects': xr.DataArray(all_promo_effects, coords=[countries, dates], dims=['country', 'date']),
'launch_date': xr.DataArray(launch_date_arr, coords=[countries], dims=['country'])
}
# Add dynamic effects if used
if apply_dynamic_effects:
ds_components['dynamic_effects'] = xr.DataArray(
all_dynamic_effects,
coords=[countries, dates, channels],
dims=['country', 'date', 'channel']
)
ds = xr.Dataset(ds_components)
return ds, global_params, country_params, dynamic_effectiveness if apply_dynamic_effects else None
def generate_potential_y(self, dataset, country_params, country, channel, t0, t1):
"""
Generate potential outcome by zeroing out specified channel during time period
Parameters:
-----------
dataset : xarray.Dataset
The dataset containing all variables
country_params : dict
Dictionary containing parameters for each country
country : str
Country to analyze
channel : str
Media channel to analyze
t0, t1 : datetime
Start and end dates for the analysis period
Returns:
--------
numpy.ndarray
Array of potential outcomes
"""
# Create a copy of the dataset to avoid modifying original
dataset = dataset.copy()
# Create mask for the intervention period
dates = dataset.coords['date'].values
mask = ~np.logical_and(dates >= t0, dates <= t1)
# Zero out the specified channel during intervention period
spends = dataset.spends.sel(country=country).copy()
spends.loc[dict(channel=channel)] = np.where(
mask,
spends.sel(channel=channel),
0
)
# Apply adstock transformation to all channels
adstocked = {
ch: geometric_adstock(
spends.sel(channel=ch).values,
country_params[country]['alphas'][ch],
l_max=8,
normalize=True
).eval()
for ch in dataset.coords['channel'].values
}
# Apply saturation transformation
saturated = {
ch: logistic_saturation(
adstocked[ch],
country_params[country]['lambdas'][ch]
).eval()
for ch in dataset.coords['channel'].values
}
# Calculate media effects
media_effects = sum(
saturated[ch] * country_params[country]['effects'][ch]
for ch in dataset.coords['channel'].values
)
# Get base components
base_sales = dataset.base_sales.sel(country=country)
trend = dataset.trend.sel(country=country)
seasonality = dataset.seasonality.sel(country=country)
noise = dataset.noise.sel(country=country)
# Calculate base response
base_response = (
base_sales +
trend +
seasonality +
media_effects +
noise
)
# Add promotional effects
promos = dataset.promotions.sel(country=country)
promo_multiplier = country_params[country]['promo_multiplier']
promo_effects = base_response * (promos * (promo_multiplier - 1))
# Final potential outcome with scaling factor
potential_y = 10 * (base_response + promo_effects)
return potential_y
def calculate_roas_by_period_dict(self, dataset, country_params, countries, channels, period='Q'):
"""
Calculate ROAS by period for each channel in each country, returning a nested dictionary
Parameters:
-----------
dataset : xarray.Dataset
The dataset containing all variables
country_params : dict
Dictionary containing parameters for each country
countries : list
List of countries to analyze
channels : list
List of media channels to analyze
period : str, optional
Time period for aggregation ('Q' for quarterly, 'M' for monthly)
Returns:
--------
dict
Nested dictionary containing ROAS values by country, channel, and period
"""
dates = pd.to_datetime(dataset.coords['date'].values)
df_dates = pd.DataFrame({'date': dates})
df_dates[period] = df_dates['date'].dt.to_period(period)
period_ranges = df_dates.groupby(period).agg({
'date': ['min', 'max']
})
roas_results = {}
for country in countries:
roas_results[country] = {}
for channel in channels:
channel_roas = {}
for idx, row in period_ranges.iterrows():
t0, t1 = row['date'][['min', 'max']]
# Get actual outcome and spend for this period
period_mask = np.logical_and(dates >= t0, dates <= t1)
actual_y = dataset.target.sel(country=country).values[period_mask].sum()
period_spend = dataset.spends.sel(
country=country,
channel=channel
).where(period_mask, 0).sum().item()
# Calculate ROAS if there was spend
if period_spend > 0:
potential_y = self.generate_potential_y(
dataset=dataset,
country_params=country_params,
country=country,
channel=channel,
t0=t0,
t1=t1
)
potential_y_sum = potential_y[period_mask].sum()
roas = (actual_y - potential_y_sum) / period_spend
else:
roas = 0
channel_roas[idx] = roas
roas_results[country][channel] = channel_roas
return roas_results
def compute_quarterly_roas(self, dataset, country_params, countries, channels):
"""
Compute ROAS by quarter for each channel in each country, returning a DataFrame
Parameters:
-----------
dataset : xarray.Dataset
The dataset containing all variables
country_params : dict
Dictionary containing parameters for each country
countries : list
List of countries to analyze
channels : list
List of media channels to analyze
Returns:
--------
pd.DataFrame
DataFrame containing quarterly ROAS values for each country-channel combination
"""
# Get ROAS results as dictionary
roas_results = self.calculate_roas_by_period_dict(
dataset=dataset,
country_params=country_params,
countries=countries,
channels=channels,
period='Q'
)
# Convert to DataFrame
roas_df = pd.DataFrame({
(country, channel): pd.Series(roas_dict)
for country, channels_dict in roas_results.items()
for channel, roas_dict in channels_dict.items()
}).round(2)
return roas_df
def compute_global_roas(self, dataset, country_params, countries, channels):
"""
Compute global ROAS for each channel in each country
Parameters:
-----------
dataset : xarray.Dataset
The dataset containing all variables
country_params : dict
Dictionary containing parameters for each country
countries : list
List of countries to analyze
channels : list
List of media channels to analyze
Returns:
--------
dict
Nested dictionary with structure {channel: {country: ROAS}}
"""
roas_dict = {channel: {} for channel in channels}
for country in countries:
actual_y = float(dataset.target.sel(country=country).values.sum())
for channel in channels:
total_spend = float(dataset.spends.sel(country=country, channel=channel).values.sum())
if total_spend > 0:
potential_y = self.generate_potential_y(
dataset=dataset,
country_params=country_params,
country=country,
channel=channel,
t0=dataset.coords['date'].values[0],
t1=dataset.coords['date'].values[-1]
)
potential_y_sum = float(potential_y.sum())
roas = (actual_y - potential_y_sum) / total_spend
else:
roas = 0.0
roas_dict[channel][country] = round(roas, 2)
return roas_dict
def plot_quarterly_roas(self, quarterly_roas, countries):
"""Plot quarterly ROAS for each country"""
fig, axes = plt.subplots(len(countries), 1, figsize=(15, 5*len(countries)))
if len(countries) == 1:
axes = [axes]
for idx, country in enumerate(countries):
ax = axes[idx]
country_data = quarterly_roas.loc[:, country]
country_data.plot(ax=ax, marker='o')
ax.set_title(f'{country} - Quarterly ROAS by Channel')
ax.set_xlabel('Quarter')
ax.set_ylabel('ROAS')
ax.grid(True, alpha=0.3)
ax.legend(title='Channel', bbox_to_anchor=(1.05, 1), loc='upper left')
plt.tight_layout()
return fig
def plot_global_roas(self, global_roas):
"""Plot global ROAS for all countries and channels"""
fig = plt.figure(figsize=(12, 6))
# Pivot the data for plotting
plot_data = global_roas.pivot(index='Channel', columns='Country', values='ROAS')
# Create the bar plot
ax = plot_data.plot(kind='bar', width=0.8)
plt.title('Global ROAS by Channel and Country')
plt.xlabel('Channel')
plt.ylabel('ROAS')
plt.xticks(rotation=45)
plt.grid(True, alpha=0.3)
plt.legend(title='Country', bbox_to_anchor=(1.05, 1), loc='upper left')
plt.tight_layout()
return fig
def plot_potential_outcomes(self, dataset, country_params, country, channel, period='Q'):
"""Plot actual vs potential outcomes for each period"""
dates = dataset.coords['date'].values
df_dates = pd.DataFrame({'date': dates})
df_dates[period] = pd.to_datetime(dates).to_period(period)
period_ranges = df_dates.groupby(period).agg({'date': ['min', 'max']})
fig, axes = plt.subplots(
nrows=len(period_ranges),
ncols=1,
figsize=(15, 4*len(period_ranges)),
sharex=True,
sharey=True
)
if len(period_ranges) == 1:
axes = [axes]
for i, (idx, row) in enumerate(period_ranges.iterrows()):
ax = axes[i]
t0, t1 = row['date'][['min', 'max']]
# Generate potential outcome
potential_y = self.generate_potential_y(
dataset=dataset,
country_params=country_params,
country=country,
channel=channel,
t0=t0,
t1=t1
)
# Plot actual vs potential
actual_y = dataset.target.sel(country=country)
ax.plot(dates, actual_y, 'k-', label='Actual')
ax.plot(dates, potential_y, 'b--', label='Potential')
# Add mask period
mask_period = np.logical_and(dates >= t0, dates <= t1)
ax.axvspan(t0, t1, alpha=0.2, color='gray')
ax.set_title(f'{period} {idx}')
ax.legend()
plt.tight_layout()
return fig
def compute_true_roas(self, dataset):
"""
Compute true ROAS values from generated data
Parameters:
-----------
dataset : xarray.Dataset
The generated dataset containing media_response and spends
Returns:
--------
dict
Nested dictionary with true ROAS values by channel and country
"""
countries = dataset.coords['country'].values
channels = dataset.coords['channel'].values
true_roas = {channel: {} for channel in channels}
for channel in channels:
for country in countries:
spends = dataset.spends.sel(country=country, channel=channel)
total_spend = float(spends.sum().values)
if total_spend > 0:
# Get media response for this channel
media_response = dataset.media_response.sel(
country=country,
channel=channel
).sum().values
# Calculate ROAS
roas = float(media_response) / total_spend
else:
roas = 0.0
true_roas[channel][country] = round(roas, 2)
return true_roas