How to get response function of the weekly data?

[Aminshnn]

When we train the model, we usually provide weekly data. However, when we plot the response function especially after budget optimization, we get the response function for the whole budget, for example 3 years of data. I am wondering how we can get the response function for weekly spends?
In general, how can we have the formula of the response function for each channel? Suppose that I want to plot it but not using the built-in function, for example, I want to plot f(x)/x where f(x) is the response function.

I also want to get the value of response function without caryyover effect from previous spending.

[dattatreyam23]

Hi @Aminshnn,

Thank you for contacting us!

1. To get a response curve mapped specifically to a single weekly spend, you must narrow the summation window using the selected_times argument:

from meridian.analysis import analyzer

analyzer_instance = analyzer.Analyzer(mmm)

# Scope both the spend scaling and outcome summation to a specific week
weekly_response_ds = analyzer_instance.response_curves(
    selected_times=['2026-06-16'], # Exact week coordinate from your dataset
    use_posterior=True
)

# The resulting Dataset coordinates ('spend' and 'incremental_outcome') 
# will represent the single-week ranges.

You can also use the response_curves method to compute the response function in any case. For example, to compute f(x)/x, you can use:

import matplotlib.pyplot as plt
from meridian.analysis import analyzer

analyzer_instance = analyzer.Analyzer(mmm)

# 1. Get the raw response curve dataset scoped to your target week
response_ds = analyzer_instance.response_curves(
    selected_times=['2026-06-16'],  # Scope to a specific week
    use_posterior=True
)

# 2. Extract values for your target channel
channel_name = 'Search'
channel_ds = response_ds.sel(channel=channel_name)

# 3. Calculate Efficiency: f(x) / x
# 'incremental_outcome' has coordinates for metrics (mean, ci_lo, ci_hi)
f_x = channel_ds['incremental_outcome'].sel(metric='mean')
x = channel_ds['spend']

# Compute the custom efficiency curve
efficiency = f_x / x

# 4. Plot using your favorite plotting library
plt.plot(x.values, efficiency.values, label='Mean Efficiency')
plt.xlabel('Weekly Spend ($)')
plt.ylabel('Efficiency (Incremental Outcome / Spend)')
plt.title(f'Custom average efficiency curve for {channel_name}')
plt.grid(True)
plt.show()

2. To evaluate a single week with zero carryover from the past, you only need to pass a 1-week tensor for your target media channel. Since the time dimension is only 1 week, Meridian has no prior history to pull from, automatically reducing prior carryover to zero. Example:

import numpy as np
from meridian.analysis.analyzer import DataTensors

# 1. Create a 1-week spend array for your target channel (e.g., Channel 0)
n_geos = mmm.model_context.n_geos
n_channels = mmm.model_context.n_media_channels

# We only define media; other channels and controls fall back to history automatically
clean_slate_media = np.zeros((n_geos, 1, n_channels))
clean_slate_media[:, 0, 0] = 50000.0  # Spend/impressions for Channel 0

new_data = DataTensors(
    media=clean_slate_media,
    time=["2026-06-16"]  # A single week date label
)

# 2. Get the response curves
curves = analyzer_instance.response_curves(new_data=new_data, use_posterior=True)

Hope this helps. Feel free to reach out to us with any further queries regarding Meridian.

Thank you,

Google Meridian Support Team