meridian.model.equations.ModelEquations

Provides core, stateless mathematical functions for Meridian MMM.

meridian.model.equations.ModelEquations(
    model_context: meridian.model.context.ModelContext
)

Methods

adstock_hill_media

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adstock_hill_media(
    media: meridian.backend.Tensor,
    alpha: meridian.backend.Tensor,
    ec: meridian.backend.Tensor,
    slope: meridian.backend.Tensor,
    decay_functions: (str | Sequence[str]) = constants.GEOMETRIC_DECAY,
    n_times_output: (int | None) = None
) -> meridian.backend.Tensor

Transforms media or using Adstock and Hill functions in the desired order.

Args
media	Tensor of dimensions (n_geos, n_media_times, n_media_channels) containing non-negative media execution values. Typically this is impressions, but it can be any metric, such as media_spend. Clicks are often used for paid search ads.
alpha	Uniform distribution for Adstock and Hill calculations.
ec	Shifted half-normal distribution for Adstock and Hill calculations.
slope	Deterministic distribution for Adstock and Hill calculations.
decay_functions	String or sequence of strings denoting the adstock decay function(s) for each channel. Default: 'geometric'.
n_times_output	Number of time periods to output. This argument is optional when the number of time periods in media equals n_media_times, in which case n_times_output defaults to n_times.

Returns
Tensor with dimensions [..., n_geos, n_times, n_media_channels] representing Adstock and Hill-transformed media.

adstock_hill_rf

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adstock_hill_rf(
    reach: meridian.backend.Tensor,
    frequency: meridian.backend.Tensor,
    alpha: meridian.backend.Tensor,
    ec: meridian.backend.Tensor,
    slope: meridian.backend.Tensor,
    decay_functions: (str | Sequence[str]) = constants.GEOMETRIC_DECAY,
    n_times_output: (int | None) = None
) -> meridian.backend.Tensor

Transforms reach and frequency (RF) using Hill and Adstock functions.

Args
reach	Tensor of dimensions (n_geos, n_media_times, n_rf_channels) containing non-negative media for reach.
frequency	Tensor of dimensions (n_geos, n_media_times, n_rf_channels) containing non-negative media for frequency.
alpha	Uniform distribution for Adstock and Hill calculations.
ec	Shifted half-normal distribution for Adstock and Hill calculations.
slope	Deterministic distribution for Adstock and Hill calculations.
decay_functions	String or sequence of strings denoting the adstock decay function(s) for each channel. Default: 'geometric'.
n_times_output	Number of time periods to output. This argument is optional when the number of time periods in reach equals n_media_times, in which case n_times_output defaults to n_times.

Returns
Tensor with dimensions [..., n_geos, n_times, n_rf_channels] representing Hill and Adstock-transformed RF.

calculate_beta_x

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calculate_beta_x(
    is_non_media: bool,
    incremental_outcome_x: meridian.backend.Tensor,
    linear_predictor_counterfactual_difference: meridian.backend.Tensor,
    eta_x: meridian.backend.Tensor,
    beta_gx_dev: meridian.backend.Tensor
) -> meridian.backend.Tensor

compute_non_media_treatments_baseline

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compute_non_media_treatments_baseline(
    non_media_baseline_values: (Sequence[str | float] | None) = None
) -> meridian.backend.Tensor

linear_predictor_counterfactual_difference_media

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linear_predictor_counterfactual_difference_media(
    media_transformed: meridian.backend.Tensor,
    alpha_m: meridian.backend.Tensor,
    ec_m: meridian.backend.Tensor,
    slope_m: meridian.backend.Tensor
) -> meridian.backend.Tensor

linear_predictor_counterfactual_difference_rf

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linear_predictor_counterfactual_difference_rf(
    rf_transformed: meridian.backend.Tensor,
    alpha_rf: meridian.backend.Tensor,
    ec_rf: meridian.backend.Tensor,
    slope_rf: meridian.backend.Tensor
) -> meridian.backend.Tensor