saturation

Saturation transformations for the MMM model.

Each of these transformations is a subclass of pymc_marketing.mmm.components.saturation.SaturationTransformation and defines a function that takes media and return the saturated media. The parameters of the function are the parameters of the saturation transformation.

Notes

The wrapper classes in this module extend the transformer functions in pymc_marketing.mmm.transformers with the priors needed to fit them in a model. Several wrappers also introduce an extra scaling parameter that the underlying transformer does not take, so the curve can reach a value other than the bounded range of the transformer:

• LogisticSaturation, InverseScaledLogisticSaturation, TanhSaturationBaselined, HillSaturation, RootSaturation, and NoSaturation multiply the output by beta.

• MichaelisMentenSaturation, TanhSaturation, and HillSaturationSigmoid do not add an extra parameter because the underlying function already exposes the asymptote (alpha, b, or sigma).

See each class for the full list of parameters and their default priors.

Examples

Create a new saturation transformation:

from pymc_marketing.mmm import SaturationTransformation
from pymc_extras.prior import Prior


from pymc_marketing.serialization import serialization


@serialization.register
class InfiniteReturns(SaturationTransformation):
    def function(self, x, b):
        return b * x

    default_priors = {"b": Prior("HalfNormal", sigma=1)}

Plot the default priors for a saturation transformation:

from pymc_marketing.mmm import HillSaturation

import matplotlib.pyplot as plt

saturation = HillSaturation()
prior = saturation.sample_prior()
curve = saturation.sample_curve(prior)
saturation.plot_curve(curve)
plt.show()

Define a hierarchical saturation function with only hierarchical parameters for saturation parameter of logistic saturation.

from pymc_extras.prior import Prior
from pymc_marketing.mmm import LogisticSaturation

hierarchical_lam = Prior(
    "Gamma",
    alpha=Prior("HalfNormal"),
    beta=Prior("HalfNormal"),
    dims="channel",
)
priors = {
    "lam": hierarchical_lam,
    "beta": Prior("HalfNormal", dims="channel"),
}
saturation = LogisticSaturation(priors=priors)

Functions

saturation_from_dict(data)

Get a saturation function from a dictionary.

Classes

HillSaturation([priors, prefix])	Wrapper around Hill saturation function.
HillSaturationSigmoid([priors, prefix])	Wrapper around Hill saturation sigmoid function.
InverseScaledLogisticSaturation([priors, prefix])	Wrapper around inverse scaled logistic saturation function.
LogisticSaturation([priors, prefix])	Wrapper around logistic saturation function.
MichaelisMentenSaturation([priors, prefix])	Wrapper around Michaelis-Menten saturation function.
NoSaturation([priors, prefix])	Wrapper around linear saturation function.
RootSaturation([priors, prefix])	Wrapper around Root saturation function.
SaturationTransformation([priors, prefix])	Subclass for all saturation transformations.
TanhSaturation([priors, prefix])	Wrapper around tanh saturation function.
TanhSaturationBaselined([priors, prefix])	Wrapper around tanh saturation function.