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.

Examples

Create a new saturation transformation:

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


class InfiniteReturns(SaturationTransformation):
    lookup_name: str = "infinite_returns"

    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.