michaelis_menten#

pymc_marketing.mmm.transformers.michaelis_menten(x, alpha, lam)[source]#

Evaluate the Michaelis-Menten function for given values of x, alpha, and lambda.

\[\alpha \cdot \frac{x}{\lambda + x}\]
where:

  • \(x\): Channel spend.

  • \(\alpha\): Maximum contribution.

  • \(\lambda\) (k): The half-saturation point.

(Source code)

(Source code)

Parameters:
xfloat

The spent on a channel.

alphafloat

The saturation point. It represents the maximium number of customers that could be acquired through this channel at any point time. Must be non-negative.

lamfloat

The half-saturation point. Larger values represent less efficient channels.

Returns:
float

The value of the Michaelis-Menten function given the parameters.