michaelis_menten

pymc_marketing.mmm.transformers.michaelis_menten(x, alpha, lam)

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

The Michaelis-Menten function models enzyme kinetics and describes how the rate of a chemical reaction increases with substrate concentration until it reaches its maximum value.

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

where:

• \(x\): Channel spend or substrate concentration.

• \(\alpha\): Maximum contribution or efficiency factor.

• \(\lambda\) (k): Michaelis constant, representing the threshold substrate concentration.

(Source code, png, hires.png, pdf)

(Source code, png, hires.png, pdf)

(png, hires.png, pdf)

Parameters:

xfloat

The spent on a channel.

alphafloat

The maximum contribution a channel can make.

lamfloat

The Michaelis constant for the given enzyme-substrate system.

Returns:

float

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