How common are S-curves in Marketing Mix Models (MMM)?
Before we dwell on the S-curves, let’s talk about the Hill function.
Did you know that the Hill function used for transforming media variables to capture diminishing effect has its origins in Biochemistry and pharmacology!!
The equation was formulated by Archibald Hill in 1910 to describe oxygen binding to Hemoglobin.
Hill Function Formula w.r.t Marketing Mix Model (MMM) is in Fig 1, where:
S, the shape parameter, or slope, decides what shape the response curve will take: S curve or C-curve.
If S>1, the curve follows an S-shape
If S <1, the curve follows c-shape
Notice in Fig 2 that at S=2, the curve is S-shaped. (Black Curve) and at S =0.7, the curve is concave. (Blue Curve)
K – Inflection Point tells when the curve starts saturating/changing. Higher the value, the saturation will set in later.
The inflection point is constant for all the cases represented in Fig 2.
Coming to, “Does S curves exist “?
Well, it does exist.
But from my experience, I would say C curves are more common than S curves in Marketing.
What is your experience? Would you say S curves are more common than C curves?
