Advertising and the S-Curve: A New Approach

Abstract

A flexible class of sigmoid or “S-shaped” functions useful in estimating the relationship between advertising and sales or market share is developed. The class, called the “odds” models, consists of functions able to depict relationships ranging from diminishing returns to nonsymmetric S-curves, including different saturation levels and nonzero intercepts. Which one of the member models applies to a given set of data can be determined on the basis of the estimated advertising coefficient, and thus it is easy to identify whether or not the relationship under analysis is S-shaped.