Modelling the Emergence of New Technologies using S-Curve Diffusion Models

Three theoretical benchmark models of diffusion of new technologies are the substitution, mortality and social-learning models. These models tend to generate symmetric, right-skewed and left-skewed S-curves respectively. The empirical literature has focused primarily on fitting either Logistic or Gompertz functions to real data. Given that Logistic is symmetric and Gompertz is right skewed, the former is typically matched with the substitution model and the latter with the mortality model. Neither function can be used to describe the left-skewed social-learning model. We show here how the Generalized- Extreme-Value (GEV) function – which includes Gompertz as a special case and can be either left or right skewed – is more flexible and can be matched with either the mortality or social-learning model. Using cumulative citations as a proxy for diffusion, we fit Logistic, Gompertz and GEV S-curves to 12 citations data sets. Logistic emerges as the best fit for 6 data sets and GEV for the other 6 (all of which are right skewed). It follows that the social-learning model does not fit with any of our data sets. Truncating our data sets in 1996 or 2001 in all but one case does not change the best fit function. This suggests that our fitted S-curves could be useful for modelling aspects (such as the asymptotic upper limit) of a new technology’s future path.