Title: An inferential approach for the influential-imitator diffusion
Authors: Ringo Thomas Tchouya - IMSP (Benin) [presenting]
Stefano Nasini - IESEG School of Management (France)
Sophie Dabo - University of Lille (France)
Abstract: A new inferential approach is proposed for influential-imitator dynamics, a widely accepted extension of the traditional Bass diffusion model, for cases where the population has two segments: influentials (who influence each other) and imitators (whose choices are affected by those of the influentials). The main difficulty in using this continuous-time diffusion model is that the solution of the underlying differential equation is not an explicit function of its unknown parameters. We have some main results in the context of estimating the parameters of the influential-imitator dynamics. (1) We develop a truncated power series, providing an explicit solution of the differential equation; this results in an asymptotically correct approximation, with increasing accuracy as the spontaneous innovation/adoption parameter decreases. (2) we show that a block decomposition of the underlying parameter matrix leads to a double truncation of the power series which allows expressing explicitly the dependence of the likelihood function on the unknown parameter. After a detailed analysis of the theoretical properties, the proposed estimation approach is empirically tested using Michell and West's dataset of cannabis use by a cohort of students during their second, third and fourth year at a Glasgow high school.