An estimation approach for the influential–imitator diffusion

This paper presents a numerical estimation procedure for the influential–imitator diffusion, an extension to the Bass model in which a population is partitioned into two segments: influentials (who influence each other) and imitators (whose choices are affected by the ones of influentials). Focusing...

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Bibliographic Details
Published in:Computers & operations research 2023-11, Vol.159, p.106315, Article 106315
Main Authors: Tchouya, Ringo Thomas, Nasini, Stefano, Dabo-Niang, Sophie
Format: Article
Language:English
Subjects:
Asymptotic approximation
Computational statistics
influential–imitator diffusion
Mathematics
Maximum likelihood
Social contagion
Statistics
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Summary:This paper presents a numerical estimation procedure for the influential–imitator diffusion, an extension to the Bass model in which a population is partitioned into two segments: influentials (who influence each other) and imitators (whose choices are affected by the ones of influentials). Focusing on the estimation of the model parameters, we propose a maximum likelihood approach and investigate its numerical solvability, building on an asymptotic approximation of the underlying differential equation. Specifically, we develop a truncated series expansion, exhibiting an increasing accuracy when the spontaneous innovation decreases. After uncovering the theoretical properties of the proposed methodology, we propose a specialized block coordinate descent method for the numerical maximization of the likelihood function. Empirical and computational tests are provided using the Michell and West dataset about the cannabis consumption of a cohort of students over their second, third and fourth year at a secondary school in Glasgow. The estimated imitation pattern confirms the well-known hypothesis on peer influences, where the choices of popular children represent the leading effects to determine the habits of others. •Maximum likelihood estimation of the influential–imitator extension of the Bass model.•Asymptotic approximation by truncated series expansion.•Block coordinate descent method.•Empirical tests focusing on the diffusion of cannabis consumption.
ISSN:0305-0548
1873-765X
DOI:10.1016/j.cor.2023.106315