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An estimation approach for the influential-imitator diffusion
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DOI：10.1016/j.cor.2023.106315.png)
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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 wellknown hypothesis on peer influences, where the choices of popular children represent the leading effects to determine the habits of others.
Keyword:
influential-imitator diffusion
Asymptotic approximation
Maximum likelihood
Computational statistics
Social contagion
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