STAR: Spread of innovations on graph structures with the Susceptible‐Tattler‐Adopter‐Removed model

Abstract

Adoptions of a new innovation such as a product, service or idea are typically driven both by peer‐to‐peer social interactions and by external influence. Social graphs are usually used to efficiently model the peer‐to‐peer interactions, where new adopters influence their peers to also adopt the innovation. However, the influence to adopt may also spread through individuals close to the adopters, known as tattlers, who only share information regarding the innovation. We extend an inhomogeneous Poisson process model accounting for both external and peer‐to‐peer influence to include an optional tattling stage, and we term the extension the Susceptible‐Tattler‐Adopter‐Removed (STAR) model. In an extensive simulation study, the proposed model is shown to be stable and identifiable and to accurately identify tattling when present. Further, using simulations, we show that both inference and prediction of the STAR model are quite robust against missing edges in the social graph, a common situation in real‐world data. Simulations and theoretical considerations demonstrate that, when edges are missing, the STAR model is able to accurately estimate the shares attributed to the external and internal sources of influence. Furthermore, the STAR model may be used to improve the inference of the external and viral parameters and subsequent predictions even when tattling is not part of the real data‐generating mechanism.