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 drivenboth by peer-to-peer social interactions and by external influence. Social graphs areusually used to efficiently model the peer-to-peer interactions, where new adoptersinfluence their peers to also adopt the innovation. However, the influence to adoptmay also spread through individuals close to the adopters, known as tattlers, whoonly share information regarding the innovation. We extend an inhomogeneousPoisson process model accounting for both external and peer-to-peer influence toinclude an optional tattling stage, and we term the extension the Susceptible-Tattler-Adopter-Removed (STAR) model. In an extensive simulation study, the proposedmodel is shown to be stable and identifiable and to accurately identify tattling whenpresent. Further, using simulations, we show that both inference and prediction ofthe STAR model are quite robust against missing edges in the social graph, a commonsituation in real-world data. Simulations and theoretical considerations demonstratethat, when edges are missing, the STAR model is able to accurately estimate theshares attributed to the external and internal sources of influence. Furthermore, theSTAR model may be used to improve the inference of the external and viral parame-ters and subsequent predictions even when tattling is not part of the real data-generating mechanism.