Modeling the adoption of innovations in the presence of geographic and media influences

While there has been much work examining the affects of social network structure on innovation adoption, models to date have lacked important features such as meta-populations reflecting real geography or influence from mass media forces. In this article, we show these are features crucial to producing more accurate predictions of a social contagion and technology adoption at the city level. Using data from the adoption of the popular micro-blogging platform, Twitter, we present a model of adoption on a network that places friendships in real geographic space and exposes individuals to mass media influence. We show that homopholy both amongst individuals with similar propensities to adopt a technology and geographic location are critical to reproduce features of real spatiotemporal adoption. Furthermore, we estimate that mass media was responsible for increasing Twitter’s user base two to four fold. To reflect this strength, we extend traditional contagion models to include an endogenous mass media agent that responds to those adopting an innovation as well as influencing agents to adopt themselves.

💡 Research Summary

The paper addresses a notable gap in the literature on diffusion of innovations: most existing models either assume homogeneous mixing or focus solely on network topology, ignoring the spatial distribution of agents and the role of mass media. Using a rich dataset of Twitter sign‑ups in the United States from March 2006 to August 2009, the authors construct a city‑level meta‑population model that incorporates (1) geographic placement of agents, (2) heterogeneity in adoption propensity (early adopters versus regular adopters), (3) homophily both in adoption type and geographic proximity, and (4) an endogenous mass‑media agent whose influence grows with the number of already‑infected users.

The empirical analysis first shows that during the first two years of Twitter’s existence, adoption was driven almost entirely by word‑of‑mouth, as evidenced by a strong correlation between weekly new users and Google search volume while media coverage was negligible. After a critical mass of users (defined as 13.5 % of the eventual user base) was reached, media coverage surged super‑linearly, producing spikes linked to high‑profile events (e.g., Oprah’s endorsement, the 2009 Iranian protests). This observation motivates the inclusion of a media term that is not exogenous but responds to the current state of adoption.

The model builds a population of N agents distributed across L = 408 cities (the cities that each had at least 1,000 users). Each city is assigned a proportion of early adopters based on real demographic cues (universities, tech hubs). Agents are linked according to a distance‑dependent probability p(r) ∝ r⁻¹·² for short distances, flattening beyond 1,000 km, reproducing the empirically observed mix of local and long‑range ties. The contagion dynamics follow a susceptible‑infected (SI) process: at each discrete time step every infected node attempts to infect its neighbors. Early adopters transmit with probability βₑ, regular adopters with βᵣ; the ratio R = βₑ/βᵣ captures the higher susceptibility of early adopters. In addition, a media agent broadcasts a global infection probability α · M(t), where M(t) = I(t‑1) + ε. Here I(t‑1) is the number of infected agents in the previous step, and ε is a random shock of magnitude comparable to M(t), designed to mimic sudden news spikes. The media term is normalized to the interval