Source-linked AI summary
Modeling the adoption of innovations in the presence of geographic and media influences
Jameson L. Toole, Meeyoung Cha, Marta C. Gonzalez
TL;DR
Prior adoption models did not characterize the interplay of media and word of mouth or represent geography in adoption networks. The paper models Twitter adoption with geographically situated friendships and an endogenous media agent; geographic bias helps reproduce city-level adoption, while media accounts for at least half of new users in the simulations.
Problem
Previous adoption models failed to characterize the interplay of media and word of mouth, and global cumulative adoption alone does not reproduce geographically resolved city-level patterns.
Source: A. Replicating standard SI model · p. 5, §IV · p. 6Method
The model places friendships in geographic space and adds a media agent whose volume depends on prior infections and whose broadcasts can prompt adoption.
Source: §II · p. 4, A. Replicating standard SI model · p. 5Results
At least half of newly joined Twitter users were attributed to mass media, while geographically biased friendships enabled city-level adoption predictions that preserved national trends.
Source: A. Replicating standard SI model · p. 5, B. Media Influence · p. 6Takeaways & Limitations
The findings may be useful for modeling opinion spreading, including elections and collective action, where demographics and geography matter.
Source: §IV · p. 7
Abstract
from arXiv · showhide
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.
I. A CASE STUDY OF TWITTER
The study uses Twitter adoption as a case study of diffusion across time and place. Its U.S. dataset records signup times and self-reported city locations for millions of users.
I. A CASE STUDY OF TWITTER
- Twitter grew from a San Francisco launch in March 2006 to roughly 190 million global users by December 2010, including nearly 80 million in the United States.The passage describes word-of-mouth as the main spreading force during the first two years, followed by buzz from traditional news and media.Source: §I · p. 2
- Figure 1 plots weekly new U.S. Twitter users, normalized by the maximum over people from mid-March 2006 through late August 2009, cumulative U.S. users for that period, and Google search and news volumes normalized to maximum 1.Source: Figure 1 · p. 2
- The dataset follows the first 3.5 million U.S. Twitter signups across 408 cities, covering roughly 65% of those users.Cities with fewer than 1,000 signups over three years were excluded.Source: §I · p. 2
A. Descriptive Statistics
The descriptive analysis compares Twitter adoption across national and city scales, grouping users and cities by adoption timing. It reports geographic patterns in diffusion and a delayed, adoption-linked rise in news coverage.
A. Descriptive Statistics
- Google Trends and Google News volumes are used alongside national weekly signup and cumulative-user counts to characterize adoption and media activity.The figure normalizes adoption measures by their maxima and Google search/news volumes so their maxima equal 1.Source: A. Descriptive Statistics · p. 2
- The city time series compare weekly new-user counts and cumulative adoption in Ann Arbor, Denver, and Arlington.Ann Arbor represents a young early-adopting demographic, Denver a large metropolitan area with mostly late-majority adopters, and Arlington a mixed area.Source: Figure 2 · p. 3, A. Descriptive Statistics · p. 3
- Cities with more early adopters tend to have large universities or technology centers that attract young, tech-savvy people, and city adopter composition is important for reproducing diffusion patterns.The analysis measures each city's shares of early adopters, early majority, late majority, and laggards, normalizing locations for population.Source: A. Descriptive Statistics · p. 3
- At 13.5% of eventual users, a city is classified as having reached critical mass; the observed path runs from Silicon Valley through college towns and metropolitan areas to suburban and rural locations.The city threshold follows the diffusion-of-innovations literature.Source: A. Descriptive Statistics · p. 3
- News coverage was nearly absent during Twitter's first two years, while Google search volume correlated with user growth; after critical mass, news coverage rose superlinearly.The reported adoption spikes included celebrity endorsements and political events.Source: A. Descriptive Statistics · p. 3
II. MODEL AND SIMULATION
The model combines contagion on a social network with agents placed in city-level metapopulations. It adds a media agent whose influence responds to adoption and includes random shocks.
II. MODEL AND SIMULATION
- The model places N agents in L cities, assigns early or regular adopter types, and connects agents in a social network whose geography and link properties can reflect observed patterns.City placements reflect empirical user distributions and adopter-type composition.Source: §II · p. 3
- Early critical-mass locations cluster near San Francisco, while early adoption in Boston-area suburbs also appears, contrasting local word-of-mouth diffusion with the Internet's flattening effects.The figure marks locations already at critical mass in gray and locations reaching it that week in black.Source: Figure 3 · p. 4
- Each infected agent attempts to infect its neighbors, with adoption probabilities βr for regular adopters and βe for early adopters; the model tracks susceptible and infected agents over time.Initial infection is seeded in a small fraction of agents, and the two state counts sum to N.Source: §II · p. 4
- The media agent broadcasts to all agents with transmission probability αM, where media volume M depends on prior infections and a random shock.Media volume is normalized to [0, 1], and the random shocks are set to the order of M.Source: §II · p. 4
A. Replicating standard SI model
The simulations show that geographically biased friendships are needed to reproduce city-level adoption timing while retaining national trends. Early adopters must be connected through both type similarity and geographic proximity.
A. Replicating standard SI model
- A simple SI version of the model cannot reproduce the empirical shape of Twitter's cumulative adoption curve.This version uses equal adoption probabilities for both agent types and removes the media agent.Source: A. Replicating standard SI model · pp. 4–5
- Having the right proportion of highly susceptible early adopters in cities is insufficient: early adopters need both similar-type and geographically close friendships to form a giant component.The figure reports that similarity-based friendship preference alone does not connect early adopters when geography is unbiased.Source: A. Replicating standard SI model · p. 5, Figure 5 · p. 5
- The study defines homopholy as the average fraction of an early adopter's friends who are also early adopters, and treats a giant component containing over 95% of geographically biased early adopters as sufficient.The giant-component estimates aggregate 100 networks of 10,000 nodes each.Source: A. Replicating standard SI model · p. 5
- With geographically biased friendships forming a giant component among early adopters, the model predicts critical-mass timing in most cities while preserving national adoption trends.Without a giant component, nearly all cities peak at the same time; national cumulative adoption can be reproduced without geographically biased links.Source: A. Replicating standard SI model · pp. 5–6
B. Media Influence
The model links media volume to adoption, with coverage accelerating after critical mass and influencing later adopters. Media influence was needed to reproduce national Twitter growth after word-of-mouth-only predictions began to fall short.
B. Media Influence
- Around week 120, word-of-mouth-only simulations began performing badly, just as mass media started reporting on Twitter.Both geographically unbiased and geographically biased predictions fit early adoption closely but fell short in later stages.Source: B. Media Influence · p. 6
- At least half of newly joined Twitter users were attributed to mass media, especially in later stages; matching national adoption required media susceptibility α = .15.The authors say predicting the timing of actual media events is beyond the work's scope.Source: B. Media Influence · p. 6
- The endogenous media model makes coverage rise superlinearly after critical mass and allows random events to increase news volume as much as twofold.Source: B. Media Influence · p. 6
- In the simulation, growth is modest before critical mass; afterward local spread is reproduced and rapidly increasing media coverage influences other agents to adopt.Source: B. Media Influence · p. 6
IV. CONCLUSION
The Twitter model combines geographically situated social ties with media influence to reproduce adoption patterns across city and national scales. The authors report that media increased the number of adopters two to four fold, while geographic bias was crucial for city-level dynamics.
IV. CONCLUSION
- Media influences in later stages accounted for a two to four fold increase in the number of adopters.Source: §IV · p. 6
- Geographical bias in the social network was crucial to reproducing adoption dynamics at the city scale.Source: §IV · p. 6, Figure 7 · p. 7
- The model is described as capable of replicating city- and national-level adoption phenomena and may improve on SI or Bass models.Source: §IV · p. 6
- Figure 6 compares simulated and actual critical-mass achievement times across four adopter-timing groups.Source: Figure 6 · p. 7
- The authors identify demographics and geography as important for future network-spread predictions, including opinion spreading in elections and collective action.Source: §IV · p. 7