Distinguishing influence-based contagion from homophily-driven diffusion in dynamic networks

Abstract

Node characteristics and behaviors are often correlated with the structure of social networks over time. While evidence of this type of assortative mixing and temporal clustering of behaviors among linked nodes is used to support claims of peer influence and social contagion in networks, homophily may also explain such evidence. Here we develop a dynamic matched sample estimation framework to distinguish influence and homophily effects in dynamic networks, and we apply this framework to a global instant messaging network of 27.4 million users, using data on the day-by-day adoption of a mobile service application and users' longitudinal behavioral, demographic, and geographic data. We find that previous methods overestimate peer influence in product adoption decisions in this network by 300-700%, and that homophily explains >50% of the perceived behavioral contagion. These findings and methods are essential to both our understanding of the mechanisms that drive contagions in networks and our knowledge of how to propagate or combat them in domains as diverse as epidemiology, marketing, development economics, and public health.

Fig. 1.

Diffusion of Yahoo! Go over time. (A–C and D–F) Two subgraphs of the Yahoo! IM network colored by adoption states on July 4 (the Go launch date), August 10, and October 29, 2007. For animations of the diffusion of Yahoo! Go over time see Movies S1 and S2.

Fig. 2.

Assortative mixing and temporal clustering. (A) The number of Go adopters per day from July 1 to October 29, 2007. (B) The fraction of adopters and nonadopters with a given number of adopter friends. (C) The ratio of the likelihood of adoption given n adopter friends P_a(n) and the likelihood of adoption given 0 adopter friends P_a(0) where the number of adopter friends is assessed at the time of adoption. (D) Frequency of observed dyadic differences in adoption times between friends compared with differences in adoption times between friends with randomly reassigned adoption times. Δt = t_i − t_j, where t_i represents the time of i's adoption.

Fig. 3.

Distinguishing homophily and influence. (A and B) The fraction of observed treated to untreated adopters (n₊/n₋) under random (A) and propensity score (B) matching over time. The dotted line shows a ratio of 1, when treatment has no effect. The Right Inset in B graphs the average marginal influence effects of having 1, 2, 3, or 4 adopter friends implied by random (open circles) and propensity score (filled circles) matching. The Left Inset graphs the average cosine distance of attribute and behavior vectors of adopters to adopter friends as the number of adopters in the local network increases (Σ_i,jⁿ cos(x_i^a, x_j^a)/n). (C) Graphs the cosine distances of adopters to their adopter friends cos(x_itⁿ, x_jt^a), their nonadopter friends cos(x_itⁿ, x_jt), and a random alter cos(x_itⁿ, x_rt) over time with trend lines fitted by ordinary least squares. (D) The fraction of treated and untreated adopters, where treatment is defined as having a friend who adopted within a certain time period (or recency) (Δt ≡ t_i^a − t_j^a = R), under random matching (open circles) and propensity score matching (filled circles). The Inset graphs the cosine distances of dyads of adopters cos(x_itⁿ, x_jt^a) by the time interval between their adoption.

Fig. 4.

Influence and homophily effects in Go adoption. (A and B) All treated adopters (filled circles) and the number of treated adopters that can be explained by homophily (open circles) per day (A) and cumulatively over time (B). (C–E) Treatment effects are then displayed when the average strength of ego's ties to adopter friends (measured by the volume of IM message traffic) is greater than and less than the median under random and propensity score matching (C); the clustering coefficient in the network around ego is greater than and less than the median (D); and ego's page views of news content are greater than and less than the median (E).