On Direct vs. Indirect Peer Influence in Large Social Networks

Abstract

With the availability of large-scale network data, peer influence in social networks can be more rigorously examined and understood than before. Peer influence can arise from immediate neighbors in the network (formally defined as cohesion or direct ties with one-hop neighbors) and from indirect peers who share common neighbors (formally defined as structural equivalence or indirect ties with two-hop neighbors). While the literature examined the role of each peer influence (direct or indirect) separately, the study of both peer network effects acting simultaneously was ignored, largely due to methodological constraints. This paper attempts to fill this gap by evaluating the simultaneous effect of both direct and indirect peer influences in technology adoption in the context of Caller Ring Back Tone (CRBT) in a cellular telephone network, using data from 200 million calls by 1.4 million users. Given that such a large-scale network makes traditional social network analysis intractable, we extract many densely-connected and self-contained subpopulations from the network. We find a regularity in these subpopulations in that they consist either of about 200 nodes or about 500 nodes. Using these sub-populations and panel data, we analyze direct and indirect peer influences using a novel auto-probit model with multiple network terms (direct and indirect peer influence, with homophily as a control variable). Our identification strategy relies on Bramoullé et al.’s (2009) spatial autoregressive model, allowing us to identify the direct and indirect peer influences on each of the extracted subpopulations. We use meta-analysis to summarize the estimated parameters from all subpopulations. The results show CRBT adoption to be simultaneously determined by both direct and indirect peer influence (while controlling for homophily and centrality). Robustness checks show model fit to improve when both peer influences are included. The size and direction of the two peer influences, however, differ by group size. Interestingly, indirect peer influence (structural equivalence) plays a negative role in diffusion when group size is about 200, but a positive role when group size is about 500. The role of direct peer influence (cohesion), on the other hand, is always positive, irrespective of group size. Our findings imply that businesses must design different target strategies for large versus small groups: for large groups, businesses should focus on consumers with both multiple one-hop and two-hop neighbors; for small groups, businesses should only focus on consumers with multiple one-hop neighbors.