Alternative Estimation Methods for Identifying Contagion Effects in Dynamic Social Networks: A Latent-Space Adjusted Approach

• In Event: Methods and Models for Your Social Network Data

Abstract

Contagion effects, also known as peer effects or social influence process, refer to the phenomenon that people tend to assimilate behavior of those with whom they have interaction in a social network. With the availability of longitudinal social network data, studies of contagion effects have become more and more central to social science, with many applications in field of education such as diffusion of innovation, change of health behaviors or academic outcomes among adolescents, implementation of practices among teachers (Valente 1995, 1996; Christakis et al 2007, 2008; Sacerdote 2000; Frank et al 2004) among others.
However, these types of contagion effects are usually difficult to identify, as it’s difficult to separate influence from other processes in the network, such as selection (homophily) process (Lazarsfeld and Merton 1954; Byrne 1971; McPherson and Smith-Lovin 1987; McPherson, Smith-Lovin, and Cook 2001) that actors seek similar others to interact; or individual preference for same social setting that people with prior similarity select themselves into same social setting, and actual friendship formation just reflects the opportunity of meeting in this social setting (Feld 1981, 1982; Kalmijn & Flap 2001).
We argue that the difficulty of identification caused by entanglement between contagion effects and other factors can essentially be framed as an omitted variable bias problem. For example the entanglement between contagion effects and confounding variables (social settings, ego’s and alter’s attributes for example) can be easily framed as an omitted variable bias problem. And dilemma caused by co-evolution of influence and selection process can also be framed as an omitted variable bias problem. As pointed out by Steglich (2010), one of the important concern for SIENA is “possibility that there may be non-observed variables codetermining the probabilities of change in network and/or behavior”. And Shalizi (2011) has shown that when there’s latent trait that codetermine both influence and selection in network data, contagion effects are generally unidentifiable, mainly due to the fact that contagion and homophily (selection) are generically confounded through this latent trait. However, most currently available methods (SIENA (Snijder et al 2007), instrumental variable methods (Bramoulle et al. 2009; An 2011), Propensity score matching( Aral et al 2009) etc.) either don’t deal with this problem or require strong assumptions.
In this paper and I propose several alternative estimation methods that have potentials to correctly identify contagion effects when there is an unobserved trait that co-determines the influence and the selection. The Monte-Carlo simulation results suggest that a latent-space adjusted estimator is especially promising. It outperforms other estimators that are traditionally used to deal with the unobserved variables, including a structural equation based estimator and an instrumental variable estimator. Together these estimators provide plausible alternatives for identifying contagion effects under various scenarios.

Author

• Ran Xu, Michigan State University