Modeling Social Networks as Mediators: A Mixed Membership Stochastic Blockmodel for Mediation

There are some educational interventions aimed at changing the ways in which individuals interact, and social networks are particularly useful for quantifying these changes. For many of these interventions, the ultimate goal is to change some outcome of interest such as teacher quality or student achievement, and social networks act as a natural mediator; the intervention changes the social networks of the teachers in schools, and teachers with certain types of social networks tend to use better teaching practices, for example. Due to lack of methodology, however, social networks have not been modeled as mediators. We present a new framework for modeling social networks as mediators in which a social network model is embedded into a mediation model and both models are estimated simultaneously. As a proof of concept, we introduce a new network model for mediation, applicable for interventions that affect subgroup structure. We provide a small simulation study to demonstrate the feasibility of this model and explore some potential operating characteristics. Finally, we apply our model to examine the effects of instructional coaches on teacher advice-seeking networks and subsequent changes in beliefs about mathematics