Causal inference, social networks, and chain graphs

Traditionally, statistical and causal inference on human subjects relies on the assumption that individuals are independently affected by treatments or exposures. However, recently there has been increasing interest in settings, such as social networks, where treatments may spill over from the treated individual to his or her social contacts and outcomes may be contagious. Existing models proposed for causal inference using observational data from networks have two major shortcomings. First, they often require a level of granularity in the data that is not often practically infeasible to collect, and second, the models are generally high-dimensional and often too big to fit to the available data. In this paper we propose and justify a parsimonious parameterization for social network data with interference and contagion. Our parameterization corresponds to a particular family of graphical models known as chain graphs. We demonstrate that, in some settings, chain graph models approximate the observed marginal distribution, which is missing most of the time points from the full data. We illustrate the use of chain graphs for causal inference about collective decision making in social networks using data from U.S. Supreme Court decisions between 1994 and 2004.