  Traditionally, statistical and causal inference on human subjects rely 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 individuals may interact with one another such
that treatments may spill over from the treated individual to their social
contacts and outcomes may be contagious. Existing models proposed for causal
inference using observational data from networks of interacting individuals
have two major shortcomings. First, they often require a level of granularity
in the data that is practically infeasible to collect in most settings, and
second, the models are high-dimensional and often too big to fit to the
available data. In this paper we illustrate and justify a parsimonious
parameterization for network data with interference and contagion. Our
parameterization corresponds to a particular family of graphical models known
as chain graphs. We argue that, in some settings, chain graph models
approximate the marginal distribution of a snapshot of a longitudinal data
generating process on interacting units. 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 and in
simulations.
