Randomization inference for spillovers in networks

Social and behavioral scientists are interested in testing of hypotheses about spillovers (i.e. interference, exogenous peer effects) in social networks; and similar questions may arise in other settings (e.g., biological and computer networks). However, when there is a single network, this is complicated by lack of independent observations. We explore Fisherian randomization inference as an approach to exact finite-population inference, where the main problem is that the relevant hypotheses are non-sharp null hypotheses. Fisherian randomization inference can be used to test these hypotheses either by (a) making the hypotheses sharp by assuming a model for direct effects or (b) conducting conditional randomization inference such that the hypotheses are sharp. I present both of these approaches, the latter of which is developed in Aronow (2012) and our paper (Athey, Eckles & Imbens, 2017). This usually involves selecting some vertices to be "focal" and conditioning on their treatment assignment and/or the assignment of some of all of their network neighbors. The selection of this set can present interesting algorithmic questions; we, for example, make use of greedy methods for finding maximal independent sets. I illustrate these methods with application to a large voter turnout experiment on Facebook (Jones et al., 2017).