1. When considering models that exclude interference, we will write H(yi,zi, wi ) = yi,wi to indicate that the entries zj ϵ z and Wj ϵ w for j ≠ i do not change the potential outcomes for subject i.
2. Note that our example model is not sensitive to the larger structure of the network. For example, a ring network would induce the same effect as a network composed entirely of triangles, as in each case, all nodes have precisely two neighbors. Theories (and models) that reflect larger network structure can be handled by this framework (e.g., Siegel 2009); however, in the interests of simplicity, we restrict our attention to immediate neighbors only in this example.
3. Toward Causal Inference With Interference
4. P-values maximized over a confidence set for the nuisance parameter;Berger;Journal of the American Statistical Association,1994
5. To further aid applied researchers, all simulations in this section and all hypothesis tests in Sections 3 and 4 are based on the development version of our freely available, open-source software package, RItools, available at https://github.com/markmfredrickson/RItools. Appendix A contains annotated code fragments used in this article, and the source code to the entire document is available in the reproduction archive (Fredrickson and Bowers 2012) (http://hdl.handle.net/1902.1/18933).