Notes

¹A turn of phrase gratefully borrowed from Ben Hansen.

²We do not mean to take sides in the dispute between the partisans of graphical causal models and those of the potential-outcomes formalism. The expressive power of the latter is strictly weaker than that of suitably-augmented graphical models [Richardson and Robins, 2013], but we could write everything here in terms of potential outcomes, albeit at some cost in space and notation.

³Latent space modeling of dynamic networks is still in its infancy. For some preliminary efforts, see, e.g., DuBois et al. [2013], Ghasemian et al. [2015] for block models, and Sarkar and Moore [2006] for continuous-space models.

⁴Some of the theory we rely on below allows the number of communities to grow with the size of the network, though with at a rate posited to be known a priori, and not too fast. We leave dealing with this complication to future work.

⁵An isometry is a transformation of a metric space which preserves distances between points. These transformations naturally form groups, and the properties of these groups control, or encode, the geometry of the metric space [Brannan et al., 1999].

⁶The GMZZ conditions also include a parameter to control the differences across communities of the within- and between-community connection probabilities. We omit this parameter as the within- and between-community connection probabilities are both constant across communities in our simulations. This restricted parameter space is discussed in Gao et al. [2017] as Θ0${\Theta }_0$.