  Social influence cannot be identified from purely observational data on
social networks, because such influence is generically confounded with latent
homophily, i.e., with a node's network partners being informative about the
node's attributes and therefore its behavior. If the network grows according to
either a latent community (stochastic block) model, or a continuous latent
space model, then latent homophilous attributes can be consistently estimated
from the global pattern of social ties. We show that, for common versions of
those two network models, these estimates are so informative that controlling
for estimated attributes allows for asymptotically unbiased and consistent
estimation of social-influence effects in linear models. In particular, the
bias shrinks at a rate which directly reflects how much information the network
provides about the latent attributes. These are the first results on the
consistent non-experimental estimation of social-influence effects in the
presence of latent homophily, and we discuss the prospects for generalizing
them.
