We consider processes on social networks that can potentially involve three
phenomena: homophily, or the formation of social ties due to matching
individual traits; social contagion, also known as social influence; and the
causal effect of an individual's covariates on their behavior or other
measurable responses. We show that, generically, all of these are confounded
with each other. Distinguishing them from one another requires strong
assumptions on the parametrization of the social process or on the adequacy of
the covariates used (or both). In particular we demonstrate, with simple
examples, that asymmetries in regression coefficients cannot identify causal
effects, and that very simple models of imitation (a form of social contagion)
can produce substantial correlations between an individual's enduring traits
and their choices, even when there is no intrinsic affinity between them. We
also suggest some possible constructive responses to these results.