  We consider processes on social networks that can potentially involve three
factors: 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.
