  Social science research increasingly benefits from statistical methods for
understanding the structured nature of social life, including for social
network data. However, the application of statistical network models within
large-scale community research is hindered by too little understanding of the
validity of their inferences under realistic data collection conditions,
including sampled or missing network data. The autologistic actor attribute
model (ALAAM) is a statistical model based on the well-established exponential
random graph model (ERGM) for social networks. ALAAMs can be regarded as a
social influence model, predicting an individual-level outcome based on the
actor's network ties, concurrent outcomes of his/her network partners, and
attributes of the actor and his/her network partners. In particular, an ALAAM
can be used to measure contagion effects, that is, the propensity of two actors
connected by a social network tie to both have the same value of an attribute.
We investigate the effect of using simple random samples and snowball samples
of network data on ALAAM parameter inference, and find that parameter inference
can still work well even with a nontrivial fraction of missing nodes. However
it is safer to take a snowball sample of the network and estimate conditional
on the snowball sampling structure.
