Inference for Social Network Models from Egocentrically-Sampled Data

Egocentric network sampling observes the network of interest
from the point of view of a set of sampled actors, who provide
information about themselves and anonymised information on their
network neighbours. In survey research, this is often the most
practical, and sometimes the only, way to observe certain classes of
networks, with the sexual networks that underlie HIV transmission being
the archetypal case. Although methods exist for recovering some
descriptive network features, there is no rigorous and practical
statistical foundation for estimation and inference for network models
from such data. We identify a subclass of exponential-family random
graph models (ERGMs) amenable to being estimated from egocentrically
sampled network data, and apply pseudo-maximum-likelihood estimation to
do so and to rigorously quantify the uncertainty of the estimates. For
ERGMs parametrised to be invariant to network size, we describe a
computationally tractable approach to this problem. We use this
methodology to help understand persistent racial disparities in HIV
prevalence in the US.