  We develop methods for estimating the size of hard-to-reach populations from
data collected using network-based questions on standard surveys. Such data
arise by asking respondents how many people they know in a specific group
(e.g., people named Michael, intravenous drug users). The Network Scale up
Method (NSUM) is a tool for producing population size estimates using these
indirect measures of respondents' networks. Killworth et al. [Soc. Netw. 20
(1998a) 23-50, Evaluation Review 22 (1998b) 289-308] proposed maximum
likelihood estimators of population size for a fixed effects model in which
respondents' degrees or personal network sizes are treated as fixed. We extend
this by treating personal network sizes as random effects, yielding principled
statements of uncertainty. This allows us to generalize the model to account
for variation in people's propensity to know people in particular subgroups
(barrier effects), such as their tendency to know people like themselves, as
well as their lack of awareness of or reluctance to acknowledge their contacts'
group memberships (transmission bias). NSUM estimates also suffer from recall
bias, in which respondents tend to underestimate the number of members of
larger groups that they know, and conversely for smaller groups. We propose a
data-driven adjustment method to deal with this. Our methods perform well in
simulation studies, generating improved estimates and calibrated uncertainty
intervals, as well as in back estimates of real sample data. We apply them to
data from a study of HIV/AIDS prevalence in Curitiba, Brazil. Our results show
that when transmission bias is present, external information about its likely
extent can greatly improve the estimates. The methods are implemented in the
NSUM R package.

Methodology