  The sampling frame in most social science surveys excludes members of certain
groups, known as hard-to-reach groups. These groups, or subpopulations, may be
difficult to access (the homeless, e.g.), camouflaged by stigma (individuals
with HIV/AIDS), or both (commercial sex workers). Even basic demographic
information about these groups is typically unknown, especially in many
developing nations. We present statistical models which leverage social network
structure to estimate demographic characteristics of these subpopulations using
Aggregated relational data (ARD), or questions of the form "How many X's do you
know?" Unlike other network-based techniques for reaching these groups, ARD
require no special sampling strategy and are easily incorporated into standard
surveys. ARD also do not require respondents to reveal their own group
membership. We propose a Bayesian hierarchical model for estimating the
demographic characteristics of hard-to-reach groups, or latent demographic
profiles, using ARD. We propose two estimation techniques. First, we propose a
Markov-chain Monte Carlo algorithm for existing data or cases where the full
posterior distribution is of interest. For cases when new data can be
collected, we propose guidelines and, based on these guidelines, propose a
simple estimate motivated by a missing data approach. Using data from McCarty
et al. [Human Organization 60 (2001) 28-39], we estimate the age and gender
profiles of six hard-to-reach groups, such as individuals who have HIV, women
who were raped, and homeless persons. We also evaluate our simple estimates
using simulation studies.
