  Aggregated relational data (ARD), formed from "How many X's do you know?"
questions, is a powerful tool for learning important network characteristics
with incomplete network data. Compared to traditional survey methods, ARD is
attractive as it does not require a sample from the target population and does
not ask respondents to self-reveal their own status. This is helpful for
studying hard-to-reach populations like female sex workers who may be hesitant
to reveal their status. From December 2008 to February 2009, the Kiev
International Institute of Sociology (KIIS) collected ARD from 10,866
respondents to estimate the size of HIV-related groups in Ukraine. To analyze
this data, we propose a new ARD model which incorporates respondent and group
covariates in a regression framework and includes a bias term that is
correlated between groups. We also introduce a new scaling procedure utilizing
the correlation structure to further reduce biases. The resulting size
estimates of those most-at-risk of HIV infection can improve the HIV response
efficiency in Ukraine. Additionally, the proposed model allows us to better
understand two network features without the full network data: 1. What
characteristics affect who respondents know, and 2. How is knowing someone from
one group related to knowing people from other groups. These features can allow
researchers to better recruit marginalized individuals into the prevention and
treatment programs. Our proposed model and several existing NSUM models are
implemented in the networkscaleup R package.
