Aggregated relational data (ARD), formed from "How many X's do you know?" questions, is a powerful tool for learning important network characters 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 subpopulations in Ukraine. To analyze this data, we propose a new ARD model which incorporates respondent and subpopulation covariates in a regression framework and adds a correlation structure to the responses. The resulting more accurate 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: 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.