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Network-based methods for accessing Hard-to-Reach populations using standard surveys

*Tyler McCormick, Departments of Statistics and Sociology  
Tian Zheng, Department of Statistics 

Keywords: Bayesian inference, Social network, Survey design

The sampling frame in most social science surveys excludes members of certain groups, known as Hard-to-Reach groups. We present statistical models which leverage social network structure to estimate 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. (2001), 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.

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