Preserving Multiple Homophilies in a Network Configuration Model

Respondent-driven sampling (RDS) is a popular method for surveying hidden populations based on friendships and existing social network connections. In such a survey the underlying hidden network remains largely unknown. However, it is useful to estimate its size as well as the relative proportions of surveyed features. The fact that linked network participants are likely to share common features is called homophily, and is an important property in understanding the topology of social networks. In this paper we present a methodology that scales up RDS data to model the underlying hidden population in a way that preserves multiple homophilies among different features. We test our model using 46 features of the population sampled by the SATHCAP RDS survey. Our network generation methodology successfully preserves the homophilic associations in a randomly generated Barabasi-Albert network. Having created a realistic model of the expanded SATHCAP network, we test our model by simulating RDS surveys over it, and comparing the resulting sub-networks with SATHCAP. In our generated network, we preserve 85% of homophilies to under 2% error. In our simulated RDS surveys we preserve 85% of homophilies to under 15% error.