Respondent-driven sampling and the homophily configuration graph

Respondent-Driven Sampling (RDS) is a popular method for surveying hard-to-reach populations, especially in the public health domain. Adjusting for the complex sampling mechanism of the RDS procedure is challenging. We propose a new model for the RDS mechanism motivated by a graph model, which we call the Homophily Configuration Graph. Under this model, we develop a new estimator for population proportions that is robust to seed bias, differential activity, differential recruitment and short recruitment chains. We also connect it to existing RDS theory by showing that, if the sample fraction is small, our estimator limits to the popular Salganik-Heckathorn estimator. We perform simulation studies on both empirically observed networks and networks with known statistical properties, suggesting that this new estimator has less bias than currently recommended estimators.