Abstract: Respondent-Driven Sampling is type of link-tracing network sampling used to study hard-to-reach populations.  Beginning with a convenience sample, each person sampled is given 2-3 uniquely identified coupons to distribute to other members of the target population, making them eligible for enrollment in the study.  This is effective at collecting large diverse samples from my populations.

Current estimation relies on sampling weights estimated by treating the sampling process as a random walk on the underlying network of social relations.  These estimates are based on strong assumptions allowing the data to be treated as a probability sample.  In particular, existing estimators assume a with-replacement sample with an ideal initial sample.  We introduce two new estimators, the first based on a without-replacement approximation to the sampling process, and the second based on fitting a social network model (ERGM), and demonstrate their ability to adjust for biases due the finite population and initial convenience sample.  Our estimators are based on a model-assisted designed-based approach, using standard errors based on a parametric bootstrap.  We conclude with an application to data collected among injecting drug users, including extension to observable features of the sampling process.