Respondent-Driven Sampling – Testing Assumptions: Sampling with Replacement

Classical Respondent-Driven Sampling (RDS) estimators are based on a Markov Process model in which sampling occurs with replacement. Given that respondents generally cannot be interviewed more than once, this assumption is counterfactual. We join recent work by Gile and Handcock in exploring the implications of the sampling-with-replacement assumption for bias of RDS estimators. We differ from previous studies in examining a wider range of sampling fractions and in using not only simulations but also formal proofs. One key finding is that RDS estimates are surprisingly stable even in the presence of substantial sampling fractions. Our analyses show that the sampling-with-replacement assumption is a minor contributor to bias for sampling fractions under 40%, and bias is negligible for the 20% or smaller sampling fractions typical of field applications of RDS.