Respondent-Driven Sampling (RDS) employs a variant of a link-tracing network sampling strategy to collect data from hard-to-reach populations. By tracing the links in the underlying social network, the process exploits the social structure to expand the sample and reduce its dependence on the initial (convenience) sample.The current estimators of population averages make strong assumptions in order to treat the data as a probability sample. We evaluate three critical sensitivities of the estimators: to bias induced by the initial sample, to uncontrollable features of respondent behavior, and to the withoutreplacement structure of sampling.Our analysis indicates: (1) that the convenience sample of seeds can induce bias, and the number of sample waves typically used in RDS is likely insufficient for the type of nodal mixing required to obtain the reputed asymptotic unbiasedness; (2) that preferential referral behavior by respondents leads to bias; (3) that when a substantial fraction of the target population is sampled the current estimators can have substantial bias. This paper sounds a cautionary note for the users of RDS. While current RDS methodology is powerful and clever, the favorable statistical properties claimed for the current estimates are shown to be heavily dependent on often unrealistic assumptions. We recommend ways to improve the methodology.

Several researchers have begun this effort already. The post-survey adjustment methods applied to non-probability sampling have largely mirrored efforts in probability samples. Although this may be appropriate and effective to some extent, further consideration of selection bias mechanisms may be needed. We believe an agenda for advancing a method must include these attributes.

Respondent-driven sampling is a form of link-tracing network sampling, which is widely used to study hard-to-reach populations, often to estimate population proportions. Previous treatments of this process have used a withreplacement approximation, which we show induces bias in estimates for large sample fractions and differential network connectedness by characteristic of interest.We present a treatment of respondent-driven sampling as a successive sampling process. Unlike existing representations, our approach respects the essential without-replacement feature of the process, while converging to an existing with-replacement representation for small sample fractions, and to the sample mean for a full-population sample.We present a successive-sampling based estimator for population means based on respondent-driven sampling data, and demonstrate its superior performance when the size of the hidden population is known. We present sensitivity analyses for unknown population sizes. In addition, we note that like other existing estimators, our new estimator is subject to bias induced by the selection of the initial sample. Using data collected among three populations in two countries, we illustrate the application of this approach to populations with varying characteristics. We conclude that the successive sampling estimator improves on existing estimators, and can also be used as a diagnostic tool when population size is not known.

Network models are widely used to represent relational information among interacting units and the structural implications of these relations. Recently, social network studies have focused a great deal of attention on random graph models of networks whose nodes represent individual social actors and whose edges represent a specified relationship between the actors. Most inference for social network models assumes that the presence or absence of all possible links is observed, that the information is completely reliable, and that there are no measurement (e.g., recording) errors. This is clearly not true in practice, as much network data is collected though sample surveys. In addition even if a census of a population is attempted, individuals and links between individuals are missed (i.e., do not appear in the recorded data). In this paper we develop the conceptual and computational theory for inference based on sampled network information. We first review forms of network sampling designs used in practice. We consider inference from the likelihood framework, and develop a typology of network data that reflects their treatment within this frame. We then develop inference for social network models based on information from adaptive network designs. We motivate and illustrate these ideas by analyzing the effect of link-tracing sampling designs on a collaboration network.