A Spectral Framework for Network-Driven Sampling

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

Probability sampling drastically reduces the burden of research in various disciplines because statistical inference can extend conclusions from a sample to the entire population. However, classical sampling techniques require a sampling frame that lists each individual in the population and a way of contacting each individual. In many settings, a sampling frame is not available. In others, a sampling frame is too expensive to compile or only covers a biased subset of the population. Particularly with hard-to-reach populations, network-driven sampling provides one of the only ways to find members of the population. Leveraging a network to find a target population appears in many disciplines with a multitude of names: respondent-driven sampling, snowball sampling, web crawling, link-tracing, breadth-first search, co-immunoprecipitation, and chromatin immunoprecipitation. These disparate techniques all provide access to hard-to-reach and networked populations by essentially asking participants to refer friends. As a result, these are all network-driven techniques. Classical sampling theory does not apply to network-driven sampling because friends are similar; this induces dependence between samples that is influenced by the underlying social network. Preliminary research conducted by the investigator identifies a critical threshold that relates the structure of the social network to the referral rate in the sampling tree; beyond this critical threshold, standard network-driven approaches produce highly uncertain estimates. This research aims to produce new statistical techniques that continue to perform well beyond the critical threshold. Moreover, this project will study novel forms of network-driven data collection that incorporate additional information to produce more representative samples. Classical sampling results are not applicable to network-driven sampling because friends are similar, inducing dependence between samples. Previous theoretical results show that some network-driven studies do not obtain square root n-consistent estimators. Whether a study obtains square root n-consistency depends on both (i) the spectral properties of the underlying social network and (ii) the growth of the sampling tree. This research aims to provide new estimators that correct for the dependence between samples. These dependence-corrected estimators can obtain square root n-consistency, even when current estimators do not. This project will also construct new diagnostics and new sampling designs for network-driven sampling. The new spectral framework will provide a suite of theory, methodology, and practices that will enable studies to obtain square root n-consistent estimators.