Abstract
Respondent-driven sampling (RDS) is a method of chain referral sampling popular for sampling hidden and/or marginalized populations. As such, even under the ideal sampling assumptions, the performance of RDS is restricted by the underlying social network: if the network is divided into communities that are weakly connected to each other, then RDS is likely to oversample one of these communities. In order to diminish the "referral bottlenecks" between communities, we propose anti-cluster RDS (AC-RDS), an adjustment to the standard RDS implementation. Using a standard model in the RDS literature, namely, a Markov process on the social network that is indexed by a tree, we construct and study the Markov transition matrix for AC-RDS. We show that if the underlying network is generated from the Stochastic Blockmodel with equal block sizes, then the transition matrix for AC-RDS has a larger spectral gap and consequently faster mixing properties than the standard random walk model for RDS. In addition, we show that AC-RDS reduces the covariance of the samples in the referral tree compared to the standard RDS and consequently leads to a smaller variance and design effect. We confirm the effectiveness of the new design using both the Add-Health networks and simulated networks.
Highlights
Theory, help Respondent-driven sampling (RDS) mix more quickly than snowball sampling, allowing for the potential to penetrate the broad target population and reduce its dependency on the initial convenience sample
We simulate the referral procedure of RDS and anti-cluster RDS (AC-RDS) starting from a uniformly selected node and continuing until a certain number of samples are collected, either 1%, 5%, or 10% of the total nodes
In respondent-driven sampling, bottlenecks create dependencies between the samples; successive samples are more likely to belong to the same community
Summary
When preparing to sample a target population with RDS, some aspects can be controlled by researchers (e.g. how many referral coupons to give each participant) and others cannot. The researchers could request referrals from specific groups (e.g. flip a coin, if heads request WEST and if tails request EAST) This does not change the underlying social network, but it does change the probability of certain referrals. In computational experiments, [29] report a decrease in the design effect, the ratio of the sampling variance to the sampling variance of simple random sampling, of this novel approach These two extensions of RDS (i.e. flipping a coin and NSM) are both forms of Designed RDS; through novel implementations of the sampling process they adjust the probability of certain referrals, thereby diminishing the referral bottlenecks. Anti-cluster RDS makes referral along that edges more probable, and potentially mixes faster and collects more representative samples from the target population.
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