Electronic Journal of Statistics

Novel sampling design for respondent-driven sampling

Mohammad Khabbazian, Bret Hanlon, Zoe Russek, and Karl Rohe

Full-text: Open access

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.

Article information

Source
Electron. J. Statist., Volume 11, Number 2 (2017), 4769-4812.

Dates
Received: March 2017
First available in Project Euclid: 27 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1511773484

Digital Object Identifier
doi:10.1214/17-EJS1358

Mathematical Reviews number (MathSciNet)
MR3729659

Zentralblatt MATH identifier
06816633

Keywords
Hard-to-reach population respondent-driven sampling social network Markov chain stochastic Blockmodels anti-cluster RDS

Rights
Creative Commons Attribution 4.0 International License.

Citation

Khabbazian, Mohammad; Hanlon, Bret; Russek, Zoe; Rohe, Karl. Novel sampling design for respondent-driven sampling. Electron. J. Statist. 11 (2017), no. 2, 4769--4812. doi:10.1214/17-EJS1358. https://projecteuclid.org/euclid.ejs/1511773484


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