Generalized least squares can overcome the critical threshold in respondent-driven sampling

Roch, Sébastien; Rohe, Karl

doi:10.1073/pnas.1706699115

Cited by 4 publications

(1 citation statement)

References 22 publications

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“…By evaluating G(λ 2 ), one can gauge where a given sample falls with respect to the critical threshold. A follow-up paper provides an approach to estimate the largest eigenvalues of the matrix P from a (T, P )-walk on G sample [Roch and Rohe, 2017]. Code is available on github (https: // github.…”

Section: The Variance Under Rdsmentioning

confidence: 99%

A critical threshold for design effects in network sampling

Rohe¹

2019

Ann. Statist.

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Web crawling, snowball sampling, and respondent-driven sampling (RDS) are three types of network sampling techniques used to contact individuals in hard-to-reach populations. This paper studies these procedures as a Markov process on the social network that is indexed by a tree. Each node in this tree corresponds to an observation and each edge in the tree corresponds to a referral. Indexing with a tree (instead of a chain) allows for the sampled units to refer multiple future units into the sample.In survey sampling, the design effect characterizes the additional variance induced by a novel sampling strategy. If the design effect is some value DE, then constructing an estimator from the novel design makes the variance of the estimator DE times greater than it would be under a simple random sample with the same sample size n. Under certain assumptions on the referral tree, the design effect of network sampling has a critical threshold that is a function of the referral rate m and the clustering structure in the social network, represented by the second eigenvalue of the Markov transition matrix, λ2. If m < 1/λ 2 2 , then the design effect is finite (i.e. the standard estimator is √ n-consistent). However, if m > 1/λ 2 2 , then the design effect grows with n (i.e. the standard estimator is no longer √ n-consistent). Past this critical threshold, the standard error of the estimator converges at the slower rate of n log m λ 2 . The Markov model allows for nodes to be resampled; computational results show that the findings hold in without-replacement sampling. To estimate confidence intervals that adapt to the correct level of uncertainty, a novel resampling procedure is proposed. Computational experiments compare this procedure to previous techniques. * Thank you Zoe Russek and Emma Krauska for recording the referral trees used in Figure 2 and helpful comments on this draft. Thank you

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Section: The Variance Under Rdsmentioning

confidence: 99%

A critical threshold for design effects in network sampling

Rohe¹

2019

Ann. Statist.

Self Cite

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Reinforcement Learning Methods in Public Health

Weltz

Volfovsky

Laber

2022

Clinical Therapeutics

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Asymptotic seed bias in respondent-driven sampling

Yan¹,

Hanlon²,

Roch³

et al. 2020

Electron. J. Statist.

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Respondent-driven sampling (RDS) collects a sample of individuals in a networked population by incentivizing the sampled individuals to refer their contacts into the sample. This iterative process is initialized from some seed node(s). Sometimes, this selection creates a large amount of seed bias. Other times, the seed bias is small. This paper gains a deeper understanding of this bias by characterizing its effect on the limiting distribution of various RDS estimators. Using classical tools and results from multi-type branching processes (Kesten and Stigum, 1966), we show that the seed bias is negligible for the Generalized Least Squares (GLS) estimator and non-negligible for both the inverse probability weighted and Volz-Heckathorn (VH) estimators. In particular, we show that (i) above a critical threshold, VH converge to a non-trivial mixture distribution, where the mixture component depends on the seed node, and the mixture distribution is possibly multi-modal. Moreover, (ii) GLS converges to a Gaussian distribution independent of the seed node, under a certain condition on the Markov process. Numerical experiments with both simulated data and empirical social networks suggest that these results appear to hold beyond the Markov conditions of the theorems.

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Generalized least squares can overcome the critical threshold in respondent-driven sampling

Cited by 4 publications

References 22 publications

A critical threshold for design effects in network sampling

A critical threshold for design effects in network sampling

Reinforcement Learning Methods in Public Health

Asymptotic seed bias in respondent-driven sampling

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