Network driven sampling; a critical threshold for design effects

arXiv1505.05461MaRDI QIDQ6261957

Author name not available (Why is that?)

Publication date: 20 May 2015

Abstract: 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, $lambd{a}_2$. If $m<1/lambd{a}_2^2$, then the design effect is finite (i.e. the standard estimator is $sqrtn$-consistent). However, if $m>1/lambd{a}_2^2$, then the design effect grows with $n$ (i.e. the standard estimator is no longer $sqrtn$-consistent). Past this critical threshold, the standard error of the estimator converges at the slower rate of $n^{lo{g}_{m}lambd{a}_2}$. 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.

Has companion code repository: https://github.com/karlrohe/mRDS

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