{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/network-driven-sampling-a-critical-threshold","title":"Network driven sampling; a critical threshold for design effects","arxiv_id":"1505.05461","date":"2015-05-20","proceeding":null,"authors":["Karl Rohe"],"abstract":"Web crawling, snowball sampling, and respondent-driven sampling (RDS) are\nthree types of network sampling techniques used to contact individuals in\nhard-to-reach populations. This paper studies these procedures as a Markov\nprocess on the social network that is indexed by a tree. Each node in this tree\ncorresponds to an observation and each edge in the tree corresponds to a\nreferral. Indexing with a tree (instead of a chain) allows for the sampled\nunits to refer multiple future units into the sample. In survey sampling, the\ndesign effect characterizes the additional variance induced by a novel sampling\nstrategy. If the design effect is some value $DE$, then constructing an\nestimator from the novel design makes the variance of the estimator $DE$ times\ngreater than it would be under a simple random sample with the same sample size\n$n$. Under certain assumptions on the referral tree, the design effect of\nnetwork sampling has a critical threshold that is a function of the referral\nrate $m$ and the clustering structure in the social network, represented by the\nsecond eigenvalue of the Markov transition matrix, $\\lambda_2$. If $m <\n1/\\lambda_2^2$, then the design effect is finite (i.e. the standard estimator\nis $\\sqrt{n}$-consistent). However, if $m > 1/\\lambda_2^2$, then the design\neffect grows with $n$ (i.e. the standard estimator is no longer\n$\\sqrt{n}$-consistent). Past this critical threshold, the standard error of the\nestimator converges at the slower rate of $n^{\\log_m \\lambda_2}$. The Markov\nmodel allows for nodes to be resampled; computational results show that the\nfindings hold in without-replacement sampling. To estimate confidence intervals\nthat adapt to the correct level of uncertainty, a novel resampling procedure is\nproposed. Computational experiments compare this procedure to previous\ntechniques.","url_abs":"http://arxiv.org/abs/1505.05461v5","url_pdf":"http://arxiv.org/pdf/1505.05461v5.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"network-driven-sampling-a-critical-threshold","repo_url":"https://github.com/karlrohe/mRDS","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"survey-sampling","task_name":"Survey Sampling"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}