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Respondent-Driven Sampling – Testing Assumptions: Sampling with Replacement

Author

Listed:
  • Barash Vladimir D.

    (Graphika Inc., 116 West 23rd Street, 5th Floor, New York NY 10011, U.S.A.)

  • Cameron Christopher J.

    (Cornell University – Sociology, 344 Uris Hall Ithaca, New York 14853, U.S.A.)

  • Spiller Michael W.

    (Cornell University – Sociology, 344 Uris Hall, Ithaca, New York 14853, U.S.A.)

  • Heckathorn Douglas D.

    (Cornell University – Sociology, 344 Uris Hall Ithaca, New York 14853, U.S.A.)

Abstract

Classical Respondent-Driven Sampling (RDS) estimators are based on a Markov Process model in which sampling occurs with replacement. Given that respondents generally cannot be interviewed more than once, this assumption is counterfactual. We join recent work by Gile and Handcock in exploring the implications of the sampling-with-replacement assumption for bias of RDS estimators. We differ from previous studies in examining a wider range of sampling fractions and in using not only simulations but also formal proofs. One key finding is that RDS estimates are surprisingly stable even in the presence of substantial sampling fractions. Our analyses show that the sampling-with-replacement assumption is a minor contributor to bias for sampling fractions under 40%, and bias is negligible for the 20% or smaller sampling fractions typical of field applications of RDS.

Suggested Citation

  • Barash Vladimir D. & Cameron Christopher J. & Spiller Michael W. & Heckathorn Douglas D., 2016. "Respondent-Driven Sampling – Testing Assumptions: Sampling with Replacement," Journal of Official Statistics, Sciendo, vol. 32(1), pages 29-73, March.
    • Handle: RePEc:vrs:offsta:v:32:y:2016:i:1:p:29-73:n:2
    DOI: 10.1515/jos-2016-0002
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    References listed on IDEAS

    as
    1. Gile, Krista J., 2011. "Improved Inference for Respondent-Driven Sampling Data With Application to HIV Prevalence Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 135-146.
    2. Wallace, Rodrick, 1991. "Social disintegration and the spread of AIDS: Thresholds for propagation along 'sociogeographic' networks," Social Science & Medicine, Elsevier, vol. 33(10), pages 1155-1162, January.
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