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Network Structure and Biased Variance Estimation in Respondent Driven Sampling

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  • Ashton M Verdery
  • Ted Mouw
  • Shawn Bauldry
  • Peter J Mucha

Abstract

This paper explores bias in the estimation of sampling variance in Respondent Driven Sampling (RDS). Prior methodological work on RDS has focused on its problematic assumptions and the biases and inefficiencies of its estimators of the population mean. Nonetheless, researchers have given only slight attention to the topic of estimating sampling variance in RDS, despite the importance of variance estimation for the construction of confidence intervals and hypothesis tests. In this paper, we show that the estimators of RDS sampling variance rely on a critical assumption that the network is First Order Markov (FOM) with respect to the dependent variable of interest. We demonstrate, through intuitive examples, mathematical generalizations, and computational experiments that current RDS variance estimators will always underestimate the population sampling variance of RDS in empirical networks that do not conform to the FOM assumption. Analysis of 215 observed university and school networks from Facebook and Add Health indicates that the FOM assumption is violated in every empirical network we analyze, and that these violations lead to substantially biased RDS estimators of sampling variance. We propose and test two alternative variance estimators that show some promise for reducing biases, but which also illustrate the limits of estimating sampling variance with only partial information on the underlying population social network.

Suggested Citation

  • Ashton M Verdery & Ted Mouw & Shawn Bauldry & Peter J Mucha, 2015. "Network Structure and Biased Variance Estimation in Respondent Driven Sampling," PLOS ONE, Public Library of Science, vol. 10(12), pages 1-27, December.
  • Handle: RePEc:plo:pone00:0145296
    DOI: 10.1371/journal.pone.0145296
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    Cited by:

    1. Dongah Kim & Krista J. Gile & Honoria Guarino & Pedro Mateu‐Gelabert, 2021. "Inferring bivariate association from respondent‐driven sampling data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(2), pages 415-433, March.
    2. José M. Coronado & Amparo Moyano & Vicente Romero & Rita Ruiz & Javier Rodríguez, 2021. "Student Long-Term Perception of Project-Based Learning in Civil Engineering Education: An 18-Year Ex-Post Assessment," Sustainability, MDPI, vol. 13(4), pages 1-16, February.
    3. Lee Sunghee & Suzer-Gurtekin Tuba & Wagner James & Valliant Richard, 2017. "Total Survey Error and Respondent Driven Sampling: Focus on Nonresponse and Measurement Errors in the Recruitment Process and the Network Size Reports and Implications for Inferences," Journal of Official Statistics, Sciendo, vol. 33(2), pages 335-366, June.

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