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Network Structure and Biased Variance Estimation in Respondent Driven Sampling.

Ashton M Verdery1, Ted Mouw2, Shawn Bauldry3

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Current methods for estimating sampling variance in Respondent Driven Sampling (RDS) are biased. This bias arises from a flawed assumption about network structure, leading to underestimation in real-world networks.

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Area of Science:

  • Social Sciences
  • Statistics
  • Network Analysis

Background:

  • Respondent-Driven Sampling (RDS) is a key method for studying hidden populations.
  • Existing research on RDS primarily addresses biases in population mean estimation.
  • Variance estimation in RDS has been largely overlooked, despite its importance for statistical inference.

Purpose of the Study:

  • To investigate bias in sampling variance estimation within Respondent-Driven Sampling (RDS).
  • To identify the assumptions underlying current RDS variance estimators.
  • To propose and evaluate alternative methods for more accurate variance estimation in RDS.

Main Methods:

  • Mathematical generalization and computational experiments were used to analyze RDS variance estimators.
  • Analysis of 215 empirical social networks from Facebook and Add Health.
  • Testing of two novel variance estimators designed to mitigate identified biases.

Main Results:

  • RDS variance estimators critically depend on the First-Order Markov (FOM) assumption.
  • The FOM assumption is consistently violated in empirical social networks.
  • Current RDS variance estimators systematically underestimate population sampling variance, with significant bias observed.

Conclusions:

  • Violations of the FOM assumption in real-world networks lead to biased sampling variance estimates in RDS.
  • Alternative estimators show potential but highlight limitations due to incomplete network information.
  • Accurate variance estimation in RDS remains a challenge, necessitating further methodological development.