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Generalized least squares can overcome the critical threshold in respondent-driven sampling.

Sebastien Roch1, Karl Rohe2

  • 1Department of Mathematics, University of Wisconsin, Madison, WI 53706.

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|September 27, 2018
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Summary

Generalized least squares (GLS) can reduce variance in respondent-driven sampling (RDS) estimates. This method improves confidence intervals for sampling hard-to-reach populations, offering a more statistically robust approach.

Keywords:
link-tracing samplingsnowball samplingspectral gap

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Area of Science:

  • Statistics
  • Network Analysis
  • Social Sciences

Background:

  • Respondent-driven sampling (RDS) is crucial for reaching marginalized populations via peer referral.
  • Previous Markov models for RDS show increased variance with high referral rates, leading to wider confidence intervals.
  • Existing methods may not fully account for complex social network structures.

Purpose of the Study:

  • To investigate the effectiveness of generalized least squares (GLS) in reducing the variance of RDS estimates.
  • To develop novel feasible GLS estimators for RDS.
  • To explore network structure beyond node degree for improved sampling estimators.

Main Methods:

  • Theoretical analysis using a Markov model for RDS.
  • Derivation of two classes of feasible GLS estimators based on network models (Degree Corrected Stochastic Blockmodel and rank-two model).
  • Estimation of spectral properties of the population network from random walk samples.

Main Results:

  • GLS estimators theoretically reduce the variance of RDS estimates, with a variance of [Formula: see text].
  • Feasible GLS estimators were derived based on network properties.
  • The study demonstrated the possibility of estimating network spectral properties from random walk samples.

Conclusions:

  • Generalized least squares offers a statistically sound method to improve the precision of respondent-driven sampling.
  • The developed GLS estimators leverage network structure for more accurate estimation.
  • Further research and development are needed for practical implementation of these advanced estimators.