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

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.