Post-Stratification in Network Driven Sampling

• Activity Number: 613 - Recent Advances in Network Data Inference
• Type: Topic Contributed
• Date/Time: Thursday, August 2, 2018 : 8:30 AM to 10:20 AM
• Sponsor: Social Statistics Section
• Author(s): Yilin Zhang* and Sebastien Roch and Karl Rohe
• Companies: University of Wisconsin-Madison and University of Wisconsin-Madison and University of Wisconsin-Madison
• Keywords: social network; respondent driven sampling; Stochastic Blockmodel; post-stratification; hard-to-reach populations; statistical consistency

Abstract

Respondent Driven Sampling (RDS) is a widely used network based approach to study marginalized or hard-to-reach populations. The dependence of samples induced by the link-tracing sampling procedure, however, inflates the variation of traditional RDS estimators. Variance of traditional RDS estimators decays at a rate slower than O(n^{-1}), where n is the sample size. A recent study shows the generalized least squares (GLS) estimator improves the rate to O(n^{-1}), but the feasible GLS (fGLS) estimator is complicated to compute and has no theoretical guarantees. In this paper, we provide a more effective and straightforward method to reduce variance. Our new Post-Stratified (PS) estimator is both easy to compute and has small variation. It also provides useful block-wise byproducts that help understand the hidden population. Theorem 1 shows that the PS estimator is O(n^{-1})-consistent under a statistical model. Simulations show that the PS estimator has smaller Root Mean Square Error (RMSE) compared to the state-of-the-art estimators.