SILO



The weekly SILO Seminar Series is made possible through the generous support of the 3M Company and its Advanced Technology Group

3M

with additional support from the Analytics Group of the Northwestern Mutual Life Insurance Company

Northwestern Mutual

A critical threshold for respondent driven sampling

Karl Rohe, Prof. at Statistics Department, University of Wisconsin-Madison

Date and Time: Apr 15, 2015 (12:30 PM)
Location: Orchard room (3280) at the Wisconsin Institute for Discovery Building

Abstract:

Respondent driven sampling (RDS) is sampling technique for studying marginalized or hard to reach populations where the study participants refer their friends into the study. To account for the fact that RDS participants are incentivized to refer up to five future participants, this talk models RDS as a Markov chain on a social network that is indexed by a referral tree. Theorem 1 gives a closed form expression for the variance of the popular Volz-Heckathorn estimator. Under reasonable assumptions on the referral tree, the design effect of RDS has a critical threshold that is a function of the referral rate m and the clustering structure in the social network, represented the second eigenvalue of the Markov transition matrix \lambda_2. Below this threshold, the estimator enjoys the standard rate of convergence, above this threshold the rate of convergence is slower and a function of m and \lambda_2. The talk will discuss consequences and potential solutions to this finding.