title: Network Structure and Biased Variance Estimation in Respondent Driven Sampling.
abstract: This paper explores bias in the estimation of sampling variance in Respondent Driven Sampling (RDS). Prior methodological work on RDS has focused on its problematic assumptions and the biases and inefficiencies of its estimators of the population mean. Nonetheless, researchers have given only slight attention to the topic of estimating sampling variance in RDS, despite the importance of variance estimation for the construction of confidence intervals and hypothesis tests. In this paper, we show that the estimators of RDS sampling variance rely on a critical assumption that the network is First Order Markov (FOM) with respect to the dependent variable of interest. We demonstrate, through intuitive examples, mathematical generalizations, and computational experiments that current RDS variance estimators will always underestimate the population sampling variance of RDS in empirical networks that do not conform to the FOM assumption. Analysis of 215 observed university and school networks from Facebook and Add Health indicates that the FOM assumption is violated in every empirical network we analyze, and that these violations lead to substantially biased RDS estimators of sampling variance. We propose and test two alternative variance estimators that show some promise for reducing biases, but which also illustrate the limits of estimating sampling variance with only partial information on the underlying population social network.
authors.affiliation: Department of Sociology and Criminology, Population Research Institute, and Institute for CyberScience, The Pennsylvania State University, University Park, Pennsylvania, United States of America.
authors.forename: Ashton M
authors.initials: AM
authors.lastname: Verdery
authors.affiliation: Department of Sociology, University of North Carolina at Chapel Hill, Chapel Hill, NC, United States of America.
authors.forename: Ted
authors.initials: T
authors.lastname: Mouw
authors.affiliation: Department of Sociology, University of Alabama at Birmingham, Birmingham, AL, United States of America.
authors.forename: Shawn
authors.initials: S
authors.lastname: Bauldry
authors.affiliation: Department of Applied Science, University of North Carolina at Chapel Hill, Chapel Hill, NC, United States of America.
authors.forename: Peter J
authors.initials: PJ
authors.lastname: Mucha
mesh_terms: D006801:Humans; D015233:Models, Statistical; D061108:Social Media / Q000706:statistics & numerical data*; D013334:Students / Q000706:statistics & numerical data