  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.
