Neighbourhood Bootstrap for Respondent-Driven Sampling

Abstract

Respondent-Driven Sampling (RDS) is a form of link-tracing sampling, a sampling technique for 'hard-to-reach' populations that aims to leverage individuals' social relationships to reach potential participants. While the methodological focus has been restricted to the estimation of population proportions, there is a growing interest in the estimation of uncertainty for RDS as recent findings suggest that most variance estimators underestimate variability. Recently, Baraff et al. (2016) proposed the tree bootstrap method based on resampling the RDS recruitment tree, and empirically showed that this method outperforms current bootstrap methods. However, some findings suggest that the tree bootstrap (severely) overestimates uncertainty. In this paper, we propose the neighbourhood bootstrap method for quantifiying uncertainty in RDS, and empirically show that our method outperforms the tree bootstrap in terms of bias and coverage under realistic RDS sampling assumptions.

General Regression Methods for Respondent-Driven Sampling Data

“…The tree bootstrap variance estimator severely overestimates uncertainty in most cases while the neighborhood bootstrap variance estimator is, in absolute value, less biased than both estimators in most cases, especially for the linear model. This aligns with previous findings in the RDS literature that, for the tree bootstrap method, covering at or above the nominal level generally comes at a significant cost in terms of power (Gile et al 2018;Yauck and Moodie 2020). Tables 4, 5 and 6 report the results for the linear, Poisson and logistic regression respectively.…”

“…We can therefore provide some general guidance for regression in RDS studies: (i) analyses that omit homophily-driven effects terms, while including a random effect for recruiter, outperform other modeling strategies in terms of bias and coverage of the confidence interval, and (ii) weighted regression methods outperform unweighted regression methods in terms of bias and precision when the predictor is correlated with degree; when the predictor is uncorrelated with degree, weighting the model only increases variability in the estimates. As observed previously (Yauck and Moodie, 2020), neighbourhood bootstrap provides better estimates of standard errors than any existing alternatives.…”

“…The tree bootstrap method mimics the recruitment tree and corresponding features such as the recruitment chain, the number of seeds and waves, thus taking into account the underlying network structure of RDS. Recent findings suggest that this method consistently outperforms existing bootstrap methods, but overestimates uncertainty (Baraff et al 2016;Gile et al 2018;Yauck and Moodie 2020).…”

“…We consider two bootstrap methods for estimating uncertainty in RDS: (i) the tree bootstrap (Baraff et al, 2016) and (ii) the neighborhood bootstrap (Yauck and Moodie, 2020).…”

“…This method captures the 'local' neighborhood structure of the network by reporting all connections that a resampled unit has within the tree, without much reliance on its branching structure. Yauck and Moodie (2020) empirically showed that the neighborhood bootstrap outperforms the tree bootstrap in terms of coverage, bias and mean interval width under realistic RDS assumptions.…”