On the impossibility of constructing good population mean estimators in a realistic Respondent Driven Sampling model

TL;DR

This paper demonstrates that under realistic Respondent Driven Sampling models, it is impossible to reliably estimate population means using current methods because inclusion probabilities cannot be determined from the sample alone.

Contribution

The paper shows that existing RDS estimators relying on simple assumptions are invalid under realistic models, highlighting fundamental limitations in current population mean estimation methods.

Findings

Inclusion probabilities cannot be derived from sample data alone in realistic RDS models.

Current RDS estimators are based on overly simplistic assumptions that do not hold in practice.

Without additional population network information, reliable mean estimation is infeasible.

Abstract

Current methods for population mean estimation from data collected by Respondent Driven Sampling (RDS) are based on the Horvitz-Thompson estimator together with a set of assumptions on the sampling model under which the inclusion probabilities can be determined from the information contained in the data. In this paper, we argue that such set of assumptions are too simplistic to be realistic and that under realistic sampling models, the situation is far more complicated. Specifically, we study a realistic RDS sampling model that is motivated by a real world RDS dataset. We show that, for this model, the inclusion probabilities, which are necessary for the application of the Horvitz-Thompson estimator, can not be determined by the information in the sample alone. An implication is that, unless additional information about the underlying population network is obtained, it is hopeless to conceive of a general theory of population mean estimation from current RDS data.