Robust network scale-up method estimators

The Network Scale-up Method (NSUM) is a relatively recent statistical approach for estimating the prevalence of unknown populations through indirect surveys utilizing information about the respondents’ social circles. The popularity of NSUM has increased in recent years due to its ability to uphold privacy and cost-effectiveness. However, the NSUM is not exempt from biases resulting from participants’ behavior. In addition, the simpler and most popular NSUM estimators are based on averages, making them sensitive to deviations in the samples, which may cause significant errors. This work aims to study how robust procedures can overcome misreporting, contamination, and deviation due to conditions such as barrier effects, prevalence, skewness, and tail length. Specifically, the central objective of the article is to analyze the statistical robustness of NSUM methods, studying whether these methods are affected by outliers or unusual data. We employ eight robust proposals for each of the two classical NSUM estimators. We analyze robust estimators through simulation experiments using synthetic random networks such as Erdős–Rényi, Scale Free, and Stochastic Block Model structures to model different degree distributions and community structures with different prevalence levels in contaminated and uncontaminated scenarios. We compare the results of the simulations with real data on COVID-19 indicators in the United Kingdom and voting intention in the Spanish General Elections of 2023. This article shows that the classical NSUM estimators perform poorly in contaminated scenarios, while most of the robust proposals are not considerably affected. However, the performance of some robust NSUM estimators decreases under barrier effects. In addition, we observe that distortions created by small prevalence play an important role in selecting the most suitable robust NSUM estimator. Particularly, the robustification of the Mean of Ratios ($\mathrm{MoR}$) estimator based on the Myriad operator typically exhibits the best performance (for MoR methods) across the various social network structures for different prevalence levels, reducing the estimation error regarding the non-robust methods by up to three orders of magnitude in contaminated scenarios.