Methodological advances in the Network Scale-up Method

Abstract

This thesis contributes to the development of the Network Scale-up Method (NSUM). This technique emerged as an alternative to traditional survey methods and estimates the size of a group from a population using Aggregated Relational Data (ARD), which consists of the number of contacts that belong to several groups. NSUM leverages the number of connections of the participants' surrounding neighborhood, effectively increasing the fraction of the network for which data are available. In addition, the use of ARD preserves the privacy of the participants and therefore increases participation and honesty, mitigating biases of traditional surveys. Due to the advantages of NSUM, it has motivated a wide range of applications in public health, epidemiology, the estimation of sensitive groups, and the quantification of disaster impacts.

Although NSUM techniques have been applied to a wide range of problems of public relevance since their introduction nearly four decades ago, several important research challenges remain unresolved. This thesis is a compendium of publications that address these previous research questions through four complementary directions. The first direction is the empirical evaluation of existing NSUM techniques. The second research line is the development of the theoretical foundations of NSUM and ARD methods. The third direction is the proposal of new methods. Finally, this thesis extends the application of these techniques to a new domain. Together, these contributions are presented across the chapters of the thesis.

Chapter 2 provides an exhaustive evaluation of the performance of most of the NSUM estimators through an extensive simulation environment. The empirical comparison reveals the impact of the biases, the design of the survey, and the sample size on the existing NSUM estimators. Chapter 3 develops a theoretical framework for analyzing the error of the NSUM estimators, providing error bounds under adversarial scenarios and random structures. Chapter 4 proposes a framework for estimating temporal trends from ARD and provides a theoretical comparison of its advantages over traditional survey methods. Chapter 5 proposes robust versions of existing NSUM estimators by replacing the sample means with alternative location estimators. These versions mitigate the sensitivity to anomalous responses due to the use of sample means in the traditional NSUM techniques. Chapter 6 extends the application of NSUM to estimating voting intention in electoral processes, outperforming several well-established polling institutions using smaller sample sizes. Chapter 7 implements NSUM to measure attributes of virtual networks used for content distribution, decentralized payment systems, and blockchain technologies. This framework estimates network attributes using only the information from a small number of nodes, considerably reducing the intrusiveness and computational cost of existing measurement techniques that require exhaustive identification of the entire network.