A Multilayer Network Model for Aggregated Relational Data

Abstract: The Network Scale-Up Method (NSUM) is a vital tool for estimating the sizes of hard-to-reach populations using Aggregated Relational Data (ARD). Recent advancements in survey design increasingly collect ARD across multiple definitions of tie strength, yielding a complex multilayer network structure. Existing statistical frameworks analyze these layers independently, sacrificing valuable shared information. We propose a latent space approach for the Multilayer ARD that enables principled joint estimation. We establish rigorous identifiability conditions for the shared latent space and mathematically prove that the joint estimator achieves asymptotic efficiency gains and finite sample bias reductions by “”borrowing strength”” across layers. We apply the framework to real-world multilayer NSUM survey data, demonstrating its practical efficacy in yielding more robust and precise subpopulation estimates.