Bayesian Modeling for Aggregated Relational Data: A Unified Perspective

Abstract: Aggregated relational data is widely collected to study social network theory. It has been used to address a variety of key problems in fields such as sociology, public health and economics. ARD models enable researchers to estimate the size of hidden populations, estimate personal network sizes, understand global network structures and fit complex latent variable models to massive network data. Many of the successes of ARD models have been driven by the utilisation of Bayesian modeling, which provides a principled and flexible way to fit and interpret these models for real data. In this work we create a coherent collection of Bayesian implementations of existing models for ARD, within the state of the art Bayesian sampling language, Stan. Our implementations incorporate within-iteration rescaling procedures by default, eliminating the typical post-processing step and improving algorithm run time and convergence diagnostics. Bayesian modelling permits natural tools for model criticism and comparison, which is largely unexplored in the ARD setting. Using synthetic data, we demonstrate how well competing models recover true personal network sizes and subpopulation sizes and how well existing posterior predictive checks compare across a range of Bayesian ARD models. We implement and provide code to leverage Stan's modelling framework for leave-one-out cross-validation, which has not previously been examined for ARD models.