Latent Network Models to Account for Noisy, Multiply-Reported Social Network Data

TL;DR

This paper introduces a probabilistic model that effectively integrates multiply-reported social network data, accounting for reporting biases and mutuality, to produce more accurate network structures from survey responses.

Contribution

It presents a novel scalable variational inference-based model that explicitly incorporates reporting tendencies and mutuality, improving the estimation of social networks from noisy, multiply-reported data.

Findings

Strong evidence of mutuality in datasets

Reciprocity varies by relationship type

Network estimates differ significantly from standard methods

Abstract

Social network data are often constructed by incorporating reports from multiple individuals. However, it is not obvious how to reconcile discordant responses from individuals. There may be particular risks with multiply-reported data if people's responses reflect normative expectations -- such as an expectation of balanced, reciprocal relationships. Here, we propose a probabilistic model that incorporates ties reported by multiple individuals to estimate the unobserved network structure. In addition to estimating a parameter for each reporter that is related to their tendency of over- or under-reporting relationships, the model explicitly incorporates a term for ``mutuality,'' the tendency to report ties in both directions involving the same alter. Our model's algorithmic implementation is based on variational inference, which makes it efficient and scalable to large systems. We apply our model to data from 75 Indian villages collected with a name-generator design, and a Nicaraguan community collected with a roster-based design. We observe strong evidence of ``mutuality'' in both datasets, and find that this value varies by relationship type. Consequently, our model estimates networks with reciprocity values that are substantially different than those resulting from standard deterministic aggregation approaches, demonstrating the need to consider such issues when gathering, constructing, and analysing survey-based network data.