Latent network models to account for noisy, multiply reported social network data

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 a Nicaraguan community collected with a roster-based design and 75 Indian villages collected with a name-generator 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.

Automated summary

Social network data often involve multiple individuals' reports, and it is challenging to reconcile conflicting responses. There are potential risks in multiply reported data if people's responses are influenced by the expectation of balanced, reciprocal relationships. We propose a probabilistic model that incorporates ties reported by multiple individuals and explicitly considers factors like over- or under-reporting tendencies and mutual relationships. Applying this model to real-world data, we find strong evidence of mutuality, which varies across relationship types. Our findings highlight the importance of addressing these issues in collecting, constructing, and analyzing survey-based network data.