A Tale of Two Datasets: Representativeness and Generalisability of Inference for Samples of Networks

The last two decades have witnessed considerable progress on foundational aspects of statistical network analysis, but less attention has been paid to the complex statistical issues arising in real-world applications. Here, we consider two samples of within-household contact networks in Belgium generated by different but complementary sampling designs: one smaller but with all contacts in each household observed, the other larger and more representative but recording contacts of only one person per household. We wish to combine their strengths to learn the social forces that shape household contact formation and facilitate simulation for prediction of disease spread, while generalising to the population of households in the region. To accomplish this, we introduce a flexible framework for specifying multi-network models in the exponential family class and identify the requirements for inference and prediction under this framework to be consistent, identifiable, and generalisable, even when data are incomplete; explore how these requirements may be violated in practice; and develop a suite of quantitative and graphical diagnostics for detecting violations and suggesting improvements to a candidate model. We report on the effects of network size, geography, and household roles on household contact patterns (activity, heterogeneity in activity, and triadic closure).