  The last two decades have seen considerable progress in foundational aspects
of statistical network analysis, but the path from theory to application is not
straightforward. Two large, heterogeneous samples of small networks of
within-household contacts in Belgium were collected using two 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 describe 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 candidate models. We report on the effects of
network size, geography, and household roles on household contact patterns
(activity, heterogeneity in activity, and triadic closure).
