Source: Ann. Appl. Stat. Volume 4, Number 1
(2010), 5-25.
Network models are widely used to represent relational information
among interacting units and the structural implications of these
relations. Recently, social network studies have focused a great
deal of attention on random graph models of networks whose nodes
represent individual social actors and whose edges represent a
specified relationship between the actors.
Most inference for social network models assumes that the presence
or absence of all possible links is observed, that the
information is completely reliable, and that there are no
measurement (e.g., recording) errors. This is clearly not true
in practice, as much network data is collected though sample
surveys. In addition even if a census of a population is
attempted, individuals and links between individuals are missed
(i.e., do not appear in the recorded data).
In this paper we develop the conceptual and computational theory
for inference based on sampled network information. We first
review forms of network sampling designs used in practice. We
consider inference from the likelihood framework, and develop a
typology of network data that reflects their treatment within
this frame. We then develop inference for social network models
based on information from adaptive network designs.
We motivate and illustrate these ideas by analyzing the effect of
link-tracing sampling designs on a collaboration network.
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