Title:

Social influence models with missing data

Authors: 

Alex Stivala (University of Melbourne)
Colin Gallagher (University of Melbourne)
David Rolls (University of Melbourne)
Peng Wang (Swinburne University of Technology)
Garry Robins (University of Melbourne)


Abstract:

The autologistic actor attribute model (ALAAM) is a statistical model
based on the well-established exponential random graph model (ERGM)
for social networks. ALAAMs can be used as a social influence model,
predicting an actor's attribute based on his or her network ties, as
well as attributes of the actor and his or her network partners. In
this way an ALAAM is similar to logistic regression, but, unlike
logistic regression or similar statistical techniques, it specifically
does not assume independence of the predicted attributes: an actor's
attribute may depend also on those of its neighbors in the network.

Using simulation studies, we investigate the effect of using simple
random samples and snowball samples of network data on ALAAM parameter
inference.  We examine both fixed choice sampling designs (in which an
actor nominates up to a fixed maximum number of network partners), and
designs with no such limit (all network partners are assumed to be
named).

One practical motivation for this study is the manner in which social
influence models may be applied to epidemiological studies of health
outcomes in community samples when the entire community network is
simply not available. These studies often use cross-sectional data to
examine the prevalence of health conditions. Outcomes are often
binary, representing probable diagnosis, and so logistic regression is
used. However, an important question in these studies is that of
interdependence of outcomes and the potential spread or co-occurrence
of such outcomes across network ties.

We examine Type I and Type II error rates, and find that parameter
inference works well even with a large fraction of missing nodes. For
a given network sample size, obtaining the sample by snowball sampling
results in higher power on certain parameters than simple random
sampling. These results give confidence that ALAAM parameter inference
can be used on sampled network data, even when the sample only covers
a relatively small proportion of the entire network.