  The rise of socially targeted marketing suggests that decisions made by
consumers can be predicted not only from their personal tastes and
characteristics, but also from the decisions of people who are close to them in
their networks. One obstacle to consider is that there may be several different
measures for "closeness" that are appropriate, either through different types
of friendships, or different functions of distance on one kind of friendship,
where only a subset of these networks may actually be relevant. Another is that
these decisions are often binary and more difficult to model with conventional
approaches, both conceptually and computationally. To address these issues, we
present a hierarchical model for individual binary outcomes that uses and
extends the machinery of the auto-probit method for binary data. We demonstrate
the behavior of the parameters estimated by the multiple network-regime
auto-probit model (m-NAP) under various sensitivity conditions, such as the
impact of the prior distribution and the nature of the structure of the
network, and demonstrate on several examples of correlated binary data in
networks of interest to Information Systems, including the adoption of Caller
Ring-Back Tones, whose use is governed by direct connection but explained by
additional network topologies.
