  Decision-making on networks can be explained by both homophily and social
influence. While homophily drives the formation of communities with similar
characteristics, social influence occurs both within and between communities.
Social influence can be reasoned through role theory, which indicates that the
influences among individuals depend on their roles and the behavior of
interest. To operationalize these social science theories, we empirically
identify the homophilous communities and use the community structures to
capture the "roles", which affect the particular decision-making processes. We
propose a generative model named Stochastic Block Influence Model and jointly
analyze both the network formation and the behavioral influence within and
between different empirically-identified communities. To evaluate the
performance and demonstrate the interpretability of our method, we study the
adoption decisions of microfinance in an Indian village. We show that although
individuals tend to form links within communities, there are strong positive
and negative social influences between communities, supporting the weak tie
theory. Moreover, we find that communities with shared characteristics are
associated with positive influence. In contrast, the communities with a lack of
overlap are associated with negative influence. Our framework facilitates the
quantification of the influences underlying decision communities and is thus a
useful tool for driving information diffusion, viral marketing, and technology
adoptions.
