Interpretable Stochastic Block Influence Model: Measuring Social Influence among Homophilous Communities

Decision-making on networks can be explained by both homophily and social influences. While homophily drives the formation of communities with similar characteristics, social influences occur both within and between communities. Social influences can be reasoned through role theory, which indicates that the influences among individuals depending 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 such 'roles', affecting particular decision-making processes. We propose a generative model named the Stochastic Block Influence Model and jointly analyze both network formation and behavioral influences within and between different empirically-identified communities. To evaluate the performance and demonstrate the interpretability of our method, we study the adoption decisions for a microfinance product in Indian villages. We show that although individuals tend to form links within communities, there are strongly positive and negative social influences between communities, supporting the weak ties theory. Moreover, communities with shared characteristics are associated with positive influences. In contrast, communities that do not overlap are associated with negative influences. Our framework facilitates the quantification of the influences underlying decision communities and is thus a helpful tool for driving information diffusion, viral marketing, and technology adoption.