Estimating the effects of network covariates on subgroup insularity with a hierarchical mixed membership stochastic blockmodel

Social networks describe the relationships and interactions among a group of individuals. In many peer relationships, individuals tend to associate more often with some members than others, forming subgroups or clusters. Subgroup structure varies across networks; subgroups may be insular, appearing distinct and isolated from one another, or subgroups may be so integrated that subgroup structure is not visually apparent, and there are numerous ways of quantifying these types of structures. We propose a new model that relates the amount of subgroup integration to network attributes, building on the mixed membership stochastic blockmodel (Airoldi et al., 2008) and subsequent work by Sweet and Zheng (2017) and Sweet et al. (2014). We explore some of the operating characteristics of this model with simulated data and apply this model to determine the relationship between teachers’ instructional practices and their classrooms’ peer network subgroup structure.     

A mixed membership model-based measure for subgroup integration in social networks

Social networks analysis often involves quantifying subgroup structure in which tie density is greater among nodes in the same subgroup than between subgroups. One such measure, subgroup insularity or segregation, is the extent that subgroups are separate from each other. We introduce a new measure, γ, which is a parameter from the mixed membership stochastic blockmodel (MMSBM; Airoldi et al., 2008), and differs from many existing measures in that γ does not depend on node membership. We compare this measure to several well-known measures and use simulation studies and real data analysis to provide insight into how this measure can be used in practice.