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.