Incorporating Covariates Into Stochastic Blockmodels

Abstract

Social networks in education commonly involve some form of grouping, such as friendship cliques or teacher departments, and blockmodels are a type of statistical social network model that accommodate these grouping or blocks by assuming different within-group tie probabilities than between-group tie probabilities. We describe a class of models, covariate stochastic blockmodels (CSBMs), that incorporates covariates into blockmodels. These models not only estimate the effects of covariates in the presence of the block structure but also can determine differential covariate effects such as within blocks versus between blocks. For example, education researchers can now determine those factors that mitigate relationships both within schools and between schools. We introduce several CSBMs as examples and present a series of simulation studies to investigate both the feasibility and some operating characteristics as well as fit CSBMs to real network data.