Hierarchical Network Models for Education Research: Hierarchical Latent Space Models

Intervention studies in school systems are sometimes aimed not at changing curriculum or classroom technique, but rather at changing the way that teachers, teaching coaches and administrators in schools work with one another—in short, changing the professional social networks of educators. Current methods of social network analysis are ill-suited to modeling the multiple partially-exchangeable networks that arise in randomized field trials and observational studies in which multiple classrooms, schools, or districts are involved, and to detecting the effect of an intervention on the social network itself. To address these needs, we introduce a new modeling framework, the Hierarchical Network Models (HNM) framework. The HNM framework can be used to extend single-network statistical network models to multiple networks, using a hierarchical modeling approach. We show how to generalize the latent space model for a single network to the HNM/multiple-network setting, and illustrate our approach with real and simulated social network data among education professionals.