HNM: Hierarchical Network Models

This project deals with the development, testing and deployment of models for multiple social networks, particularly those with conditionally independent ties.  We develop methods for single networks, as well as for partial pooling across ensembles of networks, and explore both the influence of covariates and interventions, and the evolution of networks over time. 

Data on multiple social networks arising from the same generative mechanisms, and evolving over time together, are becoming increasingly available in education research, public health and the social sciences. Our work provides new, clearly formulated methodology and models for this type of data, rather than treating each network separately or assuming that all come from exactly the same model. We are also developing R packages for fitting these models, that can be used by any researcher with multiple network data.

Our work elaborates, and explores the operating characteristics of, the Hierarchical Network Models (HNM) framework of Sweet, Thomas and Junker (2013), including the Hierarchical Latent Space Model and Hierarchical Mixed-Membership Stochastic Block Model for ensembles of networks.  With this framework one can model and detect the effects of interventions and other covariates on the structure of social networks, by pooling information across ensembles of social networks (teachers’ professional networks across multiple school buildings, students’ peer networks across multiple geographic areas, etc.).

CID: Conditionally Independent Dyads

A key computational tool is the R package CIDnet (Thomas, Dabbs, Sweet,Saldinle & Junker, 2013), which allows for mixures of network structure and pools information across multiple networks through hierarchical Bayes structure; covariates affecting some (e.g., an intervention) or all (e.g. a node or tie covariate) networks can also be modelled.  We also study how model parameters evolve through time, through model-dependent autoregression and other smoothing methods, and we illustrate our results in analyses of simulated and real-world data sets.  

Tools for model validation are also being developed, both for comparison to other models and for directly assessing the adequacy of a model's fit to data, e.g  with cross-validation methods.

Our initial implementation of CIDnet and related software for the HLSM and HMMBSM is based on standard methods such as Markov Chain Monte Carlo.  In anticipation of wider deployment of these models, we are also exploring faster inferential procedures based on Variational Inference and Sequential Monte Carlo. 

Funding

This work has been generously supported by the following grants.

• Hierarchical Models for the Formation and Evolution of Ensembles of Social Networks. National Science Foundation, Measurement Methodology and Statistics Program. Award #SES-1229271. 
• Hierarchical Network Models for Education Research. Institute of Educational Sciences (US Department of Education). Award #R305D120004. 
• Program in Interdisciplinary Education Research.  Institute of Educational Sciences (US Department of Education). Award #R305B040063.