Hierarchical Models for the Formation and Evolution of Ensembles of Social Networks

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This project deals with the development, testing, and deployment of models for multiple social networks, particularly those with conditionally independent ties. The project will explore their properties with respect to partial pooling across networks, a case that includes a single network or ensemble of networks observed over time. This research is motivated by problems in many sociological fields, particularly education research, in which multiple groups of people form their own networks, including students and teachers alike. The project will build on preliminary constructions of the Hierarchical Latent Space Model and the Hierarchical Mixed-Membership Stochastic Block Model by focusing on how information can be pooled across networks, through hierarchical structure specification, and how model parameters evolve through time, through model-dependent autoregression or other smoothing methods. Multiple ways in which an intervention can affect a subset of these networks also will be studied. These models will use both simulated and real-world data to validate their effectiveness. Standard methods for fitting these models, such as Markov Chain Monte Carlo, will be used initially, though wider deployment of these models will demand the development of quicker inferential procedures based on Variational Inference and/or Sequential Monte Carlo. Finally, model validation will be considered in each of these cases, in terms of comparison to other models as well as the adequacy of a model's fit to data.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. Instead of treating each network separately or assuming that all come from exactly the same model (which is possible only in limited circumstances), this project will provide a new, clearly formulated methodology to deal with this type of data. Researchers in related fields will have the opportunity to use the methods on their own research. Computer code for these routines also will be made available.