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Social network data are complex and dependent data. At the macro-level, social networks often exhibit clustering in the sense that social networks consist of communities; and at the micro-level, social networks often exhibit complex network features such as transitivity within communities. Modeling real-world social networks requires modeling both the macro- and micro-level, but many existing models focus on one of them while neglecting the other. In recent work, [28] introduced a class of Exponential Random Graph Models (ERGMs) capturing community structure as well as microlevel features within communities. While attractive, existing approaches to estimating ERGMs with community structure are not scalable. We propose here a scalable two-stage strategy to estimate an important class of ERGMs with community structure, which induces transitivity within communities. At the first stage, we use an approximate model, called working model, to estimate the community structure. At the second stage, we use ERGMs with geometrically weighted dyadwise and edgewise shared partner terms to capture refined forms of transitivity within communities. We use simulations to demonstrate the performance of the two-stage strategy in terms of the estimated community structure. In addition, we show that the estimated ERGMs with geometrically weighted dyadwise and edgewise shared partner terms within communities outperform the working model in terms of goodness-of-fit. Last, but not least, we present an application to high-resolution human contact network data.
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Characterizing active learning environments in physics: network analysis of Peer Instruction classroom using ERGMs
Active learning is broadly shown to improve student outcomes as compared with traditional lecture, but more work must be done to distinguish outcomes between different types of active learning. We collected self-reported student social network data at early and late-semester times in a Peer Instruction classroom. The subsequent networks are modeled using exponential random graph models (ERGMs), which are a family of statistical models used with relational data, like social networks. We discuss preliminary findings using this method for a Peer Instruction class. The best-fit ERGM predicts long "chains" of student edges, such as might arise from students talking along rows in the lecture hall. ERGMs appear to be a promising method for quantifying network topology in active learning classrooms.
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- PAR ID:
- 10177393
- Date Published:
- Journal Name:
- 2019 PERC Proceedings
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1119/perc.2019.pr.Commeford
