Joint Analysis of Social and Item Response Networks with Latent Space Models
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The adjustment of students to a school environment is fundamentally linked to the friendship networks they form with their peers. Consequently, the complete picture of a student's adjustment can only be obtained by taking into account both their friendship network and their reported perceptions of the school environment. However, there is a lack of flexible statistical models and methods that can jointly analyze a social network with an item-response data matrix. In this paper, we propose a latent space model for heterogeneous (multimodal) networks (LSMH) and its extension LSMH-Item, which combine the framework of latent space modeling in network analysis with item response theory in psychometrics. Using LSMH, we summarize the information from the social network and the item responses in a person-item joint latent space. We use a Variational Bayesian Expectation-Maximization estimation algorithm to estimate the item and person locations in the joint latent space. This methodology allows for effective integration, informative visualization, and prediction of social networks and item responses. We apply the proposed methodology to data collected from 16 third-grade classrooms comprised of 451 third-grade students' self-reported friendships and school liking, which were collected as part of the Early Learning Ohio project. Through the person-item joint latent space, we are able to identify students with potential adjustment difficulties and found consistent connection between students' friendship networks and their well-being. We believe that using LSMH, researchers will be able to easily identify students in need of intervention and revolutionize the understanding of social behaviors.
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