Developing Latent Hierarchical Network Models for Cross-Cultural Comparisons of Social and Economic Inequality

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Researchers from across the social sciences are increasingly using the tools of network analysis to represent the groups they study, mapping out friendships between students, business relations between companies, and supportive relationships between villagers. These networks are often based on surveys, where people's reports of their relationships are combined to represent the overall structure of entire communities. While these network datasets are increasingly fine-grained and complex, the tools used to study them often require simplifications and assumptions that social scientists are uncomfortable with (e.g., assuming that people's recollections are perfect, or treating people as isolated individuals rather than members of larger social groupings like households). We will develop network models that fully exploit the various facets of the information typically contained in social network datasets. In doing this, we depart from prevalent models in contemporary social network analysis that treat an observed network data set as representing the "true" network. Instead, we assume that the true network is "latent" and, therefore not empirically observed, and further frame the observed network data as an imperfect measurement of what we are modelling. In proposing this probabilistic framework, we will first account for the various individual-level biases that shape who people name (and who they do not). We will then extend our model to allow for nodes (here, people) to form into hierarchically nested groups (for example, households) and thus capture units at the different levels that are present in the system. Finally, we will expand this model to account for changes over time of both the individual units at different levels of the hierarchy and their relationships, thus capturing relevant time evolution.To do this, we will bring together a diverse team of researchers interested in the analysis and modelling of network data. We are complementing the skills and perspectives of the anthropologist (Power), psychologist (Redhead), and statistical physicist (De Bacco) co-investigators with the addition of: a mathematician studying complex networks (Prof Ginestra Bianconi, Queen Mary University of London), a computer scientist working on applied causal inference (Dr Dhanya Sridhar, Columbia University), an engineer and computer scientist working on machine learning and probabilistic inference (Prof Isabel Valera, Saarland University), a statistician developing multilevel network models (Assoc Prof Tracy Sweet, University of Maryland), an anthropologist and statistician developing Bayesian statistical tools (Prof Dir Richard McElreath, Max Planck Institute for Evolutionary Anthropology), an anthropologist gathering and developing tools for social network data (Assoc Prof Jeremy Koster, University of Cincinnati), and a social statistician with expertise in longitudinal multilevel models (Prof Fiona Steele, London School of Economics). With this diversity of perspectives (whether of discipline, application, or career stage), we are confident that our collaboration will result in the development of general, robust generative network models with wide potential for application across the sciences. We are committed to facilitating the uptake of these models, so we will be hiring a research officer to develop user-friendly R and Python packages for their use. This project is grounded in the analytical needs of the "ENDOW project," a US National Science Foundation-funded project that is primarily examining how network structure, and people's position within that network, is associated with the distribution of wealth inequality both within and between societies. Over forty researchers are collecting social network data from rural communities around the world for this project. The models we develop here will help us understand (and potentially then rectify) some of the drivers of social and economic inequality around the world.