Using Exponential Random Graph Models and Visual Analysis to Investigate Within-School Segregation

Geoffrey West


De jure academic tracking in public secondary schools has fallen out of favor over the past few decades due to immense pressure from education advocates. In today's schools, however, students are placed not into formalized "academic" or "career" tracks, but rather, put into informal groupings of "regular", "honors", and "advanced" classes. If we think about curriculum in schools as a series of connections between students and the courses they take, the school itself starts to take the form of a bipartite network. By transforming the bipartite connections between students and their courses to a monopartite network of student-to-student connections, one can create a network of a school that is based on course co-enrollment. Using a novel dataset from a large urban school district in the Southeastern United States, I use exponential random graph modeling to identify predictors of course co-enrollment of high school and middle school students. More specifically, I estimate the degree to which homophily based on grade level, ethnocracial group, sex, free-or-reduced lunch, and special education needs are associated with the formation of classmate ties. To do this, I use the R package “ergm” with terms “nodematch” and “nodemix” while adjusting for other covariates. I show that school curricular networks display a high level of homophily based on the student characteristics mentioned above. Using network-meta-analysis, I explore how school-level variables predict the degree of homophily within a school. While exponential random graph modeling can estimate the degree of clustering, visual analysis plays a vital role in understanding how students are clustered together. Using Gephi, a visualization tool for social networks, I visualize the curricular networks of schools, complementing the results from the exponential random graph models. While these visualizations initially create unruly “hairballs” with hundreds of nodes and tens of thousands of edges, I show how adjusting the color and size of nodes can provide meaningful information for education practitioners and advocates. I argue the analysis of curricular networks in schools requires both a strategy for estimating the degree of clustering as well as a strategy for visualizing where the clusters occur.

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