Minority size and ethnic homophily. Preference interpretations and misspecification of ERG models

Research using exponential random graph (p* or ERG) models of ethnic  friendship homophily in schools suggests that pupils have stronger preferences for in-group choices in classrooms with a larger ethnic minority. We demonstrate theoretically how this preference interpretation of ERG homophily coefficients could be at odds with an actor-oriented process model explicitly representing homophily preferences. We use agent-based computational modelling to represent theoretically alternative individual-level processes of network formation and derive their emergent consequences for network structure and intergroup relations in particular. This work shows that in classrooms with larger ethnic minorities, stronger segregation may arise as an emergent property from the interdependent network choices of individuals who hold the same preferences than those in classrooms with smaller minorities. We then show how misspecifications of an ERG model of the simulated cross-sectional network data can lead to this discrepancy between the preference assumptions made in the process model and the inferences researchers may draw from the statistical model of the emergent networks. ERG model specifications are presented that better align ERG model and actor-oriented model and implications are discussed for strategies to foster inter-ethnic integration in classrooms.