Envisaging the Unobserved: a Stochastic Actor-Oriented Model for Systems of Overlapping Subgroups

This paper presents a novel statistical framework for modeling cohesive subgroups in cross-sectional network data, adhering to prior ideas about the mean and variance of the number of actors per subgroup and subgroups per actor. Subgroups emerge from actors' membership decisions, with cohesion driven by their preference to co-member with network contacts. A stationary two-mode Stochastic Actor-Oriented Model is specified to obtain the distribution of memberships in subgroups. The model is estimated using the Method of Moments, with target statistics derived from the prior ideas. As a showcase, we model unobserved peer groups in a friendship network. The results indicate that actors form cohesive subgroups of varying composition, characterized by denser overlaps under preference for multiple memberships with network contacts.