From dyads to groups: a partition model for non-overlapping groups

Marion Hoffman, Per Block, Tom Ab Snijders


Many social relations are not only situated at the level of dyads but also within groups. Such groups are formed, for example, when students decide with whom to carry out their group assignments, when researchers collaborate on the writing of scientific papers, or when citizens join different political parties. Although many theories acknowledge the importance of groups to explain social outcomes, we currently lack statistical tools to explain their composition. Current network models rely on dyadic processes that express individual preferences and can only represent social groups as two-mode ties or node attributes. An important limitation of this approach is that it does not allow the modeling of coordination processes between individuals. For example, the creation of a group might not be accurately represented by successive creations of dyadic ties, as it can be the result of the joint decision of individuals to come together. Recent work on higher order links and hypergraphs shows, however, that this gap can be remedied. We contribute to these attempts by proposing a statistical model tailored for group representation inspired by previous models for social ties such as ERGMs. The proposed model aims at explaining a cross-sectional observation of group memberships. We consider the case of non-overlapping groups (i.e., actors cannot belong to more than a group) and represent groups as elements of a partition of the actor set. Our model follows the logic of well-established exponential family distributions and builds upon methods used in Social Network analysis and Biology. Dependencies between actors can then be parametrized in the definition of sufficient statistics at the group level and inference can be drawn from a Markov Chain Monte Carlo procedure. First, the mathematical definition of the model is described and its specific properties are derived. Second, some operationalization at the group level of social mechanisms is proposed. Finally, an application to the study of team formation during scientific competitions (hackathons) is presented. Some extensions to the case of dynamic memberships or to overlapping memberships are discussed.

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