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Abstract:
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Relational data indicate interactions or associations between pairs of actors. For accurate prediction and inference, models for relational data must represent the inherent dependencies among relations involving the same individual. Much recent research has focused on models that represent higher-order dependencies between multiple relations, such as transitivity and stochastic equivalence. We show that models that focus on these higher order dependencies may compromise their ability to represent pairwise dependencies between relations, which we term ``second-order'' dependencies. Thus, we propose a model for network data that exclusively represents the pairwise dependencies in relational data. This model is based on an assumption of exchangeability, which is pervasive in relational data models in the statistics literature. We show that this model is equivalent to an existing latent variable model for relational data and show that the proposed model can capture higher-order dependencies that are expected by the study of social interactions. Lastly, we provide a test for whether the modeling of dependencies beyond second-order is suggested by an observed relational data set.
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