Hierarchical longitudinal models of relationships in social networks.

Motivated by the need to understand the dynamics of relationship formation and dissolution over time in real-world social networks we develop a new longitudinal model for transitions in the relationship status of pairs of individuals ("dyads"). We first specify a model for the relationship status of a single dyad and then extend it to account for important inter-dyad dependencies (e.g., transitivity - "a friend of a friend is a friend") and heterogeneity. Model parameters are estimated using Bayesian analysis implemented via Markov chain Monte Carlo. We use the model to perform novel analyses of two diverse longitudinal friendship networks: an excerpt of the Teenage Friends and Lifestyle Study (a moderately sized network) and the Framingham Heart Study (FHS) (a large network).