Settings in Social Networks: a Measurement Model†

A class of statistical models is proposed which aims to recover latent settings structures in social networks. Settings may be regarded as clusters of vertices. The measurement model builds on two assumptions. The observed network is assumed to be generated by hierarchically nested latent transitive structures, expressed by ultrametrics. It is assumed that expected tie strength decreases with ultrametric distance. The approach could be described as model-based clustering with an ultrametric space as the underlying metric to capture the dependence in the observations. Maximum likelihood methods as well as Bayesian methods are applied for statistical inference. Both approaches are implemented using Markov chain Monte Carlo methods.