Adrian E. Raftery
Network models are widely used to represent relations between social actors. Network data often show transitivity, meaning that two actors that have ties to a third actor are more likely to be tied than actors that do not, homophily, meaning that actors who are similar are more likely to be linked, and clustering. We often want to find clusters of actors, and the number
of clusters in the data is often unknown. We propose a new model, the Latent Position Cluster Model, under which the probability of a tie between two actors depends on the distance between them in an unobserved Euclidean ``social space,'' and the actors' locations in
the latent social space arise from a mixture of distributions, each one corresponding to a cluster. We propose methods for estimating the model parameters and the number of clusters. Our model represents transitivity, homophily, and clustering, and does not require the number of clusters to be known. The model makes it easy to simulate networks with clustering, and these may be useful as inputs to models of more complex systems, such as epidemic models of infectious disease. A free software package in the statistical language, called latentnet, is available to analyze data using the model.
