A BAYESIAN APPROACH TO MODELING STOCHASTIC BLOCKSTRUCTURES WITH COVARIATES

Abstract

We consider social networks in which the relations between actors are governed by latent classes of actors with similar relational structure, i.e., blockmodeling. In Snijders and Nowicki (1997) and Nowicki and Snijders (2001), a Bayesian approach to blockmodels is presented, where the probability of a relation between two actors depends only on the classes to which the actors belong but is independent of the actors. When actors are a priori partitioned into subsets based on actor attributes such as race, sex and income, the model proposed by Nowicki and Snijders completely ignores this extra piece of information. In this paper, a blockmodel that is a simple extension of their model is proposed specifically for such data. The class affiliation probabilities are modeled conditional on the actor attributes via a multinomial probit model. Posterior distributions of the model parameters, and predictive posterior distributions of the class affiliation probabilities are computed by using a straightforward Gibbs sampling algorithm. Applications are illustrated with analysis on real and simulated data sets

Key Words:

• Bayesian analysis
• Blockmodels
• Gibbs sampling
• Multinomial probit
• Random graphs

Notes

The author would like to thank Professor Ove Frank, Dr Mattias Villani, Johan Koskinen and the referees for detailed an insightful comments.