We consider the problem of partitioning members in random graphs with
similar relational structure into subsets called blocks when the block
labels are unobserved or latent. Most statistical research on this topic
called blockmodels have been approached from a classical point of view.
Recently, a Bayesian approach to blockmodels has been presented by Snijders
and Nowicki (1997), and Nowicki and Snijders (2001), where the probability
of a relation between two actors depends only on the blocks to which the
actors belong but is independent of the actors. In this paper, we extend
their model to include covariates on actor level, and the block affiliation
probabilities are modeled conditional on the covariates via a multinomial
probit model. Posterior distributions of the model parameters, and predictive
posterior distributions of the block affiliation probabilities are computed
by using a straight forward Gibbs sampling algorithm. The proposed model
is illustrated on both real and simulated data.
Keywords: Bayesian analysis; Blockmodels; Gibbs sampling; Multinomial
probit; Random graphs.