A Bayesian Approach to Modeling Stochastic Blockstructures with Covariates

Christian Tallberg

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.

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