Building stochastic blockmodels

The literature devoted to the construction of stochastic blockmodels is relatively rare compared to that of the deterministic variety. In this paper, a general definition of a stochastic blockmodel is given and a number of techniques for building such blockmodels are presented. In the statistical approach, the likelihood ratio statistic provides a natural index to evaluate the fit of the model to the data. The model itself consists of a set of actors partitioned into positions with respect to a definition of equivalence, and a representation based on estimated probabilities. The specific statistical model that is used to illustrate the techniques is p₁, which was first introduced as a method for stochastic blockmodeling by Fienberg and Wasserman (1981), and developed by Holland et al. (1983) and Wasserman and Anderson (1987).