Sender- and receiver-specific blockmodels

We propose a sender-specific blockmodel for network data which utilizes both the group membership and the identities of the vertices. This is accomplished by introducing the edge probabilities (ŵ¿,ν) for 1 ≤ i ≤ c, 1 ≤ v ≤ n, where í specifies the group membership of a sending vertex and ν specifies the identity of the receiving vertex. In addition, group membership is consider to be random, with parameters (í>í)í=io We present methods based on the EM algorithm for the parameter estimations and discuss the recovery of latent group memberships. A companion model, the receiver-specific blockmodel, is also introduced in which the edge probabilities (≠_uj) for 1 ≤ u ≤ n, 1 < j < c depend on the membership of a vertex receiving a directed edge. We apply both models to several sets of social network data.