Structural Models of Network Contacts Between Actors Governed by Activity and Attraction

Sammanfattning: This thesis consists of five papers on the subject of statistical modeling of stochastic networks. The NG-model proposed in Paper I combines a block structure with parameters that capture the identities of vertices and thus the new approach stresses the concept of ego-nets, which describes the structure around identified vertices. The models proposed in Papers II-V are closely related to the NG-model proposed in Paper I. In Paper I, we propose a parametric digraph model which models network data utilizing vertex group memberships and the identities of vertices, namely the NG-model of independent out-nets. We present estimation methods based on the EM algorithm for the parameter estimations and the recovery of latent group memberships. A companion model (the reversed NG-model) is also introduced which reverses the parameterization of the NG-model. We apply both models to directed social networks. In Paper II, we study an undirected version of the NG-model and investigate parameter estimation and latent group membership recovery techniques. We apply the methods to model undirected social networks. In Paper III, we study various probabilistic properties of the NG-model introduced in Paper I. We propose a similarity matrix as a tool for comparing actors' ego-nets and discuss its probabilistic properties. We propose several clustering coefficients, whose probabilistic properties are investigated in the NG-model setting. In Paper IV, we propose two models as extensions of the NG-model by incorporating the effect of actors' attributes (covariates) into the modeling of network data. We propose algorithms for the parameter estimation and the recovery of latent group memberships. We apply the models to both simulated and real networks. In Paper V, we propose a parametric digraph model conditioned on given sequence of vertex out-degrees by utilizing the parameterization of the reversed NG-model proposed in Paper I. We derive the form of the probability function and the marginal distributions. We propose parameter estimation methods and methods for drawing samples from the distribution of the conditional model. We investigate several probabilistic properties of the parameter estimates and present examples of applications of the model to both simulated and real network data.