Modeling unobserved heterogeneity in social network data analysis

The analysis of network data has become a challenging and growing field in statistics in recent years. In this context, the so-called Exponential Random Graph Model (ERGM) is a promising approach for modeling network data. However, the parameter estimation proves to be demanding, not only because of computational and stability problems, especially in large networks but also because of the unobserved presence of nodal heterogeneity in the network. This thesis begins with a general introduction to graph theory, followed by a detailed discussion of Exponential Random Graph Models and the conventional parameter estimation approaches. In addition, the advantages of this class of models are presented, and the problem of model degeneracy is discussed. The first contribution of the thesis proposes a new iterative estimation approach for Exponential Random Graph Models incorporating node-specific random effects that account for unobserved nodal heterogeneity in unipartite networks and combines both maximum likelihood and pseudolikelihood estimation methods for estimating the structural effects and the nodal random effects, respectively, to ensure stable parameter estimation. Furthermore, a model selection strategy is developed to assess the presence of nodal heterogeneity in the network. In the second contribution, the iterative estimation approach is extended to bipartite networks, explaining the estimation and the evaluation techniques. Furthermore, a thorough investigation and interpretation of nodal random effects in bipartite networks for the proposed model is discussed. Simulation studies and data examples are provided to illustrate both contributions. All developed methods are implemented using the open-source statistical software R