DYNAMIC NETWORK ANALYSIS WITH MISSING DATA: THEORY AND METHODS.

Statistical methods for dynamic network analysis have advanced greatly in the past decade. This article extends current estimation methods for dynamic network logistic regression (DNR) models, a subfamily of the Temporal Exponential-family Random Graph Models, to network panel data which contain missing data in the edge and/or vertex sets. We begin by reviewing DNR inference in the complete data case. We then provide a missing data framework for DNR families akin to that of Little and Rubin (2002) or Gile and Handcock (2010a). We discuss several methods for dealing with missing data, including multiple imputation (MI). We consider the computational complexity of the MI methods in the DNR case and propose a scalable, design-based approach that exploits the simplifying assumptions of DNR. We dub this technique the "complete-case" method. Finally, we examine the performance of this method via a simulation study of induced missingness in two classic network data sets.

Analysis of the global trade network using exponential random graph models.

The global trade network has significant importance in analyzing countries' economic exchanges. Therefore, studying the global trade network and the factors influencing its structure is helpful for both economists and political decision makers. Putting these in mind, we try to analyze the global trade network from various viewpoints. We use the backbone filtering methods to construct a network of essential trades between countries. We analyze the structural, economic, geographical, political, and cultural factors and their effect on the global trade network using exponential random graph models. Additionally, we analyze the global trade network evolution using the separable temporal exponential random models. Our results show multiple structural, economic, geographical, and political factors affect the global trade network structure.

An approximation method for improving dynamic network model fitting.

There has been a great deal of interest recently in the modeling and simulation of dynamic networks, i.e., networks that change over time. One promising model is the separable temporal exponential-family random graph model (ERGM) of Krivitsky and Handcock, which treats the formation and dissolution of ties in parallel at each time step as independent ERGMs. However, the computational cost of fitting these models can be substantial, particularly for large, sparse networks. Fitting cross-sectional models for observations of a network at a single point in time, while still a non-negligible computational burden, is much easier. This paper examines model fitting when the available data consist of independent measures of cross-sectional network structure and the duration of relationships under the assumption of stationarity. We introduce a simple approximation to the dynamic parameters for sparse networks with relationships of moderate or long duration and show that the approximation method works best in precisely those cases where parameter estimation is most likely to fail-networks with very little change at each time step. We consider a variety of cases: Bernoulli formation and dissolution of ties, independent-tie formation and Bernoulli dissolution, independent-tie formation and dissolution, and dependent-tie formation models.