Topics in Exponential Random Graph Modeling
Open Access
- Author:
- Bomiriya, Rashmi Pankajai
- Graduate Program:
- Statistics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 05, 2014
- Committee Members:
- David Russell Hunter, Dissertation Advisor/Co-Advisor
David Russell Hunter, Committee Chair/Co-Chair
Murali Haran, Committee Member
Le Bao, Committee Member
Rachel Annette Smith, Committee Member - Keywords:
- ERGMs
networks
bipartite
homophily
semi-parametric Bayesian
infectious disease
SEIR - Abstract:
- Exponential-family Random Graph Models (ERGMs) are a class of models that is frequently used for modeling social networks. ERGMs allow structural features as well as covariate information on networks in the models. There are many network statistics that can be used in an ERGM that are already incorporated in the R package 'ergm'. However, for certain types of networks such as bipartite networks, some standard network statistics cannot be applied as they are. The fi rst portion-chapter 2-of this report introduces a few network statistics that can be used to measure the homophily eff ects in a bipartite network with nodal attributes and we have already added this new model terms to the R package 'ergm'. We provide some applications of these statistics and some simulations that study the performance of the introduced measure. This is joint work with Prof. David R. Hunter and Shweta Bansal. The second portion-chapter 3-of this thesis extend the idea of Bayesian inference for ERGMs to Curved-like ERGMs. Currently, the R package Bergm provides tools for Bayesian inference for ERGMs (Caimo and Friel, 2013). The extensions in this chapter have been carried out by modifying the algorithm in Bergm--which is a combination of the exchange algorithm and the parallel adaptive direction sampler--and will soon be available as a part of the same package. Chapter 4 of this report also relates to ERGMs, but describes a very different application of ERGMs--i.e., studying the dynamics of epidemics via network analysis techniques. Groendyke et al. (2011a) study the properties of a disease outbreak and the network on which it spread given epidemic data--with the help of their package `epinet'--that is assumed to come from a disease spread across some contact network, which they describe by an ERGM. However, the standard models have drawbacks in modeling varying shapes of degree distributions. Hence, we introduce a semi-parametric Bayesian model and study the improvement in the inferences made. Also, we describe few other useful extensions we have made to the package 'epinet'. This is joint work with Dr. Michael Schweinberger. Finally, in chapter 5, we summarize the work of this dissertation and discuss a few paths for future developments--mostly on chapter 4. Here, we introduce some existing problems and possible directions for tackling them.