IMPROVING ESTIMATION FOR EXPONENTIAL-FAMILY RANDOM GRAPH MODELS
Open Access
- Author:
- Hummel, Ruth M
- Graduate Program:
- Statistics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- November 29, 2010
- Committee Members:
- David Russell Hunter, Dissertation Advisor/Co-Advisor
David Russell Hunter, Committee Chair/Co-Chair
James Landis Rosenberger, Committee Member
Murali Haran, Committee Member
Scott David Gest, Committee Member - Keywords:
- composite likelihood
penalized likelihood
pseudolikelihood
maximum likelihood estimation
exponential random graph model
bias correction
Mean value parameterization
%Maximum likelihood estimation
parameter estimation
Markov chain Monte Carlo
Exponential family random graph model
contrastive divergence
exponential families
convex hull - Abstract:
- A statistical model for observed network data allows us to both summarize quantitatively the effects that give rise to the network and simulate new networks from a probability distribution that resembles the generating distribution of the original network. This thesis discusses a flexible class of statistical models for network data, called ERGMs (exponential family random graph models), and describes some of the challenges in parameter estimation for these models. We present a novel computational method that results in more usability of Markov chain Monte Carlo methods for estimation in ERGMs, enabling an MCMC MLE to be more easily found in many cases. This so-called 'stepping' algorithm is illustrated on a transcriptional regulation network for E.coli, an example where previous attempts to approximate an MLE had failed. In light of this new development in approximating the MLE, additional alternative estimators are introduced, including the frequently-used MPLE (maximum pseudolikelihood estimate), as well as bias-adjusting versions of both the MPLE and the MCMC MLE, a bias-adjustment for the latter being applied here for the first time in this context. Comparisons are made between these estimators and the MCMC MLE on a network of corporate law partnerships, showing improved accuracy and efficiency of the estimation for the bias-adjusted approximate MLE. Additional estimators are introduced in the context of contrastive divergence methods, frequently used in computer science and statistical mechanics. The connection between contrastive divergence and likelihood maximization is explored, and the wide class of composite likelihood functions is applied to ERGMs, with estimation by contrastive divergence. This work advances the current practice of parameter estimation and improves the accuracy of prediction and inference for network models. Two of the computational methods introduced in this thesis, the stepping algorithm and the penalized MLE, are now implemented in the publicly available ERGM package for R.