Computing Pseudolikelihood Estimators for Exponential-Family Random Graph Models
Volume 21, Issue 2 (2023): Special Issue: Symposium Data Science and Statistics 2022, pp. 295–309
Pub. online: 15 March 2023
Type: Computing In Data Science
Open Access
Open Access
Received
1 August 2022
1 August 2022
Accepted
24 February 2023
24 February 2023
Published
15 March 2023
15 March 2023
Abstract
The reputation of the maximum pseudolikelihood estimator (MPLE) for Exponential Random Graph Models (ERGM) has undergone a drastic change over the past 30 years. While first receiving broad support, mainly due to its computational feasibility and the lack of alternatives, general opinions started to change with the introduction of approximate maximum likelihood estimator (MLE) methods that became practicable due to increasing computing power and the introduction of MCMC methods. Previous comparison studies appear to yield contradicting results regarding the preference of these two point estimators; however, there is consensus that the prevailing method to obtain an MPLE’s standard error by the inverse Hessian matrix generally underestimates standard errors. We propose replacing the inverse Hessian matrix by an approximation of the Godambe matrix that results in confidence intervals with appropriate coverage rates and that, in addition, enables examining for model degeneracy. Our results also provide empirical evidence for the asymptotic normality of the MPLE under certain conditions.
Supplementary material
Supplementary MaterialThe R code file and the ergm package that implements the new methods.
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