JDS Journal of Data Science 1683-86021680-743X1680-743X School of Statistics, Renmin University of China JDS1094 10.6339/23-JDS1094 Computing in Data Science Computing Pseudolikelihood Estimators for Exponential-Family Random Graph Models SchmidChristian S.1 HunterDavid R.dhunter@stat.psu.edu2∗ F. Hoffmann-La Roche Ltd, Switzerland Pennsylvania State University, USA Corresponding author. Email: dhunter@stat.psu.edu. 20231532023212295309 Supplementary Material

The R code file and the ergm package that implements the new methods.

1820222422023 2023 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.2023 Open access article under the CC BY license.

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.

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