Improving and Extending STERGM Approximations Based on Cross-Sectional Data and Tie Durations

Area of Science:

• Network Science
• Statistical Modeling
• Computational Social Science

Background:

• Temporal exponential-family random graph models (TERGMs) analyze evolving network structures.
• Separable TERGMs (STERGMs) simplify dynamics by separating tie formation and dissolution.
• The Carnegie et al. (2015) approximation enables efficient STERGM estimation from cross-sectional data.

Purpose of the Study:

• To improve the Carnegie et al. approximation for separable TERGMs.
• To expand the applicability of STERGM estimation from cross-sectional designs.
• To develop more accurate methods for analyzing dynamic networks.

Main Methods:

• Derived a new approximation by taking the sparse limit of the exact STERGM result.
• Developed theoretical results for dyad-dependent TERGMs, showing asymptotic exactness as time step size approaches zero.
• Extended the framework to hypergraphs and incorporated age-dependent tie dissolution hazards.

Main Results:

• The new sparse limit approximation outperforms the Carnegie et al. approximation for sparse, dyad-independent models.
• Approximation errors increase with dependence strength in dyad-dependent models.
• Continuous-time limits of discrete-time approximations achieve desired equilibrium and duration distributions.

Conclusions:

• The proposed methods enhance the accuracy and scope of STERGM analysis using cross-sectional data.
• Theoretical advancements provide a foundation for more robust dynamic network modeling.
• The framework is adaptable to complex network structures (hypergraphs) and dissolution processes.