On the Question of Effective Sample Size in Network Modeling: An Asymptotic Inquiry.

Area of Science:

• Statistics
• Network Analysis
• Computational Social Science

Background:

• Network data analysis is a rapidly growing field in statistics.
• Foundational statistical questions for network models remain largely unaddressed.
• Understanding sample size is critical for robust statistical inference.

Purpose of the Study:

• To investigate the concept of 'sample size' for observed networks.
• To determine how network properties influence effective sample size.
• To explore the implications of effective sample size for statistical modeling.

Main Methods:

• Utilized exponential random graph models (ERGMs) for network analysis.
• Examined the asymptotic scaling of maximum likelihood parameter estimate variance.
• Defined effective sample size (n_eff) based on variance scaling.
• Employed simulation studies and real-world food-sharing network data.

Main Results:

• Effective sample size (n_eff) in ERGMs depends on network properties.
• Network sparsity (few edges) versus density (many edges) causes order-of-magnitude differences in n_eff.
• n_eff scales differently, from O(n) for dense networks to O(n^2) for sparse networks.

Conclusions:

• The definition and calculation of sample size are non-trivial for network data.
• Network sparsity is a key factor influencing the statistical power and precision of network models.
• Results have practical implications for analyzing real-world networks, such as social or ecological systems.