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Parameter Estimation Procedures for Exponential-family Random Graph Models on Count-valued Networks: A Comparative

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This summary is machine-generated.

We developed an efficient estimation method for count-valued exponential-family random graph models (ERGMs). This new method, subsampled maximum pseudo-likelihood estimation (MPLE), offers advantages over existing approaches like Contrastive Divergence (CD) and Monte Carlo Maximum Likelihood Estimation (MCMLE) for various network types.

Keywords:
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Area of Science:

  • Social Network Analysis
  • Statistical Modeling
  • Computational Statistics

Background:

  • Exponential-family random graph models (ERGMs) are crucial for analyzing relational data.
  • Valued ERGMs, particularly count-valued networks, present significant computational challenges.
  • Existing methods like Contrastive Divergence (CD) and Monte Carlo Maximum Likelihood Estimation (MCMLE) have limitations.

Purpose of the Study:

  • To propose an efficient, parallelizable subsampled maximum pseudo-likelihood estimation (MPLE) scheme for count-valued ERGMs.
  • To compare the performance of MPLE against CD and MCMLE using simulated migration flow networks.
  • To provide guidance on selecting computational methods for valued ERGMs.

Main Methods:

  • Development of a subsampled maximum pseudo-likelihood estimation (MPLE) algorithm.
  • Simulation study using migration flow networks from two U.S. states.
  • Comparative analysis of MPLE, CD, and MCMLE based on accuracy, uncertainty estimation, and computational time.

Main Results:

  • Edge value variance is a key determinant of method performance.
  • For small-variance networks, MPLE and MCMLE provide good point estimates, but CD overestimates uncertainty and MPLE underestimates it for dependence terms.
  • For large-variance networks, MPLE and MCMLE yield high-quality estimates; MPLE is faster and a better seeding method for MCMLE than CD.

Conclusions:

  • MPLE is an efficient and effective method for estimating count-valued ERGMs.
  • MCMLE and MPLE are recommended for small-variance and large-variance valued networks, respectively.
  • Method selection should consider data structure, computational resources, and analytical goals.