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Goodness of fit tests for random multigraph models.

Termeh Shafie1

  • 1GESIS - Leibniz Institute for the Social Sciences, Cologne, Germany.

Journal of Applied Statistics
|November 16, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces goodness of fit tests for two probabilistic multigraph models: random stub matching (RSM) and independent edge assignments (IEA). Simulations show these tests accurately approximate distributions, aiding social network analysis.

Keywords:
Network modeldata aggregationgoodness of fitmultivariate networksrandom multigraphsrandom stub matching

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Area of Science:

  • Graph theory
  • Statistical modeling
  • Network analysis

Background:

  • Probabilistic multigraph models are essential for analyzing complex networks.
  • Existing methods lack robust goodness of fit tests for dependent edge assignments.

Purpose of the Study:

  • To develop and evaluate goodness of fit tests for two probabilistic multigraph models: random stub matching (RSM) and independent edge assignments (IEA).
  • To assess the performance of these tests using statistical measures and simulations.

Main Methods:

  • Formulated goodness of fit tests based on edge multiplicity sequences.
  • Utilized Pearson-type and likelihood ratio test statistics.
  • Derived expected values for the Pearson statistic under different models.
  • Conducted simulations to evaluate test performance and distribution approximations.

Main Results:

  • Null distributions of test statistics are well approximated by asymptotic chi-squared distributions, even with few edges.
  • Non-null distributions can be approximated by adjusted chi-squared distributions for power analysis.
  • Random stub matching significantly shifts test statistic distributions compared to independent edge assignments for small edge counts.

Conclusions:

  • The developed goodness of fit tests are effective for probabilistic multigraph models.
  • The tests provide reliable approximations for both null and non-null distributions.
  • These methods offer valuable tools for analyzing social network structures and uncovering underlying network formation processes.