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Comparing Gaussian graphical models with the posterior predictive distribution and Bayesian model selection.

Donald R Williams1, Philippe Rast1, Luis R Pericchi2

  • 1Department of Psychology.

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This summary is machine-generated.

We introduce two novel Bayesian methods for comparing Gaussian graphical models (GGMs) to detect differences and evidence invariance between networks. Simulations show improved power and calibration for detecting network differences.

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Area of Science:

  • Statistics
  • Network Analysis
  • Psychology

Background:

  • Gaussian graphical models (GGMs) analyze conditional independence in psychological constructs.
  • Comparing networks across subpopulations is crucial for detecting differences and replicability.
  • Current methods using classical hypothesis testing have limitations in detecting network invariance.

Purpose of the Study:

  • Introduce two novel Bayesian methods for comparing GGMs.
  • Address the detection of differences and evidence for invariant network structures.
  • Overcome limitations of classical hypothesis testing in network comparison.

Main Methods:

  • Posterior predictive distribution with Kullback-Leibler divergence for testing differences between multivariate normal distributions.
  • Bayesian model comparison using Bayes factors for evidence of invariant network structures.
  • Simulation studies to assess calibration, power, and sample size requirements.

Main Results:

  • The posterior predictive method demonstrates approximate calibration under the null hypothesis (α = .05).
  • The posterior predictive method shows higher power for detecting network differences compared to alternatives.
  • Analysis of sample size needs for detecting invariant network structures, considering prior distribution choices.

Conclusions:

  • Propose two novel Bayesian methods for comparing GGMs, extending their application beyond social-behavioral sciences.
  • The methods are implemented in the R package BGGM.
  • These methods offer advancements for analyzing network structures across different groups.