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

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.