Gaussian graphical models are commonly used to characterize conditional (in)dependence structures (i.e., partial correlation networks) of psychological constructs. Recently attention has shifted from estimating single networks to those from various subpopulations. The focus is primarily to detect differences or demonstrate replicability. We introduce two novel Bayesian methods for comparing networks that explicitly address these aims. The first is based on the posterior predictive distribution, with a symmetric version of Kullback-Leibler divergence as the discrepancy measure, that tests differences between two (or more) multivariate normal distributions. The second approach makes use of Bayesian model comparison, with the Bayes factor, and allows for gaining evidence for invariant network structures. This overcomes limitations of current approaches in the literature that use classical hypothesis testing, where it is only possible to determine whether groups are significantly different from each other. With simulation we show the posterior predictive method is approximately calibrated under the null hypothesis (α = .05) and has more power to detect differences than alternative approaches. We then examine the necessary sample sizes for detecting invariant network structures with Bayesian hypothesis testing, in addition to how this is influenced by the choice of prior distribution. The methods are applied to posttraumatic stress disorder symptoms that were measured in 4 groups. We end by summarizing our major contribution, that is proposing 2 novel methods for comparing Gaussian graphical models (GGMs), which extends beyond the social-behavioral sciences. The methods have been implemented in the R package BGGM. (PsycINFO Database Record (c) 2020 APA, all rights reserved).

中文翻译：

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比较高斯图形模型与后验预测分布和贝叶斯模型选择。

高斯图形模型通常用于表征心理构造的条件（不）依赖结构（即，部分相关网络）。最近的注意力已经从估计单个网络转移到来自不同亚群的网络。重点主要是检测差异或证明可复制性。我们介绍了两种新颖的贝叶斯方法来比较明确解决这些目标的网络。第一个基于后验预测分布，以 Kullback-Leibler 散度的对称版本作为差异度量，测试两个（或多个）多元正态分布之间的差异。第二种方法利用贝叶斯模型比较和贝叶斯因子，并允许获得不变网络结构的证据。这克服了文献中使用经典假设检验的当前方法的局限性，其中只能确定组之间是否存在显着差异。通过模拟，我们表明后验预测方法在零假设 (α = .05) 下近似校准，并且比替代方法具有更大的检测差异的能力。然后，我们检查使用贝叶斯假设检验检测不变网络结构所需的样本大小，以及这如何受先验分布选择的影响。该方法应用于在 4 组中测量的创伤后应激障碍症状。我们最后总结了我们的主要贡献，即提出了 2 种比较高斯图模型 (GGM) 的新方法，它超越了社会行为科学。这些方法已在 R 包 BGGM 中实现。（PsycINFO 数据库记录 (c) 2020 APA，保留所有权利）。