Network psychometrics leverages pairwise Markov random fields to depict conditional dependencies among a set of psychological variables as undirected edge-weighted graphs. Researchers often intend to compare such psychometric networks across subpopulations, and recent methodological advances provide invariance tests of differences in subpopulation networks. What remains missing, though, is an analogue to an effect size measure that quantifies differences in psychometric networks. We address this gap by complementing recent advances for investigating whether psychometric networks differ with an intuitive similarity measure quantifying the extent to which networks differ. To this end, we build on graph-theoretic approaches and propose a similarity measure based on the Frobenius norm of differences in psychometric networks' weighted adjacency matrices. To assess this measure's utility for quantifying differences between psychometric networks, we study how it captures differences in subpopulation network models implied by both latent variable models and Gaussian graphical models. We show that a wide array of network differences translates intuitively into the proposed measure, while the same does not hold true for customary correlation-based comparisons. In a simulation study on finite-sample behavior, we show that the proposed measure yields trustworthy results when population networks differ and sample sizes are sufficiently large, but fails to identify exact similarity when population networks are the same. From these results, we derive a strong recommendation to only use the measure as a complement to a significant test for network similarity. We illustrate potential insights from quantifying psychometric network similarities through cross-country comparisons of human values networks. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

中文翻译：

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基于图论的相似性度量可以对子群体心理测量网络进行比较。


网络心理测量学利用成对马尔可夫随机场将一组心理变量之间的条件依赖性描述为无向边加权图。研究人员经常打算比较不同亚群的心理测量网络，最近的方法论进展提供了亚群网络差异的不变性检验。然而，仍然缺少的是一种类似于效应大小测量的方法，该测量可以量化心理测量网络中的差异。我们通过补充调查心理测量网络是否存在差异的最新进展来解决这一差距，并使用直观的相似性度量来量化网络差异的程度。为此，我们建立在图论方法的基础上，并提出了一种基于心理测量网络加权邻接矩阵差异的 Frobenius 范数的相似性度量。为了评估该方法在量化心理测量网络之间差异的效用，我们研究了它如何捕获潜变量模型和高斯图模型隐含的子群体网络模型中的差异。我们表明，广泛的网络差异可以直观地转化为所提出的度量，而对于通常的基于相关性的比较来说，情况并非如此。在有限样本行为的模拟研究中，我们表明，当人口网络不同且样本量足够大时，所提出的方法会产生值得信赖的结果，但当人口网络相同时，无法识别确切的相似性。从这些结果中，我们强烈建议仅使用该度量作为网络相似性显着测试的补充。 我们通过人类价值观网络的跨国比较来说明量化心理测量网络相似性的潜在见解。 （PsycInfo 数据库记录 (c) 2023 APA，保留所有权利）。