The Gaussian graphical model (GGM) is an increasingly popular technique used in psychology to characterize relationships among observed variables. These relationships are represented as elements in the precision matrix. Standardizing the precision matrix and reversing the sign yields corresponding partial correlations that imply pairwise dependencies in which the effects of all other variables have been controlled for. The graphical lasso (glasso) has emerged as the default estimation method, which uses ℓ₁‐based regularization. The glasso was developed and optimized for high‐dimensional settings where the number of variables (p) exceeds the number of observations (n), which is uncommon in psychological applications. Here we propose to go ‘back to the basics’, wherein the precision matrix is first estimated with non‐regularized maximum likelihood and then Fisher Z transformed confidence intervals are used to determine non‐zero relationships. We first show the exact correspondence between the confidence level and specificity, which is due to 1 minus specificity denoting the false positive rate (i.e., α). With simulations in low‐dimensional settings (p ≪ n), we then demonstrate superior performance compared to the glasso for detecting the non‐zero effects. Further, our results indicate that the glasso is inconsistent for the purpose of model selection and does not control the false discovery rate, whereas the proposed method converges on the true model and directly controls error rates. We end by discussing implications for estimating GGMs in psychology.

中文翻译：

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回归基础：重新思考偏相关网络方法。

高斯图形模型 (GGM) 是一种越来越流行的心理学技术，用于表征观察变量之间的关系。这些关系表示为精度矩阵中的元素。标准化精度矩阵并反转符号会产生相应的偏相关，这意味着成对依赖，其中所有其他变量的影响都已被控制。图形套索 (glasso) 已成为默认估计方法，它使用基于ℓ ₁的正则化。glasso 是为高维设置开发和优化的，其中变量的数量 ( p ) 超过了观察的数量 ( n)，这在心理学应用中并不常见。在这里，我们建议“回归基础”，其中首先使用非正则化最大似然估计精度矩阵，然后使用 Fisher Z变换置信区间来确定非零关系。我们首先显示置信水平和特异性之间的确切对应关系，这是由于 1 减去表示假阳性率（即 α）的特异性。在低维设置中进行模拟 ( p  ≪  n)，然后我们展示了与 glasso 相比在检测非零效应方面的优越性能。此外，我们的结果表明，玻璃对于模型选择的目的是不一致的，并且不控制错误发现率，而所提出的方法收敛于真实模型并直接控制错误率。我们最后讨论了在心理学中估计 GGM 的含义。