Back to the Basics: Rethinking Partial Correlation Network Methodology
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Description: Gaussian graphical models are an increasingly popular technique in psychology to characterize relationships among observed variables. These relationships are represented as covariances in the precision matrix. Standardizing this covariance 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. In order to estimate the precision matrix, the graphical lasso (glasso) has emerged as the default estimation method, which uses l-1-based regularization. Glasso was developed and optimized for high dimensional settings where the number of variables (p) exceeds the number of observations (n) which are 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 - specificity denoting the false positive rate (i.e., alpha). With simulations in low-dimensional settings (p << n), we then demonstrate superior performance compared to glasso for determining conditional relationships, in addition to frequentist risk measured with various loss functions. Further, our results indicate that glasso is inconsistent for the purpose of model selection, whereas the proposed method converged on the true model with a probability that approached 100%. We end by discussing implications for estimating Gaussian graphical models in psychology.
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