Sparse Graphical Models for Functional Connectivity Networks: Best Methods and the Autocorrelation Issue

Back to the basics: Rethinking partial correlation network methodology

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.