On Non-Regularized Estimation of Psychological Networks

An important goal for psychological science is developing methods to characterize relationships between variables. The customary approach uses structural equation models to connect latent factors to a number of observed measurements. More recently, regularized partial correlation networks have been proposed as an alternative approach for characterizing relationships among variables through covariances in the precision matrix. While the graphical lasso (glasso) method has merged as the default network estimation method, it was optimized in fields outside of psychology with very different needs, such as high dimensional data where the number of variables (p) exceeds the number of observations (n). In this paper, we describe the glasso method in the context of the fields where it was developed, and then we demonstrate that the advantages of regularization diminish in settings where psychological networks are often fitted (p ≪ n). We first show that improved properties of the precision matrix, such as eigenvalue estimation, and predictive accuracy with cross-validation are not always appreciable. We then introduce non-regularized methods based on multiple regression, after which we characterize performance with extensive simulations. Our results demonstrate that the non-regularized methods consistently outperform glasso with respect to limiting false positives, and they provide more consistent performance across sparsity levels, sample composition (p=n), and partial correlation size. We end by reviewing recent findings in the statistics literature that suggest alternative methods often have superior than glasso, as well as suggesting areas for future research in psychology.