On Non-Regularized Estimation of Psychological Networks

Abstract

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.

Expanding Network Analysis Tools in Psychological Networks: Minimal Spanning Trees, Participation Coefficients, and Motif Analysis Applied to a Network of 26 Psychological Attributes

“…Given the effort invested in estimating the network structure, it is a missed opportunity not to use the information it entails more fully to gain deeper understanding of estimated network. This "omission" may be understood and partly explained by researchers in the field being preoccupied primarily with network estimation methods [11,47,62] and replicability issues [49,63,64] that arise from the fact that network structures between variables are considerably more difficult to determine, relative to, for example, internet links or electricity nets; after all, conditional association between variables is not observable, but must be estimated from data. Appropriately dealing with sampling error in estimating network structures, as well as assessing their robustness, has therefore been the priority in psychological network analysis.…”

“…Partial correlation networks do not contain spurious correlations that are generated by common cause and chain structures within the network and can encode a basic data-generating network structure [46]. To estimate the network, we used a nonregularized method recently proposed by Williams and Rast (in press) [47] because, given our large sample size, relatively small number of variables, and our interest to detect weak ties, it is not advised to use regularization techniques like the LASSO that are often used ( [47,48], in press). More details about the process of determining the optimal estimation method for our data, and about the nonregularization method used, can be found in SM, Section 5.…”

Using network analysis to examine links between individual depression symptoms, inflammatory markers, and covariates

“…The EBIC itself has a tuning parameter gamma, which we set to 0 for the main models in the paper (see Supplementary Materials for a detailed rationale). As recommended in recent literature, we also estimated the final model without any regularization (Williams et al 2019) whilst still controlling for the false positive rate. We also estimated node predictability, which quantifies how well a node can be predicted by nodes it shares an edge with.…”

Comparing Gaussian graphical models with the posterior predictive distribution and Bayesian model selection.

“…The Gaussian graphical model (GGM) has become increasingly popular in the social-behavioral sciences (Epskamp Research reported in Williams, Rhemtulla, Wysocki, & Rast, 2018). Traditional statistical approaches, for example the structural equation model (SEM) framework, conceptualize psychological constructs as arising from a common cause (i.e., latent variable; Cramer & Borsboom, 2015).…”