On Nonregularized Estimation of Psychological Networks

Abstract

An important goal for psychological science is developing methods to characterize relationships between variables. Customary approaches use structural equation models to connect latent factors to a number of observed measurements, or test causal hypotheses between observed variables. 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) has emerged 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 and a non-parametric bootstrap strategy, after which we characterize performance with extensive simulations. Our results demonstrate that the non-regularized methods can be used to reduce the false positive rate, compared to glasso, and they appear to provide 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 performance than glasso, as well as suggesting areas for future research in psychology. The non-regularized methods have been implemented in the R package GGMnonreg.

On the Importance of Estimating Parameter Uncertainty in Network Psychometrics: A Response to Forbes et al. (2019)

“…For instance, the regularization algorithm commonly used was specifically designed for sparse underlying network structures. Under dense structures, regularization leads to a higher false positive rate than was previously known (Williams & Rast, 2018;Williams et al, 2019). We welcome such simulation studies that are important methodological contributions to the literature, as they strengthen the knowledge about methodology.…”

“…Exploratory search in this parameter space will come with sampling variability and differences in the performance across specific algorithms. Prior work has discussed these aspects in some detail, and put forward ways to address sampling variability using statistical tests (Epskamp et al, 2018;Epskamp et al, 2016;Williams & Rast, 2018;Williams et al, 2019). Recent methodological studies have led to an increased understanding of the performance of specific network estimation methods under different conditions.…”

Towards a Network Psychometrics Approach to Assessment: Simulations for Redundancy, Dimensionality, and Loadings

“…More recently, non-regularized network estimation methods have been put forward in the literature (Williams, Rhemtulla, Wysocki, & Rast, 2019). These methods have been shown to have better performance when estimating the population network structure of dense (highly connected) networks, which are common in psychology .…”

BGGM: A R Package for Bayesian Gaussian Graphical Models

“…More recently, GGMs have become increasingly popular in the social-behavioral sciences (Epskamp, Waldorp, Mottus, and Borsboom 2018b). In these applications, it is uncommon to have high dimensional data and thus regularization is not necessary (Williams, Rhemtulla, Wysocki, and Rast 2019c;Williams and Rast 2018). BGGM could accommodate high dimensional data, but the current version is explicitly built for low dimensional situations (p < n).…”