Relations between Networks, Regression, Partial Correlation, and the Latent Variable Model

Network analysis: An overview for mental health research

Network approaches to psychopathology have become increasingly common in mental health research, with many theoretical and methodological developments quickly gaining traction. This article illustrates contemporary practices in applying network analytical tools, bridging the gap between network concepts and their empirical applications. We explain how we can use graphs to construct networks representing complex associations among observable psychological variables. We then discuss key network models, including dynamic networks, time-varying networks, network models derived from panel data, network intervention analysis, latent networks, and moderated models. In addition, we discuss Bayesian networks and their role in causal inference with a focus on cross-sectional data. After presenting the different methods, we discuss how network models and psychopathology theories can meaningfully inform each other. We conclude with a discussion that summarizes the insights each technique can provide in mental health research.

An information-theoretic approach to build hypergraphs in psychometrics

Psychological network approaches propose to see symptoms or questionnaire items as interconnected nodes, with links between them reflecting pairwise statistical dependencies evaluated on cross-sectional, time-series, or panel data. These networks constitute an established methodology to visualise and conceptualise the interactions and relative importance of nodes/indicators, providing an important complement to other approaches such as factor analysis. However, limiting the representation to pairwise relationships can neglect potentially critical information shared by groups of three or more variables (higher-order statistical interdependencies). To overcome this important limitation, here we propose an information-theoretic framework to assess these interdependencies and consequently to use hypergraphs as representations in psychometrics. As edges in hypergraphs are capable of encompassing several nodes together, this extension can thus provide a richer account on the interactions that may exist among sets of psychological variables. Our results show how psychometric hypergraphs can highlight meaningful redundant and synergistic interactions on either simulated or state-of-the-art, re-analysed psychometric datasets. Overall, our framework extends current network approaches while leading to new ways of assessing the data that differ at their core from other methods, enriching the psychometrics toolbox, and opening promising avenues for future investigation.

Testing Conditional Independence in Psychometric Networks: An Analysis of Three Bayesian Methods

Network psychometrics uses graphical models to assess the network structure of psychological variables. An important task in their analysis is determining which variables are unrelated in the network, i.e., are independent given the rest of the network variables. This conditional independence structure is a gateway to understanding the causal structure underlying psychological processes. Thus, it is crucial to have an appropriate method for evaluating conditional independence and dependence hypotheses. Bayesian approaches to testing such hypotheses allow researchers to differentiate between absence of evidence and evidence of absence of connections (edges) between pairs of variables in a network. Three Bayesian approaches to assessing conditional independence have been proposed in the network psychometrics literature. We believe that their theoretical foundations are not widely known, and therefore we provide a conceptual review of the proposed methods and highlight their strengths and limitations through a simulation study. We also illustrate the methods using an empirical example with data on Dark Triad Personality. Finally, we provide recommendations on how to choose the optimal method and discuss the current gaps in the literature on this important topic.

Network Inference With the Lasso

Calculating confidence intervals and p-values of edges in networks is useful to decide their presence or absence and it is a natural way to quantify uncertainty. Since lasso estimation is often used to obtain edges in a network, and the underlying distribution of lasso estimates is discontinuous and has probability one at zero when the estimate is zero, obtaining p-values and confidence intervals is problematic. It is also not always desirable to use the lasso to select the edges because there are assumptions required for correct identification of network edges that may not be warranted for the data at hand. Here, we review three methods that either use a modified lasso estimate (desparsified or debiased lasso) or a method that uses the lasso for selection and then determines p-values without the lasso. We compare these three methods with popular methods to estimate Gaussian Graphical Models in simulations and conclude that the desparsified lasso and its bootstrapped version appear to be the best choices for selection and quantifying uncertainty with confidence intervals and p-values.

Unique Variable Analysis: A Network Psychometrics Method to Detect Local Dependence

The local independence assumption states that variables are unrelated after conditioning on a latent variable. Common problems that arise from violations of this assumption include model misspecification, biased model parameters, and inaccurate estimates of internal structure. These problems are not limited to latent variable models but also apply to network psychometrics. This paper proposes a novel network psychometric approach to detect locally dependent pairs of variables using network modeling and a graph theory measure called weighted topological overlap (wTO). Using simulation, this approach is compared to contemporary local dependence detection methods such as exploratory structural equation modeling with standardized expected parameter change and a recently developed approach using partial correlations and a resampling procedure. Different approaches to determine local dependence using statistical significance and cutoff values are also compared. Continuous, polytomous (5-point Likert scale), and dichotomous (binary) data were generated with skew across a variety of conditions. Our results indicate that cutoff values work better than significance approaches. Overall, the network psychometrics approaches using wTO with graphical least absolute shrinkage and selector operator with extended Bayesian information criterion and wTO with Bayesian Gaussian graphical model were the best performing local dependence detection methods overall.

Network analysis studies in patients with eating disorders: A systematic review and methodological quality assessment

INTRODUCTION

Network psychometrics has been enthusiastically embraced by researchers studying eating disorders (ED), but a rigorous evaluation of the methodological quality of works is still missing. This systematic review aims to assess the methodological quality of cross-sectional network analysis (NA) studies conducted on ED clinical populations.

METHODS

PRISMA and PICOS criteria were used to retrieve NA studies on ED. Methodological quality was evaluated based on five criteria: variable-selection procedure, network estimation method, stability checks, topological overlap checks, and handling of missing data.

RESULTS

Thirty-three cross-sectional NA studies were included. Most studies focused on populations that were female, white and, with an anorexia nervosa (AN) diagnosis. Depending on how many criteria were satisfied, 27.3% of studies (n = 9) were strictly adherent, 30.3% (n = 10) moderately adherent, 33.3% (n = 11) sufficiently adherent, and 9.1% (n = 3) poorly adherent. Missing topological overlap checks and not reporting missing data represented most unreported criteria, lacking, respectively, in 63.6% and 48.5% of studies.

CONCLUSIONS

Almost all reviewed cross-sectional NA studies on ED report those methodological procedures (variable-selection procedure, network estimation method, stability checks) necessary for a network study to provide reliable results. Nonetheless these minimum reporting data require further improvement. Moreover, elements closely related to the validity of an NA study (controls for topological overlap and management of missing data) are lacking in most studies. Recommendations to overcome such methodological weaknesses in future NA studies on ED are discussed together with the need to conduct NA studies with longitudinal design, to address diversity issues in study samples and heterogeneity of assessment tools.

PUBLIC SIGNIFICANCE

The present work aims to evaluate the quality of ED NA studies to support applications of this approach in ED research. Results show that most studies adopted basic procedures to produce reliable results; however, other important procedures linked to NA study validity were mostly neglected. Network methodology in ED is extremely promising, but future studies should consistently include topological overlap control procedures and provide information on missing data.

Interindividual age differences in personality structure

Most investigations in the structure of personality traits do not adequately address age; instead, they presuppose a constant structure across the lifespan. Further, few studies look at the structure of personality traits a-theoretically, often neglecting to examine the relationship among indicators within a trait (convergence) and across traits (divergence). Using a network approach, the present study examines (1) age differences in divergence and convergence, (2) the similarity between the Big Five and network structures, and (3) the consistency of network structure across age groups in a large, cross-sectional sample. Results indicate that convergence shows early gains in adolescence with few differences across the lifespan, while divergence mostly weakens across adulthood. The result of these age-related differences is that Big Five indicators only parallel the Big Five structure among young but not older adults. The structure of young adults tends to be quite similar while the network structures of older adults appear to greatly differ from one another. These results suggest that older adults have a different structure of personality than younger adults and suggest that future research should not assume consistency in personality structure across the lifespan.

On the equivalency of factor and network loadings

Recent research has demonstrated that the network measure node strength or sum of a node's connections is roughly equivalent to confirmatory factor analysis (CFA) loadings. A key finding of this research is that node strength represents a combination of different latent causes. In the present research, we sought to circumvent this issue by formulating a network equivalent of factor loadings, which we call network loadings. In two simulations, we evaluated whether these network loadings could effectively (1) separate the effects of multiple latent causes and (2) estimate the simulated factor loading matrix of factor models. Our findings suggest that the network loadings can effectively do both. In addition, we leveraged the second simulation to derive effect size guidelines for network loadings. In a third simulation, we evaluated the similarities and differences between factor and network loadings when the data were generated from random, factor, and network models. We found sufficient differences between the loadings, which allowed us to develop an algorithm to predict the data generating model called the Loadings Comparison Test (LCT). The LCT had high sensitivity and specificity when predicting the data generating model. In sum, our results suggest that network loadings can provide similar information to factor loadings when the data are generated from a factor model and therefore can be used in a similar way (e.g., item selection, measurement invariance, factor scores).