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We introduce the network model as a formal psychometric model, conceptualizing the covariance between psychometric indicators as resulting from pairwise interactions between observable variables in a network structure. This contrasts with standard psychometric models, in which the covariance between test items arises from the influence of one or more common latent variables. Here, we present two generalizations of the network model that encompass latent variable structures, establishing network modeling as parts of the more general framework of structural equation modeling (SEM). In the first generalization, we model the covariance structure of latent variables as a network. We term this framework latent network modeling (LNM) and show that, with LNM, a unique structure of conditional independence relationships between latent variables can be obtained in an explorative manner. In the second generalization, the residual variance–covariance structure of indicators is modeled as a network. We term this generalization residual network modeling (RNM) and show that, within this framework, identifiable models can be obtained in which local independence is structurally violated. These generalizations allow for a general modeling framework that can be used to fit, and compare, SEM models, network models, and the RNM and LNM generalizations. This methodology has been implemented in the free-to-use software package lvnet , which contains confirmatory model testing as well as two exploratory search algorithms: stepwise search algorithms for low-dimensional datasets and penalized maximum likelihood estimation for larger datasets. We show in simulation studies that these search algorithms perform adequately in identifying the structure of the relevant residual or latent networks. We further demonstrate the utility of these generalizations in an empirical example on a personality inventory dataset.

In recent years, network analysis has been applied to identify and analyse patterns of statistical association in multivariate psychological data. In these approaches, network nodes represent variables in a data set, and edges represent pairwise conditional associations between variables in the data, while conditioning on the remaining variables. This Primer provides an anatomy of these techniques, describes the current state of the art and discusses open problems. We identify relevant data structures in which network analysis may be applied: cross-sectional data, repeated measures and intensive longitudinal data. We then discuss the estimation of network structures in each of these cases, as well as assessment techniques to evaluate network robustness and replicability. Successful applications of the technique in different research areas are highlighted. Finally, we discuss limitations and challenges for future research.Network analysis allows the investigation of complex patterns and relationships by examining nodes and the edges connecting them. Borsboom et al. discuss the adoption of network analysis in psychological research.

Though religion has been shown to have generally positive effects on normative 'prosocial' behavior, recent laboratory research suggests that these effects may be driven primarily by supernatural punishment. Supernatural benevolence, on the other hand, may actually be associated with less prosocial behavior. Here, we investigate these effects at the societal level, showing that the proportion of people who believe in hell negatively predicts national crime rates whereas belief in heaven predicts higher crime rates. These effects remain after accounting for a host of covariates, and ultimately prove stronger predictors of national crime rates than economic variables such as GDP and income inequality. Expanding on laboratory research on religious prosociality, this is the first study to tie religious beliefs to large-scale cross-national trends in pro- and anti-social behavior.

We created a facet atlas that maps the interrelations between facet scales from 13 hierarchical personality inventories to provide a practically useful, transtheoretical description of lower-level personality traits. We generated this atlas by estimating a series of network models that visualize the correlations among 268 facet scales administered to the Eugene-Springfield Community Sample (Ns = 571-948). As expected, most facets contained a blend of content from multiple Big Five domains and were part of multiple Big Five networks. We identified core and peripheral facets for each Big Five domain. Results from this study resolve some inconsistencies in facet placement across instruments and highlight the complexity of personality structure relative to the constraints of traditional hierarchical models that impose simple structure. This facet atlas (also available as an online point-and-click app at tedschwaba.shinyapps.io/appdata/) provides a guide for researchers who wish to measure a domain with a limited set of facets as well as information about the core and periphery of each personality domain. To illustrate the value of a facet atlas in applied and theoretical settings, we examined the network structure of scales measuring impulsivity and tested structural hypotheses from the Big Five Aspect Scales inventory.

Although current classification systems have greatly contributed to the reliability of psychiatric diagnoses, they ignore the unique role of individual symptoms and, consequently, potentially important information is lost. The network approach, in contrast, assumes that psychopathology results from the causal interplay between psychiatric symptoms and focuses specifically on these symptoms and their complex associations. By using a sophisticated network analysis technique, this study constructed an empirically based network structure of 120 psychiatric symptoms of twelve major DSM-IV diagnoses using cross-sectional data of the National Epidemiologic Survey on Alcohol and Related Conditions (NESARC, second wave; N = 34,653). The resulting network demonstrated that symptoms within the same diagnosis showed differential associations and indicated that the strategy of summing symptoms, as in current classification systems, leads to loss of information. In addition, some symptoms showed strong connections with symptoms of other diagnoses, and these specific symptom pairs, which both concerned overlapping and non-overlapping symptoms, may help to explain the comorbidity across diagnoses. Taken together, our findings indicated that psychopathology is very complex and can be more adequately captured by sophisticated network models than current classification systems. The network approach is, therefore, promising in improving our understanding of psychopathology and moving our field forward.

Genetic correlations estimated from genome-wide association studies (GWASs) reveal pervasive pleiotropy across a wide variety of phenotypes. We introduce genomic structural equation modelling (genomic SEM): a multivariate method for analysing the joint genetic architecture of complex traits. Genomic SEM synthesizes genetic correlations and single-nucleotide polymorphism heritabilities inferred from GWAS summary statistics of individual traits from samples with varying and unknown degrees of overlap. Genomic SEM can be used to model multivariate genetic associations among phenotypes, identify variants with effects on general dimensions of cross-trait liability, calculate more predictive polygenic scores and identify loci that cause divergence between traits. We demonstrate several applications of genomic SEM, including a joint analysis of summary statistics from five psychiatric traits. We identify 27 independent single-nucleotide polymorphisms not previously identified in the contributing univariate GWASs. Polygenic scores from genomic SEM consistently outperform those from univariate GWASs. Genomic SEM is flexible and open ended, and allows for continuous innovation in multivariate genetic analysis. Grotzinger et al. develop a multivariate method for analysing the joint genetic architectures of complex traits: genomic structural equation modelling. They provide several applications of the method, including a joint analysis of five psychiatric traits.

Purpose Health-Related Quality of Life (HRQoL) research has typically adopted either a formative approach, in which HRQoL is the common effect of its observables, or a reflective approach—defining HRQoL as a latent variable that determines observable characteristics of HRQoL. Both approaches, however, do not take into account the complex organization of these characteristics. The objective of this study was to introduce a new approach for analyzing HRQoL data, namely a network model (NM). An NM, as opposed to traditional research strategies, accounts for interactions among observables and offers a complementary analytic approach. Methods We applied the NM to samples of Dutch cancer patients (N = 485) and Dutch healthy adults (N = 1742) who completed the 36-item Short Form Health Survey (SF-36). Networks were constructed for both samples separately and for a combined sample with diagnostic status added as an extra variable. We assessed the network structures and compared the structures of the two separate samples on the item and domain levels. The relative importance of individual items in the network structures was determined using centrality analyses. Results We found that the global structure of the SF-36 is dominant in all networks, supporting the validity of questionnaire's subscales. Furthermore, results suggest that the network structure of both samples was highly similar. Centrality analyses revealed that maintaining a daily routine despite one's physical health predicts HRQoL levels best. Conclusions We concluded that the NM provides a fruitful alternative to classical approaches used in the psychometric analysis of HRQoL data.

•Global network metrics are used to measure organizational properties of the brain.•Many metrics are highly correlated with each other and with topology-free metrics.•Network sparsity and variation in edge weights may yield greater independence between metrics. Graph-theoretic metrics derived from neuroimaging data have been heralded as powerful tools for uncovering neural mechanisms of psychological traits, psychiatric disorders, and neurodegenerative diseases. In N = 8,185 human structural connectomes from UK Biobank, we examined the extent to which 11 commonly-used global graph-theoretic metrics index distinct versus overlapping information with respect to interindividual differences in brain organization. Using unthresholded, FA-weighted networks we found that all metrics other than Participation Coefficient were highly intercorrelated, both with each other (mean |r| = 0.788) and with a topologically-naïve summary index of brain structure (mean edge weight; mean |r| = 0.873). In a series of sensitivity analyses, we found that overlap between metrics is influenced by the sparseness of the network and the magnitude of variation in edge weights. Simulation analyses representing a range of population network structures indicated that individual differences in global graph metrics may be intrinsically difficult to separate from mean edge weight. In particular, Closeness, Characteristic Path Length, Global Efficiency, Clustering Coefficient, and Small Worldness were nearly perfectly collinear with one another (mean |r| = 0.939) and with mean edge weight (mean |r| = 0.952) across all observed and simulated conditions. Global graph-theoretic measures are valuable for their ability to distill a high-dimensional system of neural connections into summary indices of brain organization, but they may be of more limited utility when the goal is to index separable components of interindividual variation in specific properties of the human structural connectome.

In many modeling contexts, the variables in the model are linear composites of the raw items measured for each participant; for instance, regression and path analysis models rely on scale scores, and structural equation models often use parcels as indicators of latent constructs. Currently, no analytic estimation method exists to appropriately handle missing data at the item level. Item-level multiple imputation (MI), however, can handle such missing data straightforwardly. In this article, we develop an analytic approach for dealing with item-level missing data—that is, one that obtains a unique set of parameter estimates directly from the incomplete data set and does not require imputations. The proposed approach is a variant of the two-stage maximum likelihood (TSML) methodology, and it is the analytic equivalent of item-level MI. We compare the new TSML approach to three existing alternatives for handling item-level missing data: scale-level full information maximum likelihood, available-case maximum likelihood, and item-level MI. We find that the TSML approach is the best analytic approach, and its performance is similar to item-level MI. We recommend its implementation in popular software and its further study.