Generalized Network Psychometrics: Combining Network and Latent Variable Models

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 performs 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.Comment: Published in Psychometrik

Two-Method Planned Missing Designs for Longitudinal Research

We examine longitudinal extensions of the two-method measurement design, which uses planned missingness to optimize cost-efficiency and validity of hard-to-measure constructs. These designs use a combination of two measures: a “gold standard” that is highly valid but expensive to administer, and an inexpensive (e.g., survey-based) measure that contains systematic measurement bias (e.g., response bias). Using simulated data on four measurement occasions, we compared the cost-efficiency and validity of longitudinal designs where the gold standard is measured at one or more measurement occasions. We manipulated the nature of the response bias over time (constant, increasing, fluctuating), the factorial structure of the response bias over time, and the constraints placed on the latent variable model. Our results showed that parameter bias is lowest when the gold standard is measured on at least two occasions. When a multifactorial structure was used to model response bias over time, it is necessary to have the “gold standard” measures included at every time point, in which case most of the parameters showed low bias. Almost all parameters in all conditions displayed high relative efficiency, suggesting that the 2-method design is an effective way to reduce costs and improve both power and accuracy in longitudinal research

Correlated longitudinal changes across linguistic, achievement, and psychomotor domains in early childhood: Evidence for a global dimension of development

This is the peer reviewed version of the following article: Rhemtulla, M., & Tucker-Drob, E. M. (2011). Correlated longitudinal changes across linguistic, achievement, and psychomotor domains in early childhood: Evidence for a global dimension of development. Developmental Science, 14(5), 1245–1254. http://doi.org/10.1111/j.1467-7687.2011.01071.x, which has been published in final form at http://doi.org/10.1111/j.1467-7687.2011.01071.x. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.An important question within developmental psychology concerns the extent to which the maturational gains that children make across multiple diverse domains of functioning can be attributed to global (domain-general) developmental processes. The present study investigated this question by examining the extent to which individual differences in change across children’s development in five different domains are correlated. Multivariate growth-curve models were fit to longitudinal data on linguistic, mathematics, reading, gross motor, and fine motor skills in 8,950 children ranging in age from 44 to 86 months (3.7 years to 7.2 years). All five rates of change were positively intercorrelated. A common factor accounted for 42% of the individual differences in change. These results suggest that a global dimension underlies substantial proportions of cognitive and psychomotor development

Gene-by-Socioeconomic Status Interaction on School Readiness

In previous work with a nationally representative sample of over 1,400 monozygotic and dizygotic twins born in the US, Tucker-Drob et al. (Psychological Science, 22, 125–133, 2011) uncovered a gene × environment interaction on scores on the Bayley Short Form test of mental ability (MA) at 2 years of age—higher socioeconomic status (SES) was associated not only with higher MA, but also with larger genetic contributions to individual differences in MA. The current study examined gene × SES interactions in mathematics skill and reading skill at 4 years of age (preschool age) in the same sample of twins, and further examined whether interactions detected at 4 years could be attributed to the persistence of the interaction previously observed at 2 years. For early mathematics skill but not early reading skill, genetic influences were more pronounced at higher levels of SES. This interaction was not accounted for by the interaction observed at 2 years. These findings indicate that SES moderates the etiological influences on certain cognitive functions at multiple stages of child development

On Nonregularized Estimation of Psychological Networks.

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 off-diagonal elements 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 article, 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 nonregularized methods based on multiple regression and a nonparametric bootstrap strategy, after which we characterize performance with extensive simulations. Our results demonstrate that the nonregularized 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 nonregularized methods have been implemented in the R package GGMnonreg

The Network Structure of Symptoms of the Diagnostic and Statistical Manual of Mental Disorders

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

Divergent Effects of Beliefs in Heaven and Hell on National Crime Rates

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

Genomic structural equation modelling provides insights into the multivariate genetic architecture of complex traits

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

R Code

R code to reproduce examples, parameter sweeps, Fig 2, and replication/reversal of results from Cole & Preacher (2014