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 generalisations 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 generalisation, 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 generalisation, the residual variance-covariance structure of indicators is modelled as a network. We term this generalisation Residual Network Modeling (RNM) and show that, within this framework, identifiable models can be obtained in which local independence is structurally violated. Both generalizations have been implemented in the free-to-use software package lvnet, which contains confirmatory model testing as well as two exploratory search algorithms: stepwise search for low-dimensional datasets and penalized maximum likelihood estimation for larger datasts. We show in simulation studies that these search performs adequately in identifying the structure of the relevant residual or latent networks. We further demonstrate the utility of these generalization in an empirical example on a personality inventory dataset.