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Generalized Network Psychometrics: Combining Network and Latent Variable Models

Published online by Cambridge University Press:  01 January 2025

Sacha Epskamp ,
Mijke Rhemtulla  and
Denny Borsboom
Sacha Epskamp*
Affiliation:
University of Amsterdam
Mijke Rhemtulla
Affiliation:
University of Amsterdam
Denny Borsboom
Affiliation:
University of Amsterdam
*
Correspondence should be made to Sacha Epskamp, University of Amsterdam, PO Box 15906, 1001 NK Amsterdam, The Netherlands. Email: sacha.epskamp@gmail.com
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Abstract

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.

Keywords

network modelsstructural equation modelingsimulation studysoftware
Type
Original Paper
Information
Psychometrika , Volume 82 , Issue 4 , December 2017 , pp. 904 - 927
Copyright
Copyright © 2017 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (doi:10.1007/s11336-017-9557-x) contains supplementary material, which is available to authorized users.

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