Hostname: page-component-5f745c7db-nzk4m Total loading time: 0 Render date: 2025-01-06T21:44:44.605Z Has data issue: true hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.

References

Arbuckle, J. L. (1996). Full information estimation in the presence of incomplete data. In G. A. Marcoulides & R. E. Schumacker (Eds.), Advanced structural equation modeling (pp. 243–277). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.Google Scholar
Benet-Martinez, V. & John, O. (1998). Los Cinco Grandes across cultures and ethnic groups: Multitrait multimethod analyses of the big five in Spanish and English. Journal of Personality and Social Psychology 75, 729–750CrossRefGoogle ScholarPubMed
Bentler, P. M. (1990). Comparative fit indexes in structural models. Psychological Bulletin 107 (2), 238–346CrossRefGoogle ScholarPubMed
Borsboom, D. (2008). Psychometric perspectives on diagnostic systems. Journal of Clinical Psychology 64 (9), 1089–1108CrossRefGoogle ScholarPubMed
Borsboom, D. & Cramer, AOJ (2013). Network analysis: An integrative approach to the structure of psychopathology. Annual Review of Clinical Psychology 9, 91–121CrossRefGoogle Scholar
Borsboom, D. Cramer, AOJ Schmittmann, V. D. Epskamp, S. & Waldorp, L. J. (2011). The small world of psychopathology. PloS ONE 6 (11), e27407CrossRefGoogle ScholarPubMed
Browne, M. W. Cudeck, R. (1992). Alternative ways of assessing model fit. Sociological Methods & Research 21 (2), 230–258CrossRefGoogle Scholar
Chandrasekaran, V. Parrilo, P. A. & Willsky, A. S. (2012). Latent variable graphical model selection via convex optimization (with discussion). The Annals of Statistics 40 (4), 1935–1967Google Scholar
Chen, J. & Chen, Z. (2008). Extended Bayesian information criteria for model selection with large model spaces. Biometrika 95 (3), 759–771CrossRefGoogle Scholar
Costantini, G. Epskamp, S. Borsboom, D. & Perugini, M. Mõttus, R. Waldorp, L. J. & Cramer, AOJ (2015). State of the aRt personality research: A tutorial on network analysis of personality data in R. Journal of Research in Personality 54, 13–29CrossRefGoogle Scholar
Cramer, AOJ Sluis, S. Noordhof, A. Wichers, M. Geschwind, N. Aggen, S. H. Kendler, K. S. & Borsboom, D. (2012). Dimensions of normal personality as networks in search of equilibrium: You can’t like parties if you don’t like people. European Journal of Personality 26 (4), 414–431CrossRefGoogle Scholar
Cramer, AOJ Waldorp, L. van der Maas, H. & Borsboom, D. (2010). Comorbidity: A network perspective. Behavioral and Brain Sciences 33 (2–3), 137–150CrossRefGoogle ScholarPubMed
Dalege, J. Borsboom, D. van Harreveld, F. van den Berg, H. Conner, M. & van der Maas, HLJ (2016). Toward a formalized account of attitudes: The causal attitude network (CAN) model. Psychological Review 123 (1), 2–22CrossRefGoogle Scholar
Dempster, A. P. (1972). Covariance selection. Biometrics 28 (1), 157–175CrossRefGoogle Scholar
Digman, J. (1989). Five robust trait dimensions: Development, stability, and utility. Journal of Personality 57 (2), 195–214CrossRefGoogle ScholarPubMed
Dziak, J. J., Coffman, D. L., Lanza, S. T., & Li, R. (2012). Sensitivity and specificity of information criteria. The Methodology Center and Department of Statistics: Penn State, The Pennsylvania State University.Google Scholar
Ellis, J. L. & Junker, B. W. (1997). Tail-measurability in monotone latent variable models. Psychometrika 62 (4), 495–523CrossRefGoogle Scholar
Epskamp, S., Maris, G., Waldorp, L., & Borsboom, D. (in press). Network psychometrics. In Irwing, P., Hughes, D., and Booth, T., (Eds.), Handbook of psychometrics. Wiley, New York, NY.Google Scholar
Epskamp, S., Waldorp, L. J., Mõttus, R., & Borsboom, D. (2016). Discovering psychological dynamics in time-series data. arXiv preprintarXiv:1609.04156.Google Scholar
Foygel, R. & Drton, M. (2010). Extended Bayesian information criteria for Gaussian graphical models. Advances in Neural Information Processing Systems 23, 2020–2028Google Scholar
Fried, E. I. Bockting, C. Arjadi, R. Borsboom, D. Amshoff, M. Cramer, O. J. Epskamp, S. Tuerlinckx, F. Carr, D. & Stroebe, M. (2015). From loss to loneliness: The relationship between bereavement and depressive symptoms. Journal of Abnormal Psychology 124 (2), 256–265CrossRefGoogle ScholarPubMed
Fried, E. I., & van Borkulo, C. (2016). Mental disorders as networks of problems: A review of recent insights.CrossRefGoogle Scholar
Gates, K. M. & Molenaar, P. C. (2012). Group search algorithm recovers effective connectivity maps for individuals in homogeneous and heterogeneous samples. NeuroImage 63 (1), 310–319CrossRefGoogle ScholarPubMed
Goldberg, L. (1993). The structure of phenotypic personality traits. American Psychologist 48 (1), 26–34CrossRefGoogle ScholarPubMed
Goldberg, L. R. (1990). An alternative “description of personality”: The big-five factor structure. Journal of Personality and Social Psychology 59 (6), 1216–1229CrossRefGoogle ScholarPubMed
Hayduk, L. A. (1987). Structural equation modeling with LISREL: Essentials and advances Baltimore, MD: Johns Hopkins University PressGoogle Scholar
Hoerl, A. E. & Kennard, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics 12 (1), 55–67CrossRefGoogle Scholar
Holland, P. W. & Rosenbaum, P. R. (1986). Conditional association and unidimensionality in monotone latent variable models. The Annals of Statistics 14, 1523–1543CrossRefGoogle Scholar
Ising, E. (1925). Beitrag zur theorie des ferromagnetismus. Zeitschrift für Physik A Hadrons and Nuclei 31 (1), 253–258Google Scholar
Isvoranu, A. M. Borsboom, D. van Os, J. & Guloksuz, S. (2016). A network approach to environmental impact in psychotic disorders: Brief theoretical framework. Schizophrenia Bulletin 42 (4), 870–873CrossRefGoogle ScholarPubMed
Isvoranu, A. M., van Borkulo, C. D., Boyette, L. L., Wigman, J. T., Vinkers, C. H., Borsboom, D., & Group Investigators. (2017). A network approach to psychosis: Pathways between childhood trauma and psychotic symptoms. Schizophrenia bulletin, 43(1), 187–196.CrossRefGoogle Scholar
Jacobucci, R. Grimm, K. J. & McArdle, J. J. (2016). Regularized structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal 23 (4), 555–566CrossRefGoogle ScholarPubMed
Jöreskog, K. G. (1967). A general approach to confirmatory maximum likelihood factor analysis. ETS Research Bulletin Series 1967 (2), 183–202CrossRefGoogle Scholar
Kaplan, D. (2000). Structural equation modeling: Foundations and extensions Thousand Oaks, CA: SageGoogle Scholar
Kolaczyk, E. D. (2009). Statistical analysis of network data New York, NY: SpringerCrossRefGoogle Scholar
Koller, D. & Friedman, N. (2009). Probabilistic graphical models: Principles and techniques Cambridge, MA: MIT PressGoogle Scholar
Kossakowski, J. J. Epskamp, S. Kieffer, J. M. van Borkulo, C. D. Rhemtulla, M. & Borsboom, D. (2015). The application of a network approach to health-related quality of life (HRQoL): Introducing a new method for assessing hrqol in healthy adults and cancer patient. Quality of Life Research 25, 781–792CrossRefGoogle Scholar
Lauritzen, S. L. (1996). Graphical models Oxford: Clarendon PressCrossRefGoogle Scholar
Lawley, D. N. (1940). VI.—the estimation of factor loadings by the method of maximum likelihood. Proceedings of the Royal Society of Edinburgh 60 (01), 64–82CrossRefGoogle Scholar
Lord, F. M. Novick, M. R. & Birnbaum, A. (1968). Statistical theories of mental test scores Oxford: Addison-WesleyGoogle Scholar
MacCallum, R. C. Wegener, D. T. Uchino, B. N. & Fabrigar, L. R. (1993). The problem of equivalent models in applications of covariance structure analysis. Psychological Bulletin 114 (1), 185–199CrossRefGoogle ScholarPubMed
Marsh, H. W. Morin, A. J. Parker, P. D. & Kaur, G. (2014). Exploratory structural equation modeling: An integration of the best features of exploratory and confirmatory factor analysis. Annual Review of Clinical Psychology 10, 85–110CrossRefGoogle ScholarPubMed
Marsman, M. Maris, G. Bechger, T. & Glas, C. (2015). Bayesian inference for low-rank ising networks. Scientific reports 5 (9050), 1–7CrossRefGoogle ScholarPubMed
McCrae, R. R. Costa, P. T. (1997). Personality trait structure as a human universal. American Psychologist 52 (5), 509–516CrossRefGoogle ScholarPubMed
McGill, R. Tukey, J. W. & Larsen, W. A. (1978). Variations of box plots. The American Statistician 32 (1), 12–16CrossRefGoogle Scholar
McNally, R. J. Robinaugh, D. J. Wu, G. W. Wang, L. Deserno, M. K. & Borsboom, D. (2015). Mental disorders as causal systems a network approach to posttraumatic stress disorder. Clinical Psychological Science 3 (6), 836–849CrossRefGoogle Scholar
Murphy, K. P. (2012). Machine learning: A probabilistic perspective Cambridge, MA: MIT pressGoogle Scholar
Neale, M. C. Hunter, M. D. Pritikin, J. N. Zahery, M. Brick, T. R. Kirkpatrick, R. M. Estabrook, R. Bates, T. C. Maes, H. H. & Boker, S. M. (2016). Openmx 2.0: Extended structural equation and statistical modeling. Psychometrika 81 (2), 535–549CrossRefGoogle ScholarPubMed
Pan, J., Ip, E., & Dube, L. (in press). An alternative to post-hoc model modification in confirmatory factor analysis: The bayesian lasso. Psychological Methods.Google Scholar
Pearl, J. (2000). Causality: Models, reasoning, and inference New York, NY: Cambridge University PressGoogle Scholar
Reckase, M. D. (2009). Multidimensional item response theory New York, NY: SpringerCrossRefGoogle Scholar
Revelle, W. (2010). psych: Procedures for Psychological, Psychometric, and Personality Research (R package version 1.0-93). Northwestern University, Evanston, IL.Google Scholar
Rosa, M. Friston, K. & Penny, W. (2012). Post-hoc selection of dynamic causal models. Journal of Neuroscience Methods 208 (1), 66–78CrossRefGoogle ScholarPubMed
Schmittmann, V. D. Cramer, AOJ Waldorp, L. J. Epskamp, S. Kievit, R. A. & Borsboom, D. (2013). Deconstructing the construct: A network perspective on psychological phenomena. New Ideas in Psychology 31 (1), 43–53CrossRefGoogle Scholar
Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society Series B (Methodological) 58, 267–288CrossRefGoogle Scholar
van Borkulo, C. D. Borsboom, D. Epskamp, S. Blanken, T. F. Boschloo, L. Schoevers, R. A. & Waldorp, L. J. (2014). A new method for constructing networks from binary data. Scientific Reports 4 (5918), 1–10CrossRefGoogle ScholarPubMed
van Borkulo, C. D. Boschloo, L. Borsboom, D. Penninx, BWJH Waldorp, L. J. & Schoevers, R. A. (2015). Association of symptom network structure with the course of depression. JAMA Psychiatry 72 (12), 1219–1226CrossRefGoogle Scholar
van der Maas, H. L. Dolan, C. V. Grasman, R. P. Wicherts, J. M. Huizenga, H. M. & Raijmakers, M. E. (2006). A dynamical model of general intelligence: The positive manifold of intelligence by mutualism. Psychological Review 113 (4), 842–861CrossRefGoogle ScholarPubMed
Ware, J. E. Jr & Sherbourne, C. D. (1992). The MOS 36-item short-form health survey (SF-36): I. Conceptual framework and item selection. Medical Care 30, 473–483CrossRefGoogle ScholarPubMed
Wright, S. (1921). Correlation and causation. Journal of Agricultural Research 20 (7), 557–585Google Scholar
Wright, S. (1934). The method of path coefficients. The Annals of Mathematical Statistics 5 (3), 161–215CrossRefGoogle Scholar
Yin, J. & Li, H. (2011). A sparse conditional gaussian graphical model for analysis of genetical genomics data. The Annals of Applied Statistics 5 (4), 2630–2650CrossRefGoogle ScholarPubMed
Zou, H. & Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 67 (2), 301–320CrossRefGoogle Scholar
Zou, H. Hastie, T. & Tibshirani, R. (2007). et al. On the degrees of freedom of the lasso. The Annals of Statistics 35 (5), 2173–2192CrossRefGoogle Scholar
Supplementary material: File

Epskamp et al. supplementary material

Epskamp et al. supplementary material
Download Epskamp et al. supplementary material(File)
File 34.7 KB