The Issues of Construction and Analysis of Ordered Partial Correlation Networks in Psychological Research

In the context of network modeling, psychological variables are understood as directly affecting each other, and not as a consequence of latent constructs. An efficient assessment of networks showing relationships between measured variables can be carried out using the methods of regularization of the network of partial correlations. This article provides an example of constructing a regularized network of partial correlations in the R software environment (it is showing the relationship between the personality traits of adolescents and their behavior in virtual space using the example of the social network VKontakte) and examines the features of constructing and analyzing ordered networks of partial correlations. A list of potential problems arising when using the considered network methodology is presented. The issues related to sample size and reproducibility of the network, difficulties in interpreting networks, and comparing different networks with each other, including both network models and models of latent variables, are considered.

1. Artemenkov S.L. Ordered Partial Correlation Networks in Psychological Research. Mod­elirovanie i analiz dannikh = Modelling and Data Analysis, 2021. Vol. 11, no. 2, pp. 31–50. doi:10.17759/mda.2021110202. (In Russ., аbstr. in Engl.)
2. Artemenkov S.L. Setevoye modelirovaniye psikhologicheskikh konstruktov // Modelirovaniye i analiz dannykh. 2017. № 1. S. 9–28.
3. Artemenkov S.L. Initsionno-semanticheskaya model’ divergentnoy kreativnosti [Elektronnyy resurs] // Psikhologicheskaya nauka i obrazovaniye psyedu.ru. 2012. № 3. S. 1–15. URL: http:// psyjournals.ru/psyedu_ru/2012/n3/55540.shtml.
4. Vachkov I.V., Vachkova S.N. Reproducibility of Psychological Experiments as a Problem of Post-Nonclassical Science. Kul’turno-istoricheskaya psikhologiya = Cultural-Historical Psychol­ogy, 2016. Vol. 12, no. 1, pp. 97–101. doi:10.17759/chp.2016120110. (In Russ., аbstr. in Engl.)
5. Zhukova E.S., Artemenkov S.L., Bogoyavlenskaya D.B. K voprosu o sootnoshenii odarennosti i osoznannoy samoregulyatsii. Lichnostnyye i regulyatornyye resursy dostizheniya obrazova­tel’nykh i professional’nykh tseley v epokhu tsifrovizatsii. Moskva: Znaniye-M, 2020. S. 104– 115. DOI: 10.38006/907345–50–8.2020.104.115.
6. Zhukova E.S., Artemenkov S.L., Bogoyavlenskaya D.B. Issledovaniye intellektual’noy aktivnos­ti v mladshem shkol’nom i podrostkovom vozraste / Modelirovaniye i analiz dannykh. 2019. № 1. S. 11–29.
7. Rubtsova O.V., Panfilova A.S., Artemenkov S.L. Relationship between Personality Traits and Online Behaviour in Adolescents and Young Adults: A Research on Dota 2 Players. Psikho­logicheskaya nauka i obrazovanie = Psychological Science and Education, 2018. Vol. 23, no. 1, pp. 137–148. doi:10.17759/pse.2018230112. (In Russ., аbstr. in Engl.)
8. Rubtsova O.V., Panfilova A.S., Smirnova V.K. Research on Relationship between Personality Traits and Online Behaviour in Adolescents (With VKontakte Social Media as an Example). Psikhologicheskaya nauka i obrazovanie = Psychological Science and Education, 2018. Vol. 23, no. 3, pp. 54–66. doi:10.17759/pse.2018230305. (In Russ., аbstr. in Engl.)
9. Bogoyavlenskaya D., Joukova E., Artemenkov S. Longitudinal Study Of The Creative Abilities // The European Proceedings of Social & Behavioural Sciences (EpSBS), 2018. 14: 125–131. doi: https://dx.doi.org/10.15405/epsbs.2018.11.02.14.
10. Borsboom D., Fried E., Epskamp S., Waldorp L., van Borkulo C., van der Maas H., & Cram­er A.O.J. Replicability of psychopathology networks: The right question but the wrong answer. a comment on “evidence that psychopathology symptom networks have limited replicability” by Forbes, Wright, Markon, and Krueger. Journal of Abnormal Psychology, 2017. 126, 989–999.
11. Chandrasekaran V., Parrilo P.A., & Willsky A.S. Latent variable graphical model selection via convex optimization (with discussion). The Annals of Statistics, 2012. 40, 1935–1967.
12. Chen Y., Li X., Liu J., & Ying Z. A fused latent and graphical model for multivariate binary data. arXiv preprint, arXiv, 2016. 1606.08925.
13. Cohen J. Statistical power analysis for the behavioral sciences. New York, NY: Academic Press. 1977.
14. Costantini G., Epskamp S., Borsboom D., Perugini M., Mõttus R., Waldorp L.J., & Cram­er A.O.J. State of the aRt personality research: A tutorial on network analysis of personality data in R. Journal of Research in Personality, 2015. 54, 13–29.
15. Epskamp S. Brief Report on Estimating Regularized Gaussian Networks from Continuous and Ordinal Data. 2016. Retrieved from http://arxiv.org/abs/1606.05771
16. Epskamp S., Cramer A., Waldorp L., Schmittmann V.D., & Borsboom D. qgraph: Network visu­alizations of relationships in psychometric data. Journal of Statistical Software, 2012. 48, 1–18.
17. Epskamp S., Borsboom D., Fried E.I. Estimating psychological networks and their accuracy: a tutorial paper. Behavior Research Methods. 2018. 50, 195–212.
18. Epskamp S., Fried E.I. A tutorial on regularized partial correlation networks. Psychological Methods, 2018. 23(4), 617–634. https://doi.org/10.1037/met0000167.
19. Epskamp S., Kruis J., & Marsman M. Estimating psychopathological networks: Be careful what you wish for. PloS ONE, 2017. 12, e0179891.
20. Epskamp S., Rhemtula M., & Borsboom D. Generalized network psychometrics: Combining net­work and latent variable models. Psychometrika, 2017. 82, 904–927. http://dx.doi.org/10.1007/ s11336–017–9557-x
21. Forbes M.K., Wright A.G.C., Markon K., & Krueger R. Evidence that psychopathology symptom networks have limited replicability. Journal of Abnormal Psychology, 2017. 126, 969–988.
22. Foygel R., & Drton M. Extended Bayesian information criteria for Gaussian graphical models. Advances in Neural Information Processing Systems, 2010. 23, 2020–2028.
23. Fried E.I., & Cramer A.O.J. Moving forward: Challenges and directions for psychopathological network theory and methodology. Perspectives on Psychological Science, 2017. 12, 999–1020. http://dx.doi.org/10.1177/1745691617705892
24. Fried E.I., Eidhof M.B., Palic S., Costantini G., Huisman-van Dijk H.M., Bockting C.L.H., Engelhard I., Armour C., Nielsen A.B.S., & Karstoft K.-I. Replicability and generalizability of posttraumatic stress disorder (PTSD) networks: A cross-cultural multisite study of PTSD symp­toms in four trauma patient samples. Clinical Psychological Science, 2018. 6(3), 335–351. https:// doi.org/10.1177/2167702617745092
25. Fried E.I., van Borkulo C.D., Cramer A.O.J., Lynn B., Schoevers R.A., & Borsboom D. Mental disorders as networks of problems: A review of recent insights. Social Psychiatry and Psychiatric Epidemiology, 2017. 52, 1–10.
26. Friedman J.H., Hastie T., & Tibshirani R. glasso: Graphical lasso-estimation of Gaussian graph­ical models (R package version 1.8). 2014. Retrieved from https://CRAN.R-project.org/pack­age&glasso
27. Fruchterman T., & Reingold E. Graph drawing by force-directed placement. Software: Practice and Experience, 1991. 21, 1129–1164.
28. Guyon H., Falissard B., & Kop J.-L. Modeling psychological attributes in psychology–an episte­mological discussion: Network analysis vs. latent variables. Frontiers in Psychology, 2017. 8, 798.
29. Holland P.W., & Rosenbaum P.R. Conditional association and unidimensionality in monotone latent variable models. The Annals of Statistics, 1986. 14, 1523–1543.
30. Koller D., & Friedman N. Probabilistic graphical models: Principles and techniques. Cambridge, MA: MIT Press. 2009.
31. Kruis J., & Maris G. Three representations of the Ising model. Scientific Reports, 2016. 6, 34175.
32. Marsman M., Maris G., Bechger T., & Glas C. Bayesian inference for low-rank ISING networks. Scientific reports, 2015. 5(9050), 1–7.
33. Muthén B.O. Factor structure in groups selected on observed scores. British Journal of Mathema-tical and Statistical Psychology, 1989. 42, 81–90.
34. Olsson U. Maximum likelihood estimation of the polychoric correlation coefficient. Psychometri­ka, 1979. 44, 443–460.
35. Open Science Collaboration. Estimating the reproducibility of psychological science. Science, 2015. 349, aac4716 –aac4716.
36. Opsahl T., Agneessens F., & Skvoretz J. Node centrality in weighted networks: Generalizing degree and shortest paths. Social Networks, 2010. 32, 245–251.
37. Pan J., Ip E., & Dube L. An alternative to post-hoc model modification in confirmatory factor analysis: The Bayesian lasso. Psychological Methods, 2017. 22, 687–704.
38. Pearl J. Causality: Models, reasoning, and inference. Cambridge, UK: Cambridge University Press. 2000.
39. Rhemtulla M., Fried E.I., Aggen S.H., Tuerlinckx F., Kendler K.S., & Borsboom D. Network analysis of substance abuse and dependence symptoms. Drug and Alcohol Dependence, 2016. 161, 230–237.
40. Rigdon E.E., & Ferguson C.E., Jr. The performance of the polychoric correlation coefficient and selected fitting functions in confirmatory factor analysis with ordinal data. Journal of Marketing Research, 1991. 28, 491–497.
41. Rosseel Y. lavaan: An R package for structural equation modeling. Journal of Statistical Software, 2012. 48(2), 1–36.
42. Schmittmann V.D., Cramer A.O.J., Waldorp L.J., Epskamp S., Kievit R.A., & Borsboom D. De­constructing the construct: A network perspective on psychological phenomena. New Ideas in Psychology, 2013. 31, 43–53.
43. van Bork R., Rhemtulla M., Waldorp L.J., Kruis J., Rezvanifar S. & Borsboom D. Latent Variable Models and Networks: Statistical Equivalence and Testability, Multivariate Behavioral Research, 2019. DOI: 10.1080/00273171.2019.1672515
44. van Borkulo C.D., Borsboom D., Epskamp S., Blanken T.F., Boschloo L., Schoevers R.A., & Waldorp L.J. A new method for constructing networks from binary data. Scientific Reports, 2014. 4(5918), 1–10.
45. van Borkulo C., Boschloo L., Kossakowski J., Tio P., Schoevers R., Borsboom D., & Wal­dorp L. Comparing network structures on three aspects: A permutation test. 2017. http://dx.doi. org/10.13140/RG.2.2.29455.38569
46. van Der Maas H.L., Dolan C.V., Grasman R.P., Wicherts J.M., Huizenga H.M., & Raijmak­ers M.E. A dynamical model of general intelligence: The positive manifold of intelligence by mutualism. Psychological review, 2006. 113, 842–861.