Abstract
The combination of network theory and network psychometric methods has opened up a variety of new ways to conceptualize and study psychological disorders. The idea of psychological disorders as dynamic systems has sparked interest in developing interventions based on results of network analytic tools. However, simply estimating a network model is not sufficient for determining which symptoms might be most effective to intervene upon, nor is it sufficient for determining the potential efficacy of any given intervention. In this paper, we attempt to remedy this gap by introducing fundamental concepts of control theory to both psychometricians and applied psychologists. We introduce two controllability statistics to the psychometric literature, average and modal controllability, to facilitate selecting the best set of intervention targets. Following this introduction, we show how intervention scientists can probe the effects of both theoretical and empirical interventions on networks derived from real data and demonstrate how simulations can account for intervention cost and the desire to reduce specific symptoms. Every step is based on rich clinical EMA data from a sample of subjects undergoing treatment for complicated grief, with a focus on the outcome suicidal ideation. All methods are implemented in an open-source R package netcontrol, and complete code for replicating the analyses in this manuscript are available online.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
We intend this manuscript to serve as an introduction to control theory both for methodologists working within clinical sciences as well as clinical psychologists wishing to better model disorders and possible treatment effects. Accordingly, although many technical details are included in the main text, some have been omitted to provide a more accessible overview. Further technical details about the models and code to replicate all results presented in this paper are included in the Supplementary Materials (SMs) and at https://osf.io/f268v/. All controllability centrality measures and optimal control inputs are calculated using netcontrol (Henry 2020), an open-source, publicly available R package implementing many methods from control theory for use in psychological and neurological data analysis.
The use of the term “average” in average controllability is an unfortunate case of naming. Here, average does not refer to any specific statistical average, rather it is used in a more colloquial sense to mean “general” or “overall.” As such, there is the distinct possibility that researchers will use the term “mean average controllability” to refer to the average of several values of average controllability. We sympathize with the confusion of any reader who encounters that term in the future.
The term mode, when applied to a linear system, refers to the set of eigenvectors along with the corresponding eigenvalues of the dynamics matrix. These eigenvectors correspond to patterns of input that, if provided, would pass through the system unchanged save for a multiplicative constant, which is the corresponding eigenvalue. To be concrete, if \(\nu \) is an eigenvector of A with corresponding eigenvalue \(\lambda \), if \(X_t = \nu \), then \(X_{t+1} = \nu {A} = \lambda \nu \)
Many interventions can be considered all or nothing, with no notion of varying intervention strength. While the exposition in the current manuscript presents optimal control with varying interventions strength, we note in the discussion that hybrid model predictive control methods allow for binary intervention strengths (i.e., 0—no intervention, 1—intervention)
These matrices should be specified with respect to the scaling of individual symptom measures. In the example of complicated grief symptoms, the measure of suicidal ideation has a maximum value of 5, whereas all others measures have a maximum value of 7. This requires a slight modification of the \(\mathbf {S}_T\) and \(\mathbf {Q}\) matrices, so that the scales are equated. Here, the element corresponding to suicidal ideation in \(\mathbf {S}_T\) and \(\mathbf {Q}\) is set to \(\frac{7}{5} = 1.4\) rather than 1. For scales with several different maximums, a common factor can be computed. Finally, this rescaling should only be done when the choice of units is arbitrary, such as in a Likert type item.
References
Åström, K. J. (2006). Introdution to stochastic control theory. Mineola, N.Y: Dover Publications.
Bemporad, A., & Morari, M. (1999). Control of systems integrating logic, dynamics, and constraints. Automatica, 35(3), 407–427. https://doi.org/10.1016/S0005-1098(98)00178-2.
Borsboom, D. (2008). Psychometric perspectives on diagnostic systems. Journal of Clinical Psychology, 64(9), 1089–1108.
Borsboom, D. (2017). A network theory of mental disorders. World Psychiatry, 16(1), 5–13. https://doi.org/10.1002/wps.20375.
Bringmann, L. F., Vissers, N., Wichers, M., Geschwind, N., Kuppens, P., Peeters, F., et al. (2013). A network approach to psychopathology: New insights into clinical longitudinal data. PLoS ONE, 8(4), e60188. https://doi.org/10.1371/journal.pone.0060188.
Burger, J., van der Veen, D. C., Robinaugh, D., Quax, R., Riese, H., Schoevers, R. A., & Epskamp, S. (2019). Bridging the gap between complexity science and clinical practice by formalizing idiographic theories: A computational model of functional analysis (Preprint). PsyArXiv. https://doi.org/10.31234/osf.io/gw2uc.
Carver, C. S., & Scheier, M. F. (1998). On the self-regulation of behavior (1st ed.). Cambridge: Cambridge University Press.
Collins, L. M., Murphy, S. A., & Bierman, K. L. (2004). A conceptual framework for adaptive preventive interventions. Prevention Science: The Official Journal of the Society for Prevention Research, 5(3), 185–196. https://doi.org/10.1023/B:PREV.0000037641.26017.00.
Contreras, A., Nieto, I., Valiente, C., Espinosa, R., & Vazquez, C. (2019). The study of psychopathology from the network analysis perspective: A systematic review. Psychotherapy and Psychosomatics, 88(2), 71–83. https://doi.org/10.1159/000497425.
Cramer, A. O. J., Waldorp, L. J., van der Maas, H. L. J., & Borsboom, D. (2010). Comorbidity: A network perspective. Behavioral and Brain Sciences, 33(2–3), 137–150. https://doi.org/10.1017/S0140525X09991567.
Epskamp, S. (2017). Network Psychometrics (Unpublished doctoral dissertation). University of Amsterdam.
Epskamp, S., Rhemtulla, M., & Borsboom, D. (2017). Generalized network psychometrics: Combining network and latent variable models. Psychometrika, 82(4), 904–927. https://doi.org/10.1007/s11336-017-9557-x.
Epskamp, S., Waldorp, L. J., Mõttus, R., & Borsboom, D. (2018). The Gaussian graphical model in cross-sectional and time-series data. Multivariate Behavioral Research 53(4), 453–480. https://doi.org/10.1080/00273171.2018.1454823
Fried, E. I. (2020). Lack of theory building and testing impedes progress in the factor and network literature. Psychological Inquiry, 31(4), 271–288. https://doi.org/10.1080/1047840X.2020.1853461.
Fried, E. I., van Borkulo, C. D., Cramer, A. O. J., Boschloo, L., Schoevers, R. A., & Borsboom, D. (2017). Mental disorders as networks of problems: A review of recent insights. Social Psychiatry and Psychiatric Epidemiology, 52(1), 1–10. https://doi.org/10.1007/s00127-016-1319-z.
Hamdan, A. M. A., & Nayfeh, A. H. (1989). Measures of modal controllability and observability for first- and second-order linear systems. Journal of Guidance, Control, and Dynamics, 12(3), 421–428. https://doi.org/10.2514/3.20424.
Haslbeck, J. M. B., Ryan, O., Robinaugh, D. J., Waldorp, L., & Borsboom, D. (2019). Modeling psychopathology: From data models to formal theories (Preprint). PsyArXiv. https://doi.org/10.31234/osf.io/jgm7f.
Henry, T. R. (2020). Netcontrol: Control theory methods for networks. https://CRAN.R-project.org/package=netcontrol (R package version 0.1)
Hyland, M. E. (1987). Control theory interpretation of psychological mechanisms of depression: Comparison and integration of several theories. Psychological Bulletin. 102(1), 109–121. https://doi.org/10.1037/0033-2909.102.1.109
Johnson, R. E., Chang, C.-H., & Lord, R. G. (2006). Moving from cognition to behavior: What the research says. Psychological Bulletin, 132(3), 381–415. https://doi.org/10.1037/0033-2909.132.3.381.
Jordan, D. G., Winer, E. S., & Salem, T. (2020). The current status of temporal network analysis for clinical science: Considerations as the paradigm shifts? Journal of Clinical Psychology, 76(9), 1591–1612. https://doi.org/10.1002/jclp.22957.
Kendler, K. S., Zachar, P., & Craver, C. (2011). What kinds of things are psychiatric disorders? Psychological Medicine, 41(6), 1143–1150.
Kim, N. S., & Ahn, W.-K. (2002). Clinical psychologist’s theory-based representations of mental disorders predict their diagnostic reasoning and memory. Journal of Experimental Psychology: General. 131(4), 451–476. https://doi.org/10.1037/0096-3445.131.4.451
Kouvaritakis, B., & Cannon, M. (2015). Model predictive control. New York, NY: Springer.
Levine, S. Z., & Leucht, S. (2016). Identifying a system of predominant negative symptoms: Network analysis of three randomized clinical trials. Schizophrenia Research, 178(1–3), 17–22. https://doi.org/10.1016/j.schres.2016.09.002.
Lewis, F. L., Vrabie, D. L., & Syrmos, V. L. (2012). Optimal control (3rd ed.). Hoboken: Wiley.
Ljung, L. (1999). System identification: Theory for the user (2nd ed.). Upper Saddle River, NJ: Prentice Hall PTR.
Molenaar, P. C. (1987). Dynamic assessment and adaptive optimization of the pschotherapeutic process. Behavioral Assessment, 9(4), 389–416.
Molenaar, P. C. (2010). Note on optimization of individual psychotherapeutic processes. Journal of Mathematical Psychology, 54(1), 208–213. https://doi.org/10.1016/j.jmp.2009.04.003.
Nahum-Shani, I., Smith, S. N., Spring, B. J., Collins, L. M., Witkiewitz, K., Tewari, A., et al. (2018). Just-in-time adaptive interventions (JITAIs) in mobile health: Key components and design principles for ongoing health behavior support. Annals of Behavioral Medicine, 52(6), 446–462. https://doi.org/10.1007/s12160-016-9830-8.
Olshevsky, A. (2014a) Minimal Controllability Problems. arXiv:1304.3071 [cs, math].
Olshevsky, A. (2014b) Minimum Input Selection for Structural Controllability. arXiv:1407.2884 [cs, math].
Pasqualetti, F., Zampieri, S., & Bullo, F. (2014). Controllability metrics, limitations and algorithms for complex networks. In: (pp. 3287–3292). IEEE. https://doi.org/10.1109/TCNS.2014.2310254
Preumont, A. (1997). Controllability and observability. In: Vibration control of active structures: An introduction (pp. 173–195). Dordrecht: Springer Netherlands.
Radden, J. (2018). Rethinking disease in psychiatry: Disease models and the medical imaginary. Journal of Evaluation in Clinical Practice, 24(5), 1087–1092. https://doi.org/10.1111/jep.12982.
Rivera, D. E. , Hekler, E. B. , Savage, J. S., & Downs, D. S. (2018). Intensively adaptive interventions using control systems engineering: Two illustrative examples. In: Collins, L. M., & Kugler, K. C. (eds), Optimization of behavioral, biobehavioral, and biomedical interventions: Advanced topics (pp. 121–173). Cham: Springer. https://doi.org/10.1007/978-3-319-91776-4_5
Rivera, D. E., Pew, M. D., & Collins, L. M. (2007). Using engineering control principles to inform the design of adaptive interventions: A conceptual introduction. Drug and Alcohol Dependence, 88, S31–S40. https://doi.org/10.1016/j.drugalcdep.2006.10.020.
Robinaugh, D. J., Haslbeck, J. M. B., Waldorp, L., Kossakowski, J. J., Fried, E. I., Millner, A., & Borsboom, D. (2019). Advancing the network theory of mental disorders: A computational model of panic disorder (Preprint). PsyArXiv. https://doi.org/10.31234/osf.io/km37w.
Robinaugh, D. J. , Hoekstra, R. H. A. , Toner, E. R., & Borsboom, D. (2019). The network approach to psychopathology: A review of the literature 2008–2018 and an agenda for future research. Psychological Medicine pp.1–14. https://doi.org/10.1017/S0033291719003404
Schultz, P. R. (1964). An optimal control problem with state vector measurement errors. In: Advances in control systems (vol. 1, pp. 197–243). Elsevier. https://doi.org/10.1016/B978-1-4831-6717-6.50010-3
Shear, M. K. (2010). Complicated grief treatment: The theory, practice and outcomes. Bereavement Care, 29(3), 10–14.
Shumway, R. H., & Stoffer, D. S. (2017). Time series analysis and its applications: With R examples (4th ed.). New York, NY: Springer.
Sinclair, K. , & Molenaar, P. C. (2008). Optimal control of psychological processes: A new computational paradigm. In: Bulletin de la Societe des Sciences Medicales Luxembourg (vol. 1, pp. 13–33). Luxembourg.
Summers, T. H., Cortesi, F. L., & Lygeros, J. (2016). On submodularity and controllability in complex dynamical networks. IEEE Transactions on Control of Network Systems, 3(1), 91–101. https://doi.org/10.1109/TCNS.2015.2453711.
Acknowledgement
This project was supported by the American Foundation for Suicide Prevention, the Charles A. King Trust Postdoctoral Research Fellowship Program, Bank of America, N.A., Co-Trustees, and a National Institute of Mental Health Career Development Award (1K23MH113805-01A1) awarded to D. Robinaugh. The content is solely the responsibility of the authors and does not necessarily represent the views of these organizations. We would like to acknowledge the two anonymous reviewers, our AE Dr. Mijke Rhemtulla, whose comments and suggestions drastically improved this work, and Dr. Jennifer MacCormack for their helpful feedback on earlier drafts.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This project was supported by the American Foundation for Suicide Prevention, the Charles A. King Trust Postdoctoral Research Fellowship Program, Bank of America, N.A., Co-Trustees, and a National Institute of Mental Health Career Development Award (1K23MH113805-01A1) awarded to D. Robinaugh. The content is solely the responsibility of the authors and does not necessarily represent the views of these organizations. Correspondence should be directed to Teague R. Henry at trhenry@virginia.edu
Rights and permissions
About this article
Cite this article
Henry, T.R., Robinaugh, D.J. & Fried, E.I. On the Control of Psychological Networks. Psychometrika 87, 188–213 (2022). https://doi.org/10.1007/s11336-021-09796-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11336-021-09796-9