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Behavior research methods
09, 2023;55 (6): 2960-2978.

Stability and spread: A novel method for quantifying transitions within multivariate binary time series data.

Katharine E Daniel, Robert G Moulder, Bethany A Teachman, Steven M Boker
Author Information
  1. Katharine E Daniel: Department of Psychology, University of Virginia, P.O. Box 400400, Charlottesville, VA, 22904, USA. ked4fd@virginia.edu. ORCID
  2. Robert G Moulder: Department of Psychology, University of Virginia, P.O. Box 400400, Charlottesville, VA, 22904, USA. ORCID
  3. Bethany A Teachman: Department of Psychology, University of Virginia, P.O. Box 400400, Charlottesville, VA, 22904, USA. ORCID
  4. Steven M Boker: Department of Psychology, University of Virginia, P.O. Box 400400, Charlottesville, VA, 22904, USA. ORCID
PMID: 36002629 DOI: 10.3758/s13428-022-01942-0

Abstract

We present a novel method for quantifying transitions within multivariate binary time series data, using a sliding series of transition matrices, to derive metrics of stability and spread. We define stability as the trace of a transition matrix divided by the sum of all observed elements within that matrix. We define spread as the number of all non-zero cells in a transition matrix divided by the number of all possible cells in that matrix. We developed this method to allow investigation into high-dimensional, sparse data matrices for which existing binary time series methods are not designed. Results from 1728 simulations varying six parameters suggest that unique information is captured by both metrics, and that stability and spread values have a moderate inverse association. Further, simulations suggest that this method can be reliably applied to time series with as few as nine observations per person, where at least five consecutive observations construct each overlapping transition matrix, and at least four time series variables compose each transition matrix. A pre-registered application of this method using 4 weeks of ecological momentary assessment data (N = 110) showed that stability and spread in the use of 20 emotion regulation strategies predict next timepoint affect after accounting for affect and anxiety's auto-regressive and cross-lagged effects. Stability, but not spread, also predicted next timepoint anxiety. This method shows promise for meaningfully quantifying two unique aspects of switching behavior in multivariate binary time series data.

Keywords

Emotion regulation High dimensionality Multivariate binary time series Switching Transition matrix

References

  1. Aldao, A., Sheppes, G., & Gross, J. J. (2015). Emotion regulation flexibility. Cognitive Therapy and Research. https://doi.org/10.1007/s10608-014-9662-4
  2. Anderson, T. W., & Goodman, L. A. (1957). Statistical inference about Markov chain. Annals of Mathematical Statistics, 28, 89–110. [DOI: 10.1214/aoms/1177707039]
  3. Birk, J. L., & Bonanno, G. A. (2016). When to throw the switch: The adaptiveness of modifying emotion regulation strategies based on affective and physiological feedback. Emotion, 16(5), 657–670. https://doi.org/10.1037/emo0000157 [DOI: 10.1037/emo0000157]
  4. Blanke, E. S., Brose, A., Kalokerinos, E. K., Erbas, Y., Riediger, M., & Kuppens, P. (2019). Mix it to fix it: Emotion regulation variability in daily life. Emotion. https://doi.org/10.1037/emo0000566
  5. Boker, S. M., Rotondo, J. L., Xu, M., & King, K. (2002). Windowed cross-correlation and peak picking for the analysis of variability in the association between behavioral time series. Psychological Methods, 7(3), 338. https://doi.org/10.1037/1082-989x.7.3.338 [DOI: 10.1037/1082-989x.7.3.338]
  6. Boker, S. M., Tiberio, S. S., & Moulder, R. G. (2018). Robustness of time delay embedding to sampling interval misspecification. In K. van Montfort, J. H. L. Oud, & M. C. Voelkle (Eds.), Continuous Time Modeling in the Behavioral and Related Sciences. Springer. https://doi.org/10.1007/978-3-319-77219-6_10 [DOI: 10.1007/978-3-319-77219-6_10]
  7. Bonanno, G. A., & Burton, C. L. (2013). Regulatory flexibility: An individual differences perspective on coping and emotion regulation. Perspectives on Psychological Science. https://doi.org/10.1177/1745691613504116
  8. Cheng, C. (2001). Assessing coping flexibility in real-life and laboratory settings: a multimethod approach. Journal of Personality and Social Psychology, 80(5), 814–833. https://doi.org/10.1037//0022-3514.80.5.814 [DOI: 10.1037//0022-3514.80.5.814]
  9. Coco, M.I., Monster, D., Leonardi, G., Dale, R., Wallot, S., Dixon, J.D., Nash, J.C. (2022). Recurrence Quantification Analysis for Categorical and Continuous Time-Series. Package version 2.0.3. https://www.cran.r-project.org/web/packages/crqa/crqa.pdf
  10. Daniel, K.E., & Moulder, R.G. (2020). transitionMetrics: R package to calculate characteristics of transitions in multivariate binary time series data. Version 0.1.0. https://www.github.com/KatharineDaniel/transitionMetrics
  11. Daniel, K. E., Daros, A. R., Beltzer, M. L., Boukhechba, M., Barnes, L. E., & Teachman, B. A. (2020). How anxious are you right now? Using ecological momentary assessment to evaluate the effects of cognitive bias modification for social threat interpretations. Cognitive Therapy and Research, 44(3), 538–556. https://doi.org/10.1007/s10608-020-10088-2 [DOI: 10.1007/s10608-020-10088-2]
  12. Eckmann, J. P., Kamphorst, S. O., & Ruelle, D. (1987). Recurrence plots of dynamical systems. EPL, 4, 973. https://doi.org/10.1209/0295-5075/4/9/004 [DOI: 10.1209/0295-5075/4/9/004]
  13. Eldesouky, L., & English, T. (2021). Always in flux: The role of attentional focus in emotion regulation dynamics. Cognition & Emotion, 1–7. Advance online publication. https://doi.org/10.1080/02699931.2021.1993146
  14. Ford, B. Q., Gross, J. J., & Gruber, J. (2019). Broadening our field of view: The role of emotion polyregulation. Emotion Review, 11(3), 197–208. https://doi.org/10.1177/1754073919850314 [DOI: 10.1177/1754073919850314]
  15. Heiy, J. E., & Cheavens, J. S. (2014). Back to basics: a naturalistic assessment of the experience and regulation of emotion. Emotion (Washington, D.C.). https://doi.org/10.1037/a0037231
  16. Jazaieri, H., Morrison, A. S., Goldin, P. R., & Gross, J. J. (2014). The role of emotion and emotion regulation in social anxiety disorder. Current Psychiatry Reports. https://doi.org/10.1007/s11920-014-0531-3
  17. Kashdan, T. B., Weeks, J. W., & Savostyanova, A. A. (2011). Whether, how, and when social anxiety shapes positive experiences and events: A self-regulatory framework and treatment implications. Clinical Psychology Review, 31(5), 786–799. https://doi.org/10.1016/j.cpr.2011.03.012 [DOI: 10.1016/j.cpr.2011.03.012]
  18. Lougheed, J. P., & Hollenstein, T. (2012). A limited repertoire of emotion regulation strategies is associated with internalizing problems in adolescence. Social Development, 21(4), 704–721. https://doi.org/10.1111/j.1467-9507.2012.00663.x [DOI: 10.1111/j.1467-9507.2012.00663.x]
  19. Marwan, N., & Kurths, J. (2002). Nonlinear analysis of bivariate data with cross recurrence plots. Physics Letters A, 302(5–6), 299–307. https://doi.org/10.1016/S0375-9601(02)01170-2 [DOI: 10.1016/S0375-9601(02)01170-2]
  20. Mattick, R. P., & Clarke, J. C. (1998). Development and validation of measures of social phobia scrutiny fear and social interaction anxiety. Behaviour Research and Therapy, 36(4), 455–470. [DOI: 10.1016/S0005-7967(97)10031-6]
  21. Molenaar, P. C. M., Huizenga, H. M., & Nesselroade, J. R. (2003). The relationship between the structure of interindividual and intraindividual variability: A theoretical and empirical vindication of developmental systems theory. In U. M. Staudinger & U. Lindenberger (Eds.), Understanding human development: Dialogues with lifespan psychology (pp. 339–360). Kluwer Academic Publishers. https://doi.org/10.1007/978-1-4615-0357-6_15= [DOI: 10.1007/978-1-4615-0357-6_15=]
  22. Moulder, R.G., Daniel, K.E., Teachman, B.A., & Boker, S.M. (2021). Tangle: A metric for quantifying complexity and erratic behavior in short time series. Psych Methods. Advance online publication. https://doi.org/10.1037/met0000386
  23. Muenz, L. R., & Rubinstein, L. V. (1985). Markov models for covariate dependence of binary sequences. Biometrics, 41, 91–101. [DOI: 10.2307/2530646]
  24. 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), 535–549. https://doi.org/10.1007/s11336-014-9435-8 [DOI: 10.1007/s11336-014-9435-8]
  25. R Core Team. (2022). R: A language and environment for statistical computing. R Foundation for Statistical Computing https://www.R-project.org/
  26. Rajaram, R., Castellani, B., & Wilson, A. N. (2017). Advancing Shannon entropy for measuring diversity in systems. Complexity. https://doi.org/10.1155/2017/8715605
  27. Revelle, W. (2022). psych: Procedures for Psychological, Psychometric, and Personality Research. Northwestern University. R package version 2.2.3. https://www.CRAN.R-project.org/package=psych .
  28. Romano, M. C., Thiel, M., Kurths, J., & von Bloh, M. (2004). Multivariate recurrence plots. Physics Letters A, 330(3–4), 214–223. [DOI: 10.1016/j.physleta.2004.07.066]
  29. Rusch, S., Westermann, S., & Lincoln, T. M. (2012). Specificity of emotion regulation deficits in social anxiety: an internet study. Psychology and Psychotherapy: Theory, Research and Practice, 85(3), 268–277. https://doi.org/10.1111/j.2044-8341.2011.02029.x [DOI: 10.1111/j.2044-8341.2011.02029.x]
  30. Southward, M. W., Altenburger, E. M., Moss, S. A., Cregg, D. R., & Cheavens, J. S. (2018). Flexible, yet firm: A model of healthy emotion regulation. Journal of Social and Clinical Psychology, 37(4), 231–251. https://doi.org/10.1521/jscp.2018.37.4.231 [DOI: 10.1521/jscp.2018.37.4.231]
  31. Tian, W., & Anderson, S. J. (2000). Markov chain models for multivariate repeated binary data analysis. Communications in Statistics: Simulation and Computation, 29(4), 1001–1019. https://doi.org/10.1080/03610910008813651 [DOI: 10.1080/03610910008813651]
  32. Wallot, S. (2019). Multidimensional Cross-Recurrence Quantification Analysis (MdCRQA) - A Method for Quantifying Correlation between Multivariate Time-Series. Multivariate Behavioral Research, 54(2), 173–191. https://doi.org/10.1080/00273171.2018.1512846 [DOI: 10.1080/00273171.2018.1512846]
  33. Webber, C. L., & Marwan, N. (2015). Recurrence Quantification Analysis: Theory and Best Practices. Springer International Publishing. https://doi.org/10.1007/978-3-319-07155-8 [DOI: 10.1007/978-3-319-07155-8]
  34. Webber, C. L., & Zbilut, J. P. (1994). Dynamical assessment of physiological systems and states using recurrence plot strategies. Journal of Applied Physiology, 76(2), 965–973. https://doi.org/10.1152/jappl.1994.76.2.965 [DOI: 10.1152/jappl.1994.76.2.965]
  35. Wen, A., Quigley, L., Yoon, K. L., & Dobson, K. S. (2021). Emotion regulation diversity in current and remitted depression. Clinical Psychological Science, 9(4), 563–578. https://doi.org/10.1177/2167702620978616 [DOI: 10.1177/2167702620978616]
  36. Zbilut, J. P., Giuliani, A., & Webber, C. (1998). Recurrence quantification analysis and principal components in the detection of short complex signals. Physics Letters A, 3(237), 131–135. https://doi.org/10.1016/S0375-9601(97)00843-8 [DOI: 10.1016/S0375-9601(97)00843-8]

MeSH Term

Humans
Time Factors
Anxiety
Journal Article Research Support, Non-U.S. Gov't Research Support, N.I.H., Extramural
Article has an altmetric score of 23

Word Cloud

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