Hostname: page-component-5f745c7db-q8b2h Total loading time: 0 Render date: 2025-01-06T07:42:59.567Z Has data issue: true hasContentIssue false
  • English
  • Français

A Network Approach for Evaluating Coherence in Multivariate Systems: An Application to Psychophysiological Emotion Data

Published online by Cambridge University Press:  01 January 2025

Fushing Hsieh ,
Emilio Ferrer ,
Shuchun Chen ,
Iris B. Mauss ,
Oliver John  and
James J. Gross
Fushing Hsieh
Affiliation:
University of California, Davis
Emilio Ferrer*
Affiliation:
University of California, Davis
Shuchun Chen
Affiliation:
Academia Sinica
Iris B. Mauss
Affiliation:
University of Denver
Oliver John
Affiliation:
University of California, Berkeley
James J. Gross
Affiliation:
Stanford University
*
Requests for reprints should be sent to Emilio Ferrer, Department of Psychology, University of California, Davis, Davis, CA 95616-8686, USA. E-mail: eferrer@ucdavis.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We present an approach for evaluating coherence in multivariate systems that considers all the variables simultaneously. We operationalize the multivariate system as a network and define coherence as the efficiency with which a signal is transmitted throughout the network. We illustrate this approach with time series data from 15 psychophysiological signals representing individuals’ moment-by-moment emotional reactions to emotional films. First, we summarize the time series through nonparametric Receiver Operating Characteristic (ROC) curves. Second, we use Spearman rank correlations to calculate relationships between each pair of variables. Third, based on the obtained associations, we construct a network using the variables as nodes. Finally, we examine signal transmission through all the nodes in the network. Our results indicate that the network consisting of the 15 psychophysiological signals has a small-world structure, with three clusters of variables and strong within-cluster connections. This structure supports an effective signal transmission across the entire network. When compared across experimental conditions, our results indicate that coherence is relatively stronger for intense emotional stimuli than for neutral stimuli. These findings are discussed in relation to multivariate methods and emotion theories.

Keywords

multivariate analysisdynamical systemstime seriesemotion
Type
Original Paper
Information
Psychometrika , Volume 76 , Issue 1 , January 2011 , pp. 124 - 152
Copyright
Copyright © 2010 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

This study was supported in part by grants from the National Science Foundation (BCS-05-27766 and BCS-08-27021) and NIH-NINDS (R01 NS057146-01).

References

Albert, R., Jeong, H., Barabási, A.-L. (1999). Diameter of the world–wide web. Nature, 401, 130–131.CrossRefGoogle Scholar
Amaral, L.A.N., Diaz–Guilera, A., Moreira, A.A., Goldberger, A.L., Lipsitz, L.A. (2004). Emergence of complex dynamics in a simple model of signaling network. Proceedings of the National Academy of Sciences, 101, 155551–155555.CrossRefGoogle Scholar
Boker, S.M., Xu, M., Rotondo, J.L., King, K. (2002). Windowed cross-correlation and peak picking for the analysis of variability in the association between behavioral time series. Psychological Methods, 7, 338–355.CrossRefGoogle ScholarPubMed
Brillinger, D.R. (2001). Does anyone know when the correlation coefficient is useful? A study of the times of extreme river flows. Technometrics, 43, 266–273.CrossRefGoogle Scholar
Browne, M.W., Nesselroade, J.R. (2005). Representing psychological processes with dynamic factor models: some promising uses and extensions of ARMA time series models. In Maydeu-Olivares, A., McArdle, J.J. (Eds.), Advances in psychometrics: a Festschrift to Roderick P. McDonald (pp. 415–451). Mahwah: Erlbaum.Google Scholar
Cattell, R.B., Cattell, A.K.S., Rhymer, R.M. (1947). P-technique demonstrated in determining psychophysical source traits in a normal individual. Psychometrika, 12, 267–288.CrossRefGoogle Scholar
Ekman, P. (1972). Universals and cultural differences in facial expressions of emotion. In Cole, J. (Eds.), Nebraska symposium on motivation (pp. 207–282). Lincoln: University of Nebraska Press.Google Scholar
Ekman, P. (1992). An argument for basic emotions. Cognition and Emotion, 6, 169–200.CrossRefGoogle Scholar
Ekman, P., Friesen, W.V. (1978). The facial action coding system, Palo Alto: Consulting Psychologists Press.Google Scholar
Feldman-Barrett, L. (2006). Are emotions natural kinds?. Perspectives in Psychological Science, 1, 28–58.CrossRefGoogle Scholar
Ferrer, E., Nesselroade, J.R. (2003). Modeling affective processes in dyadic relations via dynamic factor analysis. Emotion, 3, 344–360.CrossRefGoogle ScholarPubMed
Gottman, J.M. (1990). Time-series analysis applied to physiological data. In Cacioppo, J.T., Tassinary, L.G. (Eds.), Principles of psychophysiology: physical, social, and inferential elements (pp. 754–774). New York: Cambridge University Press.Google Scholar
Gottman, J.M., Levenson, R.W. (1985). A valid procedure for obtaining self-report of affect in marital interaction. Journal of Consulting and Clinical Psychology, 53, 151–160.CrossRefGoogle ScholarPubMed
Hamaker, E.L., Dolan, C.V., Molenaar, P.C.M. (2005). Statistical modeling of the individual: rationale and application of multivariate stationary time series analysis. Multivariate Behavioral Research, 40, 207–233.CrossRefGoogle ScholarPubMed
Hastie, T., Tibshirani, R., Friedman, J. (2009). The elements of statistical learning, (2nd ed.). New York: Springer.CrossRefGoogle Scholar
Hsieh, F., Turnbull, B.W. (1996). Non- and semi-parametric estimation of the receiver operating characteristics (ROC) curve. Annals of Statistics, 24, 25–40.CrossRefGoogle Scholar
Johnson, S.C. (1967). Hierarchical clustering schemes. Psychometrika, 32, 241–254.CrossRefGoogle ScholarPubMed
Klinkner, K.L., Shalizi, C.R., Camperi, M.F. (2006). Measuring shared information and coordinated activity in neuronal networks. In Weiss, Y., Scholkopf, B., Platt, J.C. (Eds.), Advances in neural information processing systems (pp. 667–674). Cambridge: MIT Press.Google Scholar
Lazarus, R.S. (1991). Emotion and adaptation, London: Oxford University Press.CrossRefGoogle Scholar
Levenson, R.W. (1994). Human emotions: a functional view. In Ekman, P., Davidson, R.J. (Eds.), The nature of emotion: fundamental questions (pp. 123–126). New York: Oxford University Press.Google Scholar
Levenson, R.W. (2003). Blood, sweat, and fears: the autonomic architecture of emotion. In Ekman, P., Campos, J.J., Davidson, R.J., de Waal, F.B.M. (Eds.), Emotions inside out (pp. 348–366). New York: The New York Academy of Sciences.Google Scholar
Levenson, R.W., Gottman, J.M. (1983). Marital interaction: physiological linkage and affective exchange. Journal of Personality and Social Psychology, 45, 587–597.CrossRefGoogle ScholarPubMed
Matsumoto, D., Nezlek, J.B., Koopmann, B. (2007). Evidence for universality in phenomenological emotion response system coherence. Emotion, 7, 57–67.CrossRefGoogle ScholarPubMed
Mauss, I.B., Evers, C., Wilhelm, F.H., Gross, J.J. (2006). How to bite your tongue without blowing your top: implicit evaluation of emotion regulation predicts affective responding to anger provocation. Personality and Social Psychology Bulletin, 32, 389–602.CrossRefGoogle ScholarPubMed
Mauss, I.B., Levenson, R.W., McCarter, L., Wilhelm, F.H., Gross, J.J. (2005). The tie that binds? Coherence among emotional experience, behavior, and autonomic physiology. Emotion, 5, 175–190.CrossRefGoogle Scholar
McAssey, M., Hsieh, F., Ferrer, E. (2010). Optimal and robust design for efficient system-wide synchronization in networks of randomly-wired neuron-nodes. Statistics and Its Interface, 3, 159–168.Google Scholar
Milgram, S. (1967). The small world problem. Psychology Today, 2, 60–67.Google Scholar
Molenaar, P.C.M. (2004). A manifesto on psychology as idiographic science: bringing the person back into scientific psychology—this time forever. Measurement, 2, 201–218.Google Scholar
Nesselroade, J.R., Molenaar, P.C.M. (1999). Pooling lagged covariance structures based on short, multivariate time-series for dynamic factor analysis. In Hoyle, R.H. (Eds.), Statistical strategies for small sample research (pp. 224–251). Newbury Park: Sage.Google Scholar
Pikovsky, A., Rosenblum, M., Kurths, J. (2001). Synchronization: a universal concept in nonlinear sciences, Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Priestley, M.B. (1988). Nonlinear and non-stationary time series, New York: Academic Press.Google Scholar
Quian Quiroga, R., Kraskov, A., Kreuz, T., Grassberger, P. (2002). Performance of different synchronization measures in real data: a case study on electroencephalographic signals. Physical Review E, 65.CrossRefGoogle Scholar
Rohatgi, V.K. (1984). Statistical inference, Mineola: Dover Publications.Google Scholar
Rosenberg, E.L., Ekman, P. (1994). Coherence between expressive and experiential systems in emotion. Cognition & Emotion, 8, 201–229.CrossRefGoogle Scholar
Rottenberg, J., Ray, R.R., Gross, J.J. (2007). Emotion elicitation using films. In Coan, J.A., Allen, J.J.B. (Eds.), The handbook of emotion elicitation and assessment (pp. 9–28). New York: Oxford University Press.CrossRefGoogle Scholar
Scherer, K.R. (1984). On the nature and function of emotion: a component process approach. In Scherer, K.R., Ekman, P. (Eds.), Approaches to emotion (pp. 293–317). Hillsdale: Erlbaum.Google Scholar
Schneidman, E., Still, S., Berry, M.J., Bialek, W. (2003). Network information and connected correlations. Physical Review Letters, 91.CrossRefGoogle ScholarPubMed
Swets, J.A. (1996). Signal detection theory and ROC analysis in psychology and diagnostics: collected papers, Mahwah: Erlbaum.Google Scholar
Tomkins, S.S. (1962). Affect, imagery, consciousness: I. The positive affects, Oxford: Springer.Google Scholar
Tsonis, P.A., Tsonis, A.A. (2004). A “small-world” network hypothesis for memory and dreams. Perspectives in Biology and Medicine, 47, 176–180.CrossRefGoogle Scholar
van der Maas, H.L.J., Dolan, C.V., Grasman, R.P.P., Wicherts, J.M., Huizenga, H.M., Raijmakers, M.E.J. (2006). A dynamical model of general intelligence: the positive manifold of intelligence by mutualism. Psychological Review, 113, 842–861.CrossRefGoogle ScholarPubMed
Watts, D.J., Strogatz, S.H. (1998). Collective dynamics of ‘small-world’ networks. Nature, 393, 440–442.CrossRefGoogle ScholarPubMed
Watts, D.J. (1999). Small worlds: the dynamics of networks between order and randomness, Princeton: Princeton University Press.CrossRefGoogle Scholar