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Exploring the Dynamics of Dyadic Interactions via Hierarchical Segmentation

Published online by Cambridge University Press:  01 January 2025

Fushing Hsieh ,
Emilio Ferrer ,
Shu-Chun Chen  and
Sy-Miin Chow
Fushing Hsieh
Affiliation:
University of California, Davis
Emilio Ferrer*
Affiliation:
University of California, Davis
Shu-Chun Chen
Affiliation:
University of California, Davis
Sy-Miin Chow
Affiliation:
University of North Carolina, Chapel Hill
*
Requests for reprints should be sent to Emilio Ferrer, Department of Psychology, University of California, One Shields Ave., Davis, CA 95616-8686, USA. E-mail: [email protected]
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Abstract

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In this article we present an exploratory tool for extracting systematic patterns from multivariate data. The technique, hierarchical segmentation (HS), can be used to group multivariate time series into segments with similar discrete-state recurrence patterns and it is not restricted by the stationarity assumption. We use a simulation study to describe the steps and properties of HS. We then use empirical data on daily affect from one couple to illustrate the use of HS for describing the affective dynamics of the dyad. First, we partition the data into three periods that represent different affective states and show different dynamics between both individuals’ affect. We then examine the synchrony between both individuals’ affective states and identify different patterns of coherence across the periods. Finally, we discuss the possibilities of using results from HS to construct confirmatory dynamic models with multiple change points or regime-specific dynamics.

Keywords

dynamic systemsmultivariate analysisexploratory data analysisdyadic interactions
Type
Original Paper
Information
Psychometrika , Volume 75 , Issue 2 , June 2010 , pp. 351 - 372
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NC
This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Copyright
Copyright © 2010 The Psychometric Society

Footnotes

R code for the HS algorithm is available upon request.

References

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.CrossRefGoogle Scholar
Bisconti, T.L., Bergeman, C.S., & Boker, S.M. (2004). Emotional well–being in recently bereaved widows: A dynamical systems approach. Journal of Gerontology: Psychological Sciences, 59 B158–167.CrossRefGoogle ScholarPubMed
Bobitt, R., Gourevitch, V., Miller, L., & Jensen, G. (1969). Dynamics of social interactive behavior: A computerized procedure for analyzing trends, patterns, and sequences. Psychological Bulletin, 71, 110–121.CrossRefGoogle Scholar
Boker, S.M., & Laurenceau, J.-P. (2006). Dynamical systems modeling: An application to the regulation of intimacy and disclosure in marriage. In Walls, T., & Schafer, J. (Eds.), Models for intensive longitudinal data (pp. 195–218). New York: Oxford University Press.CrossRefGoogle Scholar
Boker, S.M., & Rotondo, J. (2003). Symmetry building and symmetry breaking in synchronized movement. In Stamenov, M., & Gallese, V. (Eds.), Mirror neurons and the evolution of brain and language (pp. 163–171). Amsterdam: John Benjamins.Google 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(1), 338–355.CrossRefGoogle ScholarPubMed
Campbell, L., & Kashy, D. (2002). Estimating actor, partner, and interaction effects for dyadic data using proc mixed and hlm: A guided tour. Personal Relationships, 9, 327–342.CrossRefGoogle Scholar
Carlin, B., Gelfand, A., & Smith, A. (1992). Hierarchical Bayesian analysis of changepoints problems. Applied Statistics, 41, 389–405.CrossRefGoogle Scholar
Casdagli, M. (1997). Recurrence plots revisited. Physica D, 108, 12–44.CrossRefGoogle Scholar
Castellan, N. (1979). The analysis of behavior sequences. In Cairns, R. (Eds.), The analysis of social interactions: Methods, issues, and illustrations (pp. 81–116). Hillsdale: Lawrence Erlbaum Associates.Google Scholar
Chaitin, G. (1987). Algorithmic information theory, Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Chow, S.-M., Ferrer, E., & Nesselroade, J. (2007). An unscented Kalman filter approach to the estimation of nonlinear dynamical systems models. Multivariate Behavioral Research, 42, 283–321.CrossRefGoogle Scholar
Chow, S.-M., Hamaker, E.J., Fujita, F., & Boker, S.M. (2009). Representing time-varying cyclic dynamics using multiple-subject state-space models. British Journal of Mathematical and Statistical Psychology, 62, 683–716.CrossRefGoogle ScholarPubMed
Chow, S.-M., Ram, N., Boker, S.M., Fujita, F., & Clore, G. (2005). Emotion as thermostat: Representing emotion regulation using a damped oscillator model. Emotion, 5(2), 208–225.CrossRefGoogle ScholarPubMed
de Rooij, M., & Kroonenberg, P. (2003). Multivariate multinomial logit models for dyadic sequential interaction data. Multivariate Behavioral Research, 38, 463–504.CrossRefGoogle ScholarPubMed
Dolan, C., Schmittmann, V., Lubke, G., & Neale, M. (2005). Regime switching in the latent growth curve mixture model. Structural Equation Modeling, 12(1), 94–119.CrossRefGoogle Scholar
Eckmann, J.-P., Kamphorst, S., & Ruell, D. (1987). Recurrence plots of dynamical systems. Europhysics Letters, 5, 973–977.CrossRefGoogle Scholar
Ewens, J.W., & Grant, G.R. (2005). Statistical methods in bioinformatics, New York: Springer.CrossRefGoogle Scholar
Felmlee, D.H., & Greenberg, D.F. (1999). A dynamic systems model of dyadic interaction. Journal of Mathematical Sociology, 23(3), 155–180.CrossRefGoogle Scholar
Ferrer, E., Chen, S.-C., Chow, S.-M., & Hsieh, F. (2010). Exploring intra-individual, inter-individual and inter-variable dynamics in dyadic interactions. In Chow, S.M., Ferrer, E., & Hsieh, F. (Eds.), Statistical methods for modeling human dynamics: An interdisciplinary dialogue (pp. 381–411). New York: Taylor and Francis.Google Scholar
Ferrer, E., & Nesselroade, J.R. (2003). Modeling affective processes in dyadic relations via dynamic factor analysis. Emotion, 3(4), 344–360.CrossRefGoogle ScholarPubMed
Frühwirth-Schnatter, S. (2006). Finite mixture and Markov switching models, New York: Springer.Google Scholar
Gardner, W. (1993). Hierarchical continuous-time sequential analysis: A strategy for clinical research. Journal of Consulting and Clinical Psychology, 61, 975–983.CrossRefGoogle ScholarPubMed
Gardner, W., & Griffin, W. (1989). Methods for the analysis of parallel streams of continuously recorded social behaviors. Psychological Bulletin, 105, 446–455.CrossRefGoogle Scholar
Geman, S., Potter, D., & Chi, Z. (2002). Composition systems. Quarterly of Applied Mathematics, 60, 707–736.CrossRefGoogle Scholar
Goodman, L. (1970). The multivariate analysis of qualitative data: Interactions among multiple classifications. Journal of the American Statistical Associations, 65, 226–256.CrossRefGoogle Scholar
Gottman, J. (1979). Detecting cyclicity in social interaction. Psychological Bulletin, 86, 338–348.CrossRefGoogle Scholar
Gottman, J., Murray, J., Swanson, C., Tyson, R., & Swanson, K. (2002). The mathematics of marriage: Dynamic nonlinear models, Cambridge: MIT Press.CrossRefGoogle Scholar
Granic, I., & Hollenstein, T. (2003). Dynamic systems methods for models of developmental psychopathology. Development and Psychopathology, 15, 641–669.CrossRefGoogle ScholarPubMed
Hamilton, J. (1988). Rational-expectations econometric analysis of change in regime: An investigation of the term structure of interest rates. Journal of Economic Dynamics and Control, 12, 385–423.CrossRefGoogle Scholar
Hinkley, D.V. (1970). Inference about the changepoint in a sequence of random variables. Biometrika, 57, 1–17.CrossRefGoogle Scholar
Hinkley, D.V. (1971). Inference about the changepoint from cumulative sum tests. Biometrika, 58, 509–523.CrossRefGoogle Scholar
Hsieh, F., Hwang, C.-R., Lee, H.-C., Lan, Y.-C., & Horng, S.-B. (2006). Testing and mapping non-stationarity in animal behavioral processes: A case study on an individual female bean weevil. Journal of Theoretical Biology, 238(4), 805–816.Google Scholar
Kashy, D., & Kenny, D. (2000). The analysis of data from dyads and groups. In Reiss, H., & Judd, C. (Eds.), Handbook of research methods in social psychology (pp. 451–477). New York: Cambridge University Press.Google Scholar
Kim, C.-J., & Nelson, C.R. (1999). State-space models with regime switching: Classical and Gibbs-sampling approaches with applications, Cambridge: MIT Press.CrossRefGoogle Scholar
Kitagawa, G. (1981). A non-stationary time series model and its fitting by a recursive filter. Journal of Time Series Analysis, 2, 103–116.CrossRefGoogle Scholar
Lempel, A., & Ziv, J. (1976). On the complexity of finite sequences. IEEE Transactions on Information Theory, 22, 21–27.CrossRefGoogle Scholar
Levenson, R., & Gottman, J. (1983). Marital interactio: Physiological linkage and affective exchange. Journal of Personality and Social Psychology, 45(3), 587–597.CrossRefGoogle Scholar
Manuca, R., & Savit, D. (1996). Stationarity and nonstationarity in time series analysis. Physica D, 99, 134–161.CrossRefGoogle Scholar
Marwan, N., & Kurths, J. (2002). Nonlinear analysis of bivariate data with cross recurrence plots. Physics Letters A, 302, 299–307.CrossRefGoogle Scholar
Molenaar, P.C.M., & Newell, K.M. (2003). Direct fit of a theoretical model of phase transition in oscillatory finger motions. British Journal of Mathematical and Statistical Psychology, 56, 199–214.CrossRefGoogle ScholarPubMed
Newsom, J. (2002). A multilevel structural equation model for dyadic data. Structural Equation Modeling, 9, 431–447.CrossRefGoogle Scholar
Newtson, D. (1993). The dynamics of action and interaction. In Smith, L., & Thelen, E. (Eds.), A dynamic systems approach to development: Applications (pp. 241–264). Cambridge: MIT Press.CrossRefGoogle Scholar
Priestley, M. (1988). Nonlinear and non-stationary time series, New York: Academic Press.Google Scholar
Raudenbush, S., Brennan, R., & Barnett, R. (1995). A multivariate hierarchical model for studying psychological change within married couples. Journal of Family Psychology, 9, 161–174.CrossRefGoogle Scholar
Sackett, G. (1979). The lag sequential analysis of contingency and cyclicity in behavioral interaction research. In Osofsky, J. (Eds.), Handbook of infant development, New York: Wiley.Google Scholar
Shockley, K., Butwill, M., Zbilut, C., & Webber, C. (2002). Cross recurrence quantification of coupled oscillators. Physics Letters A, 305 1–259–69.CrossRefGoogle Scholar
Shumway, R., & Stoffer, D. (2006). Time series analysis and its applications: With R examples, New York: Springer.Google Scholar
Stephens, D. (1994). Bayesian retrospective multiple changepoint identification. Applied Statistics, 43, 159–178.CrossRefGoogle Scholar
Stoffer, D. (1991). Walsh–Fourier analysis and its statistical application. Journal of the American Statistical Association, 86, 461–479.CrossRefGoogle Scholar
Watson, D., Lee, A.C., & Tellegen, A. (1988). Development and validation of brief measures of positive and negative affect: The PANAS scale. Journal of Personality and Social Psychology, 54(6), 1063–1070.CrossRefGoogle Scholar
Watts, D., & Strogatz, S. (1998). Collective dynamics of ’small-world’ networks. Nature, 393, 440–442.CrossRefGoogle ScholarPubMed
Weber, E., Molenaar, P., & Van der Molen, M. (1992). A nonstationarity test for the spectral analysis of physiological time series with an application to respiratory sinus arrhythmia. Psychophysiology, 29(1), 55–65.CrossRefGoogle ScholarPubMed
West, B. (1985). An essay on the importance of being nonlinear, Berlin: Springer.CrossRefGoogle Scholar
Ziv, J., & Lempel, A. (1977). A universal algorithm for sequential data compression. IEEE Transactions on Information Theory, 23, 337–343.CrossRefGoogle Scholar