Advertisement

Psychometrika

, Volume 75, Issue 2, pp 351–372 | Cite as

Exploring the Dynamics of Dyadic Interactions via Hierarchical Segmentation

  • Fushing Hsieh
  • Emilio FerrerEmail author
  • Shu-Chun Chen
  • Sy-Miin Chow
Open Access
Article

Abstract

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 systems multivariate analysis exploratory data analysis dyadic interactions 

References

  1. 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. CrossRefGoogle Scholar
  2. 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(B), 158–167. Google Scholar
  3. 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
  4. 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. Google Scholar
  5. Boker, S.M., & Rotondo, J. (2003). Symmetry building and symmetry breaking in synchronized movement. In M. Stamenov, & V. Gallese (Eds.), Mirror neurons and the evolution of brain and language (pp. 163–171). Amsterdam: John Benjamins. Google Scholar
  6. 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. CrossRefPubMedGoogle Scholar
  7. 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
  8. Carlin, B., Gelfand, A., & Smith, A. (1992). Hierarchical Bayesian analysis of changepoints problems. Applied Statistics, 41, 389–405. CrossRefGoogle Scholar
  9. Casdagli, M. (1997). Recurrence plots revisited. Physica D, 108, 12–44. CrossRefGoogle Scholar
  10. Castellan, N. (1979). The analysis of behavior sequences. In R. Cairns (Ed.), The analysis of social interactions: Methods, issues, and illustrations (pp. 81–116). Hillsdale: Lawrence Erlbaum Associates. Google Scholar
  11. Chaitin, G. (1987). Algorithmic information theory. Cambridge: Cambridge University Press. CrossRefGoogle Scholar
  12. 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. Google Scholar
  13. 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. CrossRefPubMedGoogle Scholar
  14. 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. CrossRefPubMedGoogle Scholar
  15. de Rooij, M., & Kroonenberg, P. (2003). Multivariate multinomial logit models for dyadic sequential interaction data. Multivariate Behavioral Research, 38, 463–504. CrossRefGoogle Scholar
  16. 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
  17. Eckmann, J.-P., Kamphorst, S., & Ruell, D. (1987). Recurrence plots of dynamical systems. Europhysics Letters, 5, 973–977. CrossRefGoogle Scholar
  18. Ewens, J.W., & Grant, G.R. (2005). Statistical methods in bioinformatics. New York: Springer. CrossRefGoogle Scholar
  19. Felmlee, D.H., & Greenberg, D.F. (1999). A dynamic systems model of dyadic interaction. Journal of Mathematical Sociology, 23(3), 155–180. Google Scholar
  20. Ferrer, E., Chen, S.-C., Chow, S.-M., & Hsieh, F. (2010). Exploring intra-individual, inter-individual and inter-variable dynamics in dyadic interactions. In S.M. Chow, E. Ferrer, & F. Hsieh (Eds.), Statistical methods for modeling human dynamics: An interdisciplinary dialogue (pp. 381–411). New York: Taylor and Francis. Google Scholar
  21. Ferrer, E., & Nesselroade, J.R. (2003). Modeling affective processes in dyadic relations via dynamic factor analysis. Emotion, 3(4), 344–360. CrossRefPubMedGoogle Scholar
  22. Frühwirth-Schnatter, S. (2006). Finite mixture and Markov switching models. New York: Springer. Google Scholar
  23. Gardner, W. (1993). Hierarchical continuous-time sequential analysis: A strategy for clinical research. Journal of Consulting and Clinical Psychology, 61, 975–983. CrossRefPubMedGoogle Scholar
  24. Gardner, W., & Griffin, W. (1989). Methods for the analysis of parallel streams of continuously recorded social behaviors. Psychological Bulletin, 105, 446–455. CrossRefGoogle Scholar
  25. Geman, S., Potter, D., & Chi, Z. (2002). Composition systems. Quarterly of Applied Mathematics, 60, 707–736. Google Scholar
  26. Goodman, L. (1970). The multivariate analysis of qualitative data: Interactions among multiple classifications. Journal of the American Statistical Associations, 65, 226–256. CrossRefGoogle Scholar
  27. Gottman, J. (1979). Detecting cyclicity in social interaction. Psychological Bulletin, 86, 338–348. CrossRefGoogle Scholar
  28. Gottman, J., Murray, J., Swanson, C., Tyson, R., & Swanson, K. (2002). The mathematics of marriage: Dynamic nonlinear models. Cambridge: MIT Press. Google Scholar
  29. Granic, I., & Hollenstein, T. (2003). Dynamic systems methods for models of developmental psychopathology. Development and Psychopathology, 15, 641–669. CrossRefPubMedGoogle Scholar
  30. 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
  31. Hinkley, D.V. (1970). Inference about the changepoint in a sequence of random variables. Biometrika, 57, 1–17. CrossRefGoogle Scholar
  32. Hinkley, D.V. (1971). Inference about the changepoint from cumulative sum tests. Biometrika, 58, 509–523. CrossRefGoogle Scholar
  33. 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. CrossRefGoogle Scholar
  34. Kashy, D., & Kenny, D. (2000). The analysis of data from dyads and groups. In H. Reiss, & C. Judd (Eds.), Handbook of research methods in social psychology (pp. 451–477). New York: Cambridge University Press. Google Scholar
  35. Kim, C.-J., & Nelson, C.R. (1999). State-space models with regime switching: Classical and Gibbs-sampling approaches with applications. Cambridge: MIT Press. Google Scholar
  36. 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
  37. Lempel, A., & Ziv, J. (1976). On the complexity of finite sequences. IEEE Transactions on Information Theory, 22, 21–27. CrossRefGoogle Scholar
  38. Levenson, R., & Gottman, J. (1983). Marital interactio: Physiological linkage and affective exchange. Journal of Personality and Social Psychology, 45(3), 587–597. CrossRefPubMedGoogle Scholar
  39. Manuca, R., & Savit, D. (1996). Stationarity and nonstationarity in time series analysis. Physica D, 99, 134–161. CrossRefGoogle Scholar
  40. Marwan, N., & Kurths, J. (2002). Nonlinear analysis of bivariate data with cross recurrence plots. Physics Letters A, 302, 299–307. CrossRefGoogle Scholar
  41. 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. CrossRefPubMedGoogle Scholar
  42. Newsom, J. (2002). A multilevel structural equation model for dyadic data. Structural Equation Modeling, 9, 431–447. CrossRefGoogle Scholar
  43. Newtson, D. (1993). The dynamics of action and interaction. In L. Smith, & E. Thelen (Eds.), A dynamic systems approach to development: Applications (pp. 241–264). Cambridge: MIT Press. Google Scholar
  44. Priestley, M. (1988). Nonlinear and non-stationary time series. New York: Academic Press. Google Scholar
  45. 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
  46. Sackett, G. (1979). The lag sequential analysis of contingency and cyclicity in behavioral interaction research. In J. Osofsky (Ed.), Handbook of infant development. New York: Wiley. Google Scholar
  47. Shockley, K., Butwill, M., Zbilut, C., & Webber, C. (2002). Cross recurrence quantification of coupled oscillators. Physics Letters A, 305(1–2), 59–69. CrossRefGoogle Scholar
  48. Shumway, R., & Stoffer, D. (2006). Time series analysis and its applications: With R examples. New York: Springer. Google Scholar
  49. Stephens, D. (1994). Bayesian retrospective multiple changepoint identification. Applied Statistics, 43, 159–178. CrossRefGoogle Scholar
  50. Stoffer, D. (1991). Walsh–Fourier analysis and its statistical application. Journal of the American Statistical Association, 86, 461–479. CrossRefGoogle Scholar
  51. 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. CrossRefPubMedGoogle Scholar
  52. Watts, D., & Strogatz, S. (1998). Collective dynamics of ’small-world’ networks. Nature, 393, 440–442. CrossRefPubMedGoogle Scholar
  53. 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. CrossRefPubMedGoogle Scholar
  54. West, B. (1985). An essay on the importance of being nonlinear. Berlin: Springer. Google Scholar
  55. Ziv, J., & Lempel, A. (1977). A universal algorithm for sequential data compression. IEEE Transactions on Information Theory, 23, 337–343. CrossRefGoogle Scholar

Copyright information

© The Psychometric Society 2010

Authors and Affiliations

  • Fushing Hsieh
    • 1
  • Emilio Ferrer
    • 2
    Email author
  • Shu-Chun Chen
    • 1
  • Sy-Miin Chow
    • 3
  1. 1.Department of StatisticsUniversity of CaliforniaDavisUSA
  2. 2.Department of PsychologyUniversity of CaliforniaDavisUSA
  3. 3.Department of PsychologyUniversity of North CarolinaChapel HillUSA

Personalised recommendations