Advertisement

Applicability of Dimension Analysis to Data in Psychology

  • Arno Steitz
  • Wolfgang Tschacher
  • Klaus Ackermann
  • Dirk Revenstorf
Part of the Springer Series in Synergetics book series (SSSYN, volume 58)

Abstract

This paper is motivated by the question of whether dimension analysis is a valid and practical method for the reduction of data in psychology. The paper presents a short introduction to the analysis of chaotic systems by the Grassberger-Procaccia algorithm. General aspects of this method are demonstrated; we tested the limits of dimension analysis depending on signal-to-noise ratio, length of time series, and resolution of measurement. For this purpose, the Hénon map was used as a basic model. The Grassberger-Procaccia algorithm was also applied to a simulated time series of group processes and an empirical time series of smoking behavior. To compensate for artefacts induced by local correlations a revised dimension analysis was performed with the group simulation data. Results suggest that neither group simulation nor cigarette consumption data can be reduced to a low-dimensional deterministic system.

Keywords

Time Series Chaotic System Smoking Behavior Dimension Analysis Correlation Dimension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. BABLOYANTZ, A. 1985. Strange Attractors in the Dynamics of Brain Actitivity. In H. Haken (Ed.): Complex Systems — Operational Approaches to Neurobiology, Physics, and Computers. Berlin: Springer, 116–122.Google Scholar
  2. GLASS, L., SHRIER, A., & BéLAIR, J. 1986. Chaotic Cardiac Rhythms. In A.V. Holden (Ed.). Chaos. Princeton: University Press, 237–256.Google Scholar
  3. GRAF, K.-E. & ELBERT, T. 1989. Dimensional Analysis of the Waking-EEG. In E. Başar & T.H. Bullock (Eds.). Brain Dynamics. Progress and Perspectives. Berlin: Springer, 174–191.Google Scholar
  4. GRASSBERGER, P., & PROCACCIA, I. 1983. Characterization of Strange Attractors. Physical Review Letters, 50, 346–349.MathSciNetADSCrossRefGoogle Scholar
  5. HENTSCHEL, H.G.E. & PROCACCIA, I. 1983. The Infinitiv Number of Generalized Dimensions of Fractals and Strange Attractors. Physica 8D, 435–444.MathSciNetADSGoogle Scholar
  6. LICHTENSTEIN, E. & BROWN, R.A. 1982. Current Trends in the Modification of Cigarette Dependence. New York: Plenum.Google Scholar
  7. MAYER-KRESS, G. 1987. Application of Dimension Algorithms to Experimental Data. In H. Bai-lin (Ed.). Directions in Chaos. Singapore: World Scientific.Google Scholar
  8. MORENO, J.L. 1953. Who Shall Survive? Foundations of Sociometry, Group Psychotherapy, and Sociodrama. New York: Beacon House.Google Scholar
  9. PACKARD, N.H, CRUTCHFIELD, J.P., FARMER, J.D., & SHAW, R.S. 1980. Geometry From a Time Series. Phys.Rev.Lett., 45, 712–716.ADSCrossRefGoogle Scholar
  10. SCHAFFER, W.M. & KOT, M. 1986. Differential Systems in Ecology and Epidemiology. In A.V. Holden (Ed.). Chaos. Princeton: University Press, 158–178.Google Scholar
  11. SCHWEITZER, J. & WEBER, G. 1983. Beziehung als Metapher. Die Familienskulptur als diagnostische, therapeutische und Ausbildungstechnik. Familiendynamik, 8, 113–128.Google Scholar
  12. SIMM, C.W., SAWLEY, M.L., SKIFF, F. & POCHELON, A. 1987. On the Analysis of Experimental Signals for Evidence of Deterministic Chaos. Helvetica Physica Acta, 60, 510–551.MathSciNetGoogle Scholar
  13. TAKENS, F. 1981. Detecting Strange Attractors in Turbulence. In D.A. Rand & L.S. Young (Eds.). Lecture Notes in Mathematics. New York: Springer.Google Scholar
  14. TSCHACHER, 1990. Interaktion in selbstorganisierten Systemen. Grundlegung eines dynamisch-synergetischen Forschungsprogramms in der Psychologie. Heidelberg: Asanger.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Arno Steitz
  • Wolfgang Tschacher
  • Klaus Ackermann
  • Dirk Revenstorf

There are no affiliations available

Personalised recommendations