Journal of Nonlinear Dynamics
Volume 2014 (2014), Article ID 901838, 16 pages
http://dx.doi.org/10.1155/2014/901838
Research Article

Dynamics from Multivariable Longitudinal Data

School of Computational and Applied Mathematics, University of the Witwatersrand (Wits), Private Bag 3, Johannesburg 2050, South Africa

Received 15 July 2013; Revised 12 December 2013; Accepted 15 December 2013; Published 19 March 2014

Academic Editor: Mitsuhiro Ohta

Copyright © 2014 Maria Vivien Visaya and David Sherwell. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. E. S. Fung, W. K. Ching, S. Chu, M. K. Ng, and W. Zang, “Multivariate Markov chain models,” in Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, vol. 3, pp. 298–302, Hammamet, Tunisia, October 2002. View at Scopus
  2. C. Bijleveld, L. J. T. van der Kamp, A. Mooijaart, W. van der Kloot, R. van der Leeden, and E. van der Burg, Longitudinal Data Analysis: Designs, Models and Methods, Sage, Thousand Oaks, Calif, USA, 1998.
  3. H. Verbeke, S. Fiews, G. Molenberhghs, and M. Davidian, “The analysis of multivariate longitudinal data: a review,” Statistical Methods in Medical Research, 2012. View at Publisher · View at Google Scholar
  4. I. Vlachos and D. Kugiumtzis, “State space reconstruction for multivariate time series prediction,” Nonlinear Phenomena in Complex Systems, vol. 11, no. 2, pp. 241–249, 2008. View at Google Scholar
  5. J. Al-Aziz, N. Christou, and I. D. Dinov, “SOCR motion charts: an efficient, open-source, interactive and dynamic applet for visualizing longitudinal multivariate data,” Journal of Statistics Education, vol. 18, no. 3, pp. 1–29, 2010. View at Google Scholar · View at Scopus
  6. A. Grossenbacher, “The globalisation of statistical content,” Statistical Journal of the IAOS, vol. 25, no. 3-4, pp. 133–144, 2008. View at Google Scholar · View at Scopus
  7. A. Inselberg, Parallel Coordinates: Visual Multidimensional Geometry and Its Applications, Springer, New York, NY, USA, 2009.
  8. H. Zhou, X. Yuan, H. Qu, W. Cui, and B. Chen, “Visual clustering in parallel coordinates,” in Proceedings of the Eurographics/IEEE-VGTC Symposium on Visualization, A. Vilanova, A. Telea, G. Scheuermann, and T. Möller, Eds., vol. 27, 2008.
  9. V. Basios, G. Forti, and G. Nicolis, “Symbolic dynamics generated by a combination of graphs,” International Journal of Bifurcation and Chaos, vol. 18, no. 8, pp. 2265–2274, 2008. View at Publisher · View at Google Scholar · View at Scopus
  10. F. Durand, “Combinatorics on Bratteli diagrams and dynamical systems,” in Combinatorics, Automata and Number Theory, V. Berth and M. Rigo, Eds., pp. 324–372, 2010. View at Google Scholar
  11. L. Beckett and P. Diaconis, “Spectral analysis for discrete longitudinal data,” Advances in Mathematics, vol. 103, no. 1, pp. 107–128, 1994. View at Publisher · View at Google Scholar · View at Scopus
  12. A. Gottschau, “Markov chain models for multivariate binary panel data,” Scandinavian Journal of Statistics, vol. 21, no. 1, pp. 57–71, 1994. View at Google Scholar
  13. M. Mrozek, “Inheritable properties and computer assisted proofs in dynamics,” in Scientific Computing and Validated Numerics, G. Alefeld, A. Frommer, and B. Lang, Eds., vol. 90, pp. 245–257, Akademie, Berlin, Germany, 1996. View at Google Scholar
  14. H. Minc, Nonnegative Matrices, John Wiley & Sons, New York, NY, USA, 1998.
  15. C. Robinson, Dynamical Systems: Stability, Symbolic Dynamics and Chaos, CRC Press, New York, NY, USA, 2nd edition, 1999.
  16. B. Kitchens, Symbolic Dynamics: One-Sided, Two-Sided and Countable State Markov Chains, Springer, New York, NY, USA, 1998.
  17. D. Lind and B. Marcus, An Introduction to Symbolic Dynamics and Coding, Cambridge University Press, New York, NY, USA, 1995.
  18. R. Varga, Matrix Iterative Analysis, Prentice Hall, Englewood Cliffs, NJ, USA, 1962.
  19. P. Arnoux and A. M. Fisher, “Anosov families, renormalization and non-stationary subshifts,” Ergodic Theory and Dynamical Systems, vol. 25, no. 3, pp. 661–709, 2005. View at Publisher · View at Google Scholar · View at Scopus
  20. A. H. Fan and M. Pollicott, “Non-homogeneous equilibrium states and convergence speeds of averaging operators,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 129, no. 1, pp. 99–115, 2000. View at Google Scholar · View at Scopus
  21. A. M. Fisher, “Nonstationary mixing and the unique ergodicity of adic transformations,” Stochastics and Dynamics, vol. 9, no. 3, pp. 335–391, 2009. View at Publisher · View at Google Scholar · View at Scopus
  22. K. Kahn, S. M. Tollman, M. A. Collinson et al., “Research into health, population and social transitions in rural South Africa: data and methods of the Agincourt health and demographic surveillance system,” Scandinavian Journal of Public Health, vol. 35, supplement 69, pp. 8–20, 2007. View at Publisher · View at Google Scholar · View at Scopus