Table of Contents
Journal of Nonlinear Dynamics
Volume 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.

Abstract

We introduce a method of analysing longitudinal data in variables and a population of observations. Longitudinal data of each observation is exactly coded to an orbit in a two-dimensional state space . At each time, information of each observation is coded to a point , where is the physical condition of the observation and is an ordering of variables. Orbit of each observation in is described by a map that dynamically rearranges order of variables at each time step, eventually placing the most stable, least frequently changing variable to the left and the most frequently changing variable to the right. By this operation, we are able to extract dynamics from data and visualise the orbit of each observation. In addition, clustering of data in the stable variables is revealed. All possible paths that any observation can take in are given by a subshift of finite type (SFT). We discuss mathematical properties of the transition matrix associated to this SFT. Dynamics of the population is a nonautonomous multivalued map equivalent to a nonstationary SFT. We illustrate the method using a longitudinal data of a population of households from Agincourt, South Africa.