Dynamics from Multivariable Longitudinal Data. (19th March 2014) - Visaya, Maria Vivien
Abstract : We introduce a method of analysing longitudinal data inn ≥ 1 variables and a population ofK ≥ 1 observations. Longitudinal data of each observation is exactly coded to an orbit in a two-dimensional state spaceS n . At each time, information of each observation is coded to a point( x, y ) ∈ S n, wherex is the physical condition of the observation andy is an ordering of variables. Orbit of each observation inS n 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 inS n 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.