Deterministic dynamics in questionnares in the social sciences

Abstract

In this thesis a novel mathematical technique for the analysis of longitudinal surveys in the social sciences is given. This analysis maps the longitudinal data of a fixed number n of demographic variables of a single social unit into an orbit of a single point in the unit square. The x, y−axes denote fitness, and, significance of social variables. A finite set of 2n×n! states in the unit square is thereby defined. Data from the rural Agincourt Health and Demographic Surveillance Site survey is analysed. The data set consists of the following demographic variables: biological mother outmigration, household head is a minor and adult death. For a sample of 2669 households we record orbits for the period 1998 to 2007. Social variables relate to educational progression. The flow of household orbits is found to describe temporary in- and out-migration of biological mothers of children. The densities of the flows show that educational default is associated with out-migration. The method predicts an increase of 52 defaulting households per year for the period 2007 to 2015. This result is facilitated by visualization of orbits and by identification of appropriate dynamical models, directly from the longitudinal data. It is hoped that visualization of household fitness can better influence policy makers.