Statistical Vector Field Analysis Applied to Mixed Cross-Sectional and Longitudinal Data

Abstract

Combined cross-sectional and longitudinal data often present complex patterns of change. Growth functions representing the change in some measure as a function of chronological age can be a function of initial values of the measurement. Individual differences in developmental age with respect to chronological age tend to distort attempts to fit a single growth curve through combined cross-sectional and longitudinal data. We present a method by which these data can be visualized along with several examples from a data set comprising measurements of intellectual abilities with respect to aging. We call this new method a statistical vector field (svf) plot. An svf plot simultaneously allows the visualization of cross-sectional information summarizing sampling densities and longitudinal information summarizing how individuals at each particular age and ability are likely to change over time. The C source code for the svf software described in this paper may be obtained free from the University of Virginia anonymous ftp archive server (ftp. Virginia.EDU), or from the authors.