Implementation of Hills' growth curve analysis for unequal-time intervals using GAUSS

Longitudinal data are widely regarded as the most efficient and informative type of data with which to investigate growth. Paradoxically, appropriate statistical methods for analyzing longitudinal data have been unavailable; with the exception of a computer program for executing Rao's (Biometrika 46:49-58, 1959) one-sample polynomial growth curve analysis (Schneiderman and Kowalski, Am. J. Phys. Anthropol. 67:323-333, 1985) and another applying the Preece-Baines function (Brown and Townsend, Ann. Hum. Biol. 9:495-505, 1982), no programs for analyzing longitudinal data are generally available to the scientific community. Whereas much of the pediatrically oriented work has involved fitting growth curves for individual children, the concern here is the estimation of growth trends for populations. An Adequate understanding of average tendencies is a prerequisite to understanding the growth of individuals. The present paper implements Hills' (Biometrics 24:189-196, 1968) analysis, which is formally equivalent to Rao's but uses finite differences instead of orthogonal polynomials. This method is suitable for data collected at unequal time points and generates explicit measures of velocity and acceleration. The polynomial specification of the curve that best fits the data is also determined with this method. An additional advantage of this approach is that it is conceptually simpler than the classic model of Rao. An application of this method is given using the same craniofacial growth data as in our earlier (1985) paper for comparability. We provide an easy to use program written in GAU's (Edlefson and Jones, Kent, WA; Applied Technical Systems, 1985), a matrix programming language that runs on PC-compatible microcomputers. This implementation for PCs extends the accessibility to investigators who may not have access to mainframe computers.