Estimation of growth velocities from individual longitudinal data.

Since the construction of growth velocity curves using the simple increment method (i.e., plotting the increments deltaxt vs, time, t) involves a number of methodological problems, when mathematical curves are fit, they are generally fit to the "distance traveled", plot (of xt vs. t) and the corresponding velocity curve is then obtained by differentiation. However, most of the traditional methods for accomplishing this (e.g., fitting the Gompertz or logistic curves) require that the course of growth be studied over a sufficiently long time period to allow accurate determinations of the upper and lower asymptotes of these S-shaped functions. This is not always feasible in practice: a case in point being the mixed-longitudinal Nijmegen Growth Study where each of the cohorts comprising the sample is followed for but a five-year period. In such situations, alternative approaches to the problem of constructing growth velocity curves may be of considerable practical as well as theoretical interest. One such approach is developed in this paper and its use is illustrated on some data collected as part of the Nijmegen Growth Study. These results are then compared with those obtained using the increment method on the same data.