Shape-invariant modelling of human growth.

A new approach to modelling human height growth is presented which is also suitable for other variables. In a mathematical algorithm, some guess about the functional form of this growth process is improved consistently using the data; the resulting shape-invariant model (SIM) allows an approximately bias-free fitting for longitudinal data from 1 to 20 years with six parameters assigned to each individual. The SIM approach and the use of velocities rather than distances proved to be suitable for biomathematical modelling in order to answer questions qualitative in nature. In comparison of an additive two-component SIM and one where the appearance of puberty inhibits further growth of the non-pubertal component ('switch-off model'), the latter proved to be superior in various aspects. Among the qualitative features found are notable: a pronounced midspurt, and a dip before the onset of puberty, as well as the asymmetry of the pubertal peak. A preliminary analysis of individual parameters confirmed some results found previously by other methods regarding sex differences and relations between parameters and with adult height.