We propose an asymptotic mathematical growth model for 386 Japanese longitudinal measurements of height from birth to adulthood, This model is compared with JPA2 proposed by Jolicoeur, Pontier and Abidi (1992). We discuss some relationships between various biological parameters (including mid-childhood growth spurt).
There is no linear relationship between age at one biological phenomenon P-1 and height at another biological phenomenon P-2. When we statistically control a contrapair of the biological parameters (i. e., height at P-1 and age at P-2), there exists a strong relationship between those biological parameters for Japanese boys and girls. For example, the correlation coefficient between adult height and age at peak height velocity is almost zero for boys and girls. However, their partial correlation coefficients are, respectively, 0.524 and 0.579 for boys and girls when height at peak height velocity is controlled. The younger the age at peak height velocity, the taller the adult height when height at peak height velocity is fixed. This is shown by the scatter diagrams with 80% confidence ellipsoids by height groups at peak height velocity. A similar relationship holds for adult height and menarcheal age. The mean-constant growth curves classified by height group at MHV and by height group at the age of six are presented. The taller the height at the age of six, the taller are the height at each age and adult height on average. The relative amount of expected information being an extension to Fisher's instinct information relates to the influence of each parameter in the growth model (Ledford and Cole, 1998). This information may be very useful as a guideline for collecting longitudinal records for non-linear phenomena. Copyright (C) 2001 John Wiley & Sons, Ltd.