Assessing non-linear estimation procedures for human growth models

In the last 20 years several non-linear models with a relatively small number of parameters have provided useful descriptions of the complete human growth curve. However, some aspects of the estimation procedures used have not been properly studied, e.g. estimation of biases, measures of non-linearity, and the possibility of autocorrelated errors and heteroscedasticity.

To present a detailed analysis of these aspects for five well-known non-linear models (Preece-Baines, Shohoji-Sasaki and three models proposed by Jolicoeur et al.) and a large data set (the MRC Edinburgh Longitudinal Study).

A cohort of 74 females and 103 males collected for the Edinburgh Longitudinal Study for the MRC Human Genetics Unit, Edinburgh, UK, comprising approximately quarterly height measurements for small ages and semestral height measurements for the remaining ages up to the early twenties.

We found little evidence of extreme curvature and relatively small, cyclical patterns in the residuals. The estimates obtained with ordinary non-linear least squares were very close to those obtained with more complicated estimation procedures.

The five models studied are reasonably robust against most of the problems encountered when fitting non-linear models to human growth data; this confirms some conjectures which have been taken for granted by a large number of authors. The presence of cyclical patterns is a consequence of the global description of growth attempted by these five models.