Parametric models of height-at-a-given-age (HGA) and weight-at-a-given-age (WGA) are useful for smoothing observed HGA and WGA distributions, for assessing the growth performance of individuals at given ages, and for determining the underlying parameters of observed HGA and WGA distributions that are truncated by either (1) the nature of the collection procedure (e.g., minimum height standards in the military) or (2) the design of researchers who wish to purge their samples of suspicious outliers. Constructing such models is not entirely straightforward, though, because the shapes of HGA and WGA distributions vary by age. One solution to this problem is to transform the observed data so that they conform to a normal distribution. An extremely flexible class of transformations, which in the present context achieves this result quite satisfactorily, was proposed by Box and Cox : Yi = [(Xi — a)13 — l]/β where a and β are parameters of the transformation, the Xi are the original height or weight observations, and the Yj are the transformed observations. This class of transformations includes the linear (β =1) and the logarithmic (β = 0). For illustrative purposes, this model was fit to data on the heights and weights of girls in a well-known U.S. growth study; chi square tests of goodness of fit were conducted and uniformly indicated a good fit of the model to the data. In addition, the model provided a good fit to truncated data on the heights of British military recruits demonstrating the usefulness of originally constructing the model to fit doubly-truncated distributions.
Trussell, James and Bloom, David E.
"A Model Distribution of Height or Weight at a Given Age,"
4, Article 8.
Available at: https://digitalcommons.wayne.edu/humbiol/vol51/iss4/8