Using a nonlinear mixed model to evaluate three models of human stature.

The modern mixed model approach is used to evaluate three current nonlinear models of development of human stature. By combining both fixed and random effects in the same model, the mixed approach incorporates variability between subjects in the estimation of the mean parameter values. This allows us to provide a single statistical test for the differences between each pair of statistical models. Asymptotic growth models from Preece and Baines (1978), Jolicoeur et al. (1988, 1991,1992), and Kanefuji and Shohoji (1990) were applied to height data collected from 28 males and 25 females. The NLINMIX Macro from SAS was used to evaluate the fit of each model allowing for two random components in addition to the fixed mean parameter values. In every case, the addition of random parameters improved the fit of each growth model. Models were evaluated by the calculation of the Akaike Information Criterion, differences in -2 log likelihood, and determination of the residual variance. For males, the Jolicoeur et al. model was superior, while for females, the Kanefuji and Shohoji model provided the best fit. This new approach is more parsimonious than previous techniques by allowing for individual variation in the estimation of model parameters in a population average model of growth.