A critical analysis of the double and triple logistic growth curves

Recently a model of human growth from the age of one year to maturity, based on two logistic terms, has been proposed. The originators of the model claim that it provides biologically meaningful parameters, and allows total growth to be partitioned into a pre-pubertal and an adolescent component. More recently, they have suggested an improved model, with three logistic terms, which gives a better fit. While the double logistic model gives an adequate fit to the observed height curve, differentiating it leads to a height velocity curve which differs considerably from the observed velocity curve. The triple logistic model gives an excellent fit to both the attained height and height velocity curves. Both models, however, imply a considerable time interval during which both the pre-pubertal and adolescent components are simultaneously contributing to growth, a situation that is difficult to justify biologically. The double model should therefore be discarded, and the triple logistic model considered to be of descriptive, rather than of interpretative, value.