Conditional distributions arising from variation of parameters in non-linear response functions

Abstract

This paper proposed the idea that the growth of an individual organism follows a mathematical model very closely and that different individuals follow different members of the same parametric family of models. This idea implies that the variation observed between individuals measured at the same time arises not from an additive term as has been previously supposed, but primarily from variation of the parameters of the model. A graph of data from an experiment on chickens is included which points up this individuality and the increased variation resulting from the passage of time. The four models considered were growth curves employing two, three, and four parameters with biological interpretations existing for the parameters. The parameters were allowed to follow independent uniform distributions and independent gamma distributions.