ABSTRACT
There are many examples of nonlinear models in the biological literature. An example is the Michaelis-Menten pharmacokinetics model which approaches a horizontal asymptote caused by saturation in the reaction. The corrections to the estimates at the previous iterations in the form of a linear equation with the residuals from the iteration on the left hand side and the partial derivatives of the nonlinear function with respect to the parameters as the independent variables. The field of nonlinear optimization is highly developed and there are many experts in this field. A sensible way for fitting nonlinear random effects models is to start by fitting the model with the random effects set to zero. The model is fit by maximum likelihood using a variance function which is the square of the estimated mean. The method of estimation is a modification of the method of Lindstrom and Bates. The nonlinear model is expanded with respect to the random effects only.
