Nonlinear Models and Regression

Abstract

A model is nonlinear if any of the partial derivatives with respect to any of the model parameters are dependent on any other model parameter or if any of the derivatives do not exist or are discontinuous. This chapter expands on the previous chapter and introduces nonlinear regression within a least squares (NLS) and maximum likelihood framework. The concepts of minima, both local and global, and the gradient and Hessian are introduced and provide a basis for NLS algorithm selection. Ill-conditioning and its role in model instability are prominently discussed, as are influence diagnostics for the nonlinear problem and how to use prior information to obtain better model parameter estimates.