Nonlinear Regression Models

Abstract

Nonlinear models arise when E[y] is a nonlinear function of unknown parameters. Hypotheses about these parameters may be linear or nonlinear. Such models tend to be used when they are suggested by theoretical considerations or used to build non-linear behavior into a model. Even when a linear approximation works well, a nonlinear model may still be used to retain a clear interpretation of the parameters. Once we have established a nonlinear relationship the next problem is how to incorporate the “error” term $\varepsilon$. Sometimes a nonlinear relationship can be transformed into a linear one but in doing so we may end up with an error term that has awkward properties. In this case it is usually better to work with the non-linear model. These kinds of problems are demonstrated by several examples.