NONSENSE REGRESSION
Nonlinear regression methods are appropriate when the form of the nonlinear model is known in advance. For example, a typical pharmacological model will have the form A exp[bX] + C exp[dW]. The presence of numerous locally optimal but globally suboptimal solutions creates challenges, and validation is essential. See, for example, Gallant [1987] and Carroll et al. [1995].
To be avoided are a recent spate of proprietary algorithms available solely in software form that guarantee to find a best-fitting solution. In the words of John von Neumann, “With four parameters I can fit an elephant and with five I can make him wiggle his trunk.” Goodness of fit is no guarantee of predictive success, a topic we take up repeatedly in subsequent chapters.
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