Common Errors in Statistics (and How to Avoid Them), 4th Edition
by Phillip I. Good, James W. Hardin
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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