11 Response surface designs

Publisher Summary This chapter focuses on response surface designs. When the mechanism that produced the data is either unknown or poorly understood, so that the mathematical form of the true response surface is unknown, an empirical model is often fitted to the data. An empirical model is usually linear in the parameters and often of polynomial form, either in the basic predictor variables or in transformed entities constructed from these basic predictors. The purpose of fitting empirical models is to provide a mathematical French curve that summarizes the data. The chapter discusses the design of experiments for such empirical models. There is another useful type of model, however, the mechanistic model. If knowledge of the underlying mechanism that produced the data is available, it is sometimes possible to construct a model that represents the mechanism reasonably well. An empirical model usually contains fewer parameters, fits the data better, and extrapolates more sensibly. However, mechanistic models are often nonlinear in the parameters, and more difficult to formulate, to fit, and to evaluate.

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