Response surface models: To reduce or not to reduce?

Abstract In classical response surface methodology, the optimization step uses a small number of important factors. However, in practice, experimenters sometimes fit a second-order model without previous experimentation. In this case, the true model is uncertain and the full model may overfit. Here, we use an extensive simulation to evaluate several analysis strategies in terms of their optimum locating ability, and use both simulation and published experiments to evaluate their general prediction facility. We consider traditional (reducing via p-values; forward selection), regularization (LASSO; Gauss-LASSO), and Bayesian analysis methods.

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