David A. Vaccari
Empirical, Modeling, Multivariate, Polynomial
A novel approach is described for empirically modeling multivariate response surfaces, either time-series or non-time series. The approach uses multivariate polynomial regression (MPR) with a step-wise algorithm to select terms. The approach includes advantages of multilinear regression such as simplicity and transparency. It also has the advantages of more complex modeling approaches such as artificial neural networks (ANNs) it its ability to model complex response surfaces, including high degree curvilinear interactions. Furthermore, MPR has advantages over ANNs in its transparency, tractability, parsimony and resistance to overfitting. These advantages are illustrated by an example and a freely-available online tool for fitting these models is described. Despite similarities to Response Surface Methodology (RSM), the models produced by this method tend to be different. An example response surface analysis is used to illustrate these characteristics.
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