Simplifying multivariate second-order response surfaces by fitting constrainedmodels using automatic differentiation.

摘要

Multivariate regression models for second-order polynomial response surfaces areproposed. The fitted surfaces for each response variable are constrained so thatwhen expressed in their canonical forms they have features in common, such ascommon stationary points or common sets of eigenvectors. This can greatly reducethe number of parameters required and make the set of surfaces easier tointerpret together, at the cost of a greater computational burden. However, theuse of automatic differentiation within the package Matlab is shown to be easyand to reduce this burden considerably. We describe the models and how to fitthem and derive standard errors, and report a small simulation study and anapplication to a dataset.