Simplifying multivariate second-order response surfaces by fitting constrained models using automatic differentiation
Trevor J. Ringrose & Shaun A. Forth
TECHNOMETRICS 47 (3): 249-259 AUG 2005,
ISSN:
0040-1706
Abstract:
Multivariate regression models for second-order polynomial response
surfaces are proposed. The fitted surfaces for each response variable are
constrained so that when expressed in their canonical forms they have features
in common, such as common stationary points or common sets of eigenvectors.
This can greatly reduce the number of parameters required and make the set of
surfaces easier to interpret together, at the cost of a greater computational
burden. However, the use of automatic differentiation within the package Matlab
is shown to be easy and to reduce this burden considerably. We describe the
models and how to fit them and derive standard errors, and report a small
simulation study and an application to a dataset.