Citation:
Trevor J. Ringrose & Shaun A. Forth, Simplifying multivariate second-order response surfaces by fitting constrained models using automatic differentiation. Technometrics, Volume 47, number 3, August 2005, pp249-259
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.