Optimal design for additive partially nonlinear models
Loading...
Date
2010-04-12T08:44:28Z
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
We develop optimal design theory for additive partially nonlinear regression models, and show that D-optimal designs can be found as the products of the corresponding D-optimal designs in one dimension. For partially nonlinear models, D-optimal designs depend on the unknown nonlinear model parameters, and misspecifications of these parameters can lead to poor designs. Hence we generalise our results to parameter robust optimality criteria, namely Bayesian and standardised maximin D-optimality. A sufficient condition under which analogous results hold for Ds-optimality is derived to accommodate situations in which only a subset of the model parameters is of interest. To facilitate prediction of the response at unobserved locations, we prove similar results for Q-optimality in the class of all
product designs. The usefulness of this approach is demonstrated through an application from the automotive industry where optimal designs for least squares regression splines are determined and compared with designs commonly used in practice.
Description
Table of contents
Keywords
Additive model, Bayesian D-optimality, Partially nonlinear model, Product design, Q-optimality, Standardised maximin D-optimality