Robust Optimum Designs for Transformation of the Responses in a Multivariate Chemical Kinetic Model

Abstract

Transformation of both sides of a nonlinear model is often necessary to obtain tractable error distributions, but can have a dramatic effect on optimum designs for the parameters of the model. This article develops methods for the design of experiments when the value of the power transformation parameter is not precisely known. Optimum designs for particular transformations, together with the efficiency of these designs as the transformation varies, are studied for a multivariate model. It is shown that by a suitable choice of prior, Bayesian designs can be found that are robust to the correct transformation. A typical equispaced design is evaluated and the properties of designs are studied under various departures from the assumptions.

KEY WORDS :

• Bayesian D-optimality
• Box–Cox transformation
• Chemical kinetics
• D-optimum design
• Nonlinear model
• Parameter sensitivities
• Robust designs
• Transform both sides