Improving D-Optimality in Nonlinear Situations

Abstract

Experimental designs based on the classical D-optimal criterion minimize the volume of the linear-approximation inference regions for the parameters using local sensitivity coefficients. For nonlinear models, these designs can be unreliable because the linearized inference regions do not always provide a true indication of the exact parameter inference regions. In this article, we apply the profile-based sensitivity coefficients developed by Sulieman et.al. [12] in designing D-optimal experiments for parameter estimation in some selected nonlinear models. Profile-based sensitivity coefficients are defined by the total derivative of the model function with respect to the parameters. They have been shown to account for both parameter co-dependencies and model nonlinearity up to second order-derivative. This work represents a first attempt to construct experiments using profile-based sensitivity coefficients. Two common nonlinear models are used to illustrate the computational aspects of the profile-based designs and simulation studies are conducted to demonstrate the efficiency of the constructed experiments.