Optimal Design for the Bounded Log-Linear Regression Model

Abstract

Wang and Flournoy (2012) developed estimation procedures for the bounded log-linear regression model, an alternative to the four parameter logistic model which has a bounded response with non-homogeneous variance. In the present paper, we prove that an optimal design that minimizes an information-based criterion requires at most five design points including the two boundary points of the design space. The D-optimal design does not depend on the two parameters representing the boundaries of the response, but it does depend on the variance of the error. Furthermore, if the error variance is known and bigger than a certain constant, we prove that the D-optimal design is the two-point design supported at boundary points with equal weights. Numerical examples are provided.