Designing for a Response Transformation Parameter

We investigate D -optimum designs for experiments in which a linear model holds after an unknown power transformation of the univariate response variable. This is a departure from standard D -optimal design in which an appropriate scale for the response is assumed known before data collection. The design problem that we formulate is intrinsically non-linear, requiring characterization of likely parameter values. Several applications are presented to illustrate the importance of recognizing the role of response transformations at the design stage.