Designing for a Response Transformation Parameter |
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Authors: | Anthony C. Atkinson,& R. Dennis Cook |
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Affiliation: | London School of Economics and Political Science, UK,;University of Minnesota, St Paul, USA |
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Abstract: | 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. |
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Keywords: | Box—Cox power transformations D-optimum designs D S -optimum designs heteroscedasticity linear models |
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