Efficiencies for optimum designs when transforming the response in nonlinear models with nonconstant variance |
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Authors: | Anthony C Atkinson |
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Institution: | (1) Department of Statistics, London School of Economics, London, WC2A 2AE, UK |
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Abstract: | Often the responses from mechanistic models have to be transformed to achieve error distributions that are symmetric and have
constant variance. Because of the nature of the relationship between the response and the mechanistic model, it is necessary
to transform both sides of the model. Expressions are given for the parameter sensitivities in the transformed model and examples
given of optimum designs for particular values of λ, together with the efficiency of these designs as λ varies. Approaches
to finding designs robust to variations in λ are indicated and exemplified. |
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Keywords: | Design efficiency Box-Cox transformation Chemical kinetics D-optimum design Mechanistic model Parameter sensitivities Robust designs Transform both sides |
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