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Horwitz's rule, transforming both sides and the design of experiments for mechanistic models

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  • Anthony C. Atkinson

Abstract

Summary. The paper develops methods for the design of experiments for mechanistic models when the response must be transformed to achieve symmetry and constant variance. The power transformation that is used is partially justified by a rule in analytical chemistry. 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 are given of optimum designs, not only for single‐response models, but also for experiments in which multivariate responses are measured and for experiments in which the model is defined by a set of differential equations which cannot be solved analytically. The extension to designs for checking models is discussed.

Suggested Citation

  • Anthony C. Atkinson, 2003. "Horwitz's rule, transforming both sides and the design of experiments for mechanistic models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(3), pages 261-278, July.
    • Handle: RePEc:bla:jorssc:v:52:y:2003:i:3:p:261-278
    DOI: 10.1111/1467-9876.00403
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    Cited by:

    1. Anthony C. Atkinson & Atanu Biswas, 2005. "Bayesian Adaptive Biased-Coin Designs for Clinical Trials with Normal Responses," Biometrics, The International Biometric Society, vol. 61(1), pages 118-125, March.
    2. Rongling Wu & Chang-Xing Ma & Min Lin & Zuoheng Wang & George Casella, 2004. "Functional Mapping of Quantitative Trait Loci Underlying Growth Trajectories Using a Transform-Both-Sides Logistic Model," Biometrics, The International Biometric Society, vol. 60(3), pages 729-738, September.
    3. Patan, Maciej & Bogacka, Barbara, 2007. "Optimum experimental designs for dynamic systems in the presence of correlated errors," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5644-5661, August.
    4. Ucinski Dariusz & Atkinson Anthony C., 2004. "Experimental Design for Time-Dependent Models with Correlated Observations," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-16, May.

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