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Optimal designs for treatment comparisons represented by graphs

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  • Samuel Rosa

    (Comenius University in Bratislava)

Abstract

Consider an experiment for comparing a set of treatments: in each trial, one treatment is chosen and its effect determines the mean response of the trial. We examine the optimal approximate designs for the estimation of a system of treatment contrasts under this model. These designs can be used to provide optimal treatment proportions in more general models with nuisance effects. For any system of pairwise treatment comparisons, we propose to represent such a system by a graph. Then, we represent the designs by the inverses of the vertex weights in the corresponding graph and we show that the values of the eigenvalue-based optimality criteria can be expressed using the Laplacians of the vertex-weighted graphs. We provide a graph theoretic interpretation of D-, A- and E-optimality for estimating sets of pairwise comparisons. We apply the obtained graph representation to provide optimality results for these criteria as well as for ’symmetric’ systems of treatment contrasts.

Suggested Citation

  • Samuel Rosa, 2018. "Optimal designs for treatment comparisons represented by graphs," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(4), pages 479-503, October.
    • Handle: RePEc:spr:alstar:v:102:y:2018:i:4:d:10.1007_s10182-017-0312-5
    DOI: 10.1007/s10182-017-0312-5
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    References listed on IDEAS

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    1. J. W. Stallings & J. P. Morgan, 2015. "General weighted optimality of designed experiments," Biometrika, Biometrika Trust, vol. 102(4), pages 925-935.
    2. Samuel Rosa & Radoslav Harman, 2016. "Optimal approximate designs for estimating treatment contrasts resistant to nuisance effects," Statistical Papers, Springer, vol. 57(4), pages 1077-1106, December.
    3. Radoslav Harman, 2004. "Minimal efficiency of designs under the class of orthogonally invariant information criteria," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(2), pages 137-153, September.
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    Citations

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    Cited by:

    1. Samuel Rosa, 2019. "Equivalence of weighted and partial optimality of experimental designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(6), pages 719-732, August.
    2. Belmiro P. M. Duarte & Anthony C. Atkinson & Satya P. Singh & Marco S. Reis, 2023. "Optimal design of experiments for hypothesis testing on ordered treatments via intersection-union tests," Statistical Papers, Springer, vol. 64(2), pages 587-615, April.
    3. Duarte, Belmiro P.M. & Atkinson, Anthony C. & P. Singh, Satya & S. Reis, Marco, 2023. "Optimal design of experiments for hypothesis testing on ordered treatments via intersection-union tests," LSE Research Online Documents on Economics 115187, London School of Economics and Political Science, LSE Library.

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