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On Optimal Designs for Nonlinear Models: A General and Efficient Algorithm

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  • Min Yang
  • Stefanie Biedermann
  • Elina Tang

Abstract

Finding optimal designs for nonlinear models is challenging in general. Although some recent results allow us to focus on a simple subclass of designs for most problems, deriving a specific optimal design still mainly depends on numerical approaches. There is need for a general and efficient algorithm that is more broadly applicable than the current state-of-the-art methods. We present a new algorithm that can be used to find optimal designs with respect to a broad class of optimality criteria, when the model parameters or functions thereof are of interest, and for both locally optimal and multistage design strategies. We prove convergence to the optimal design, and show in various examples that the new algorithm outperforms the current state-of-the-art algorithms.

Suggested Citation

  • Min Yang & Stefanie Biedermann & Elina Tang, 2013. "On Optimal Designs for Nonlinear Models: A General and Efficient Algorithm," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1411-1420, December.
    • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:504:p:1411-1420
    DOI: 10.1080/01621459.2013.806268
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    Cited by:

    1. Weng Kee Wong & Ray-Bing Chen & Chien-Chih Huang & Weichung Wang, 2015. "A Modified Particle Swarm Optimization Technique for Finding Optimal Designs for Mixture Models," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-23, June.
    2. Yu, Jun & Meng, Xiran & Wang, Yaping, 2023. "Optimal designs for semi-parametric dose-response models under random contamination," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    3. Hyun Seung Won & Wong Weng Kee, 2015. "Multiple-Objective Optimal Designs for Studying the Dose Response Function and Interesting Dose Levels," The International Journal of Biostatistics, De Gruyter, vol. 11(2), pages 253-271, November.
    4. Duarte, Belmiro P.M. & Atkinson, Anthony C. & Granjo, Jose F.O & Oliveira, Nuno M.C, 2019. "Optimal design of experiments for liquid–liquid equilibria characterization via semidefinite programming," LSE Research Online Documents on Economics 102500, London School of Economics and Political Science, LSE Library.
    5. García-Ródenas, Ricardo & García-García, José Carlos & López-Fidalgo, Jesús & Martín-Baos, José Ángel & Wong, Weng Kee, 2020. "A comparison of general-purpose optimization algorithms for finding optimal approximate experimental designs," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    6. Nedka Dechkova Nikiforova & Rossella Berni & Jesús Fernando López‐Fidalgo, 2022. "Optimal approximate choice designs for a two‐step coffee choice, taste and choice again experiment," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1895-1917, November.
    7. Belmiro P. M. Duarte, 2023. "Exact Optimal Designs of Experiments for Factorial Models via Mixed-Integer Semidefinite Programming," Mathematics, MDPI, vol. 11(4), pages 1-17, February.
    8. Haoyu Wang & Chongqi Zhang, 2022. "The mixture design threshold accepting algorithm for generating $$\varvec{D}$$ D -optimal designs of the mixture models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(3), pages 345-371, April.
    9. Qing Liu & Yihui (Elina) Tang, 2015. "Construction of Heterogeneous Conjoint Choice Designs: A New Approach," Marketing Science, INFORMS, vol. 34(3), pages 346-366, May.
    10. Lianyan Fu & Faming Ma & Zhuoxi Yu & Zhichuan Zhu, 2023. "Multiplication Algorithms for Approximate Optimal Distributions with Cost Constraints," Mathematics, MDPI, vol. 11(8), pages 1-14, April.
    11. Chen, Ping-Yang & Chen, Ray-Bing & Chen, Yu-Shi & Wong, Weng Kee, 2023. "Numerical Methods for Finding A-optimal Designs Analytically," Econometrics and Statistics, Elsevier, vol. 28(C), pages 155-162.
    12. Radoslav Harman & Eva Benková, 2017. "Barycentric algorithm for computing D-optimal size- and cost-constrained designs of experiments," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(2), pages 201-225, February.
    13. Rosa, Samuel & Harman, Radoslav, 2022. "Computing minimum-volume enclosing ellipsoids for large datasets," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    14. Duarte, Belmiro P.M. & Atkinson, Anthony C. & Granjo, Jose F.O & Oliveira, Nuno M.C, 2022. "Optimal design of experiments for implicit models," LSE Research Online Documents on Economics 107584, London School of Economics and Political Science, LSE Library.
    15. Lenka Filová & Radoslav Harman, 2020. "Ascent with quadratic assistance for the construction of exact experimental designs," Computational Statistics, Springer, vol. 35(2), pages 775-801, June.

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