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Optimal designs for mixed continuous and binary responses with quantitative and qualitative factors

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  • Kao, Ming-Hung
  • Khogeer, Hazar

Abstract

This work is concerned with optimal designs for multivariate regression of responses of mixed variable types (continuous and binary) on quantitative and qualitative factors. New complete class results with respect to the Loewner ordering, and relevant Chebyshev systems are derived to identify a small class of designs, within which locally optimal designs can be found for a group of models and optimality criteria. The complete class results facilitate the search of optimal designs via some general-purpose optimization techniques. Extensions of some previous results for characterizing optimal designs are also provided.

Suggested Citation

  • Kao, Ming-Hung & Khogeer, Hazar, 2021. "Optimal designs for mixed continuous and binary responses with quantitative and qualitative factors," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:jmvana:v:182:y:2021:i:c:s0047259x20302931
    DOI: 10.1016/j.jmva.2020.104712
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    References listed on IDEAS

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    1. Imhof, Lorens, 2000. "Optimum Designs for a Multiresponse Regression Model," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 120-131, January.
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    4. Yue, Rong-Xian & Liu, Xin & Chatterjee, Kashinath, 2014. "D-optimal designs for multiresponse linear models with a qualitative factor," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 57-69.
    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. Shih-Hao Huang & Mong-Na Lo Huang & Kerby Shedden & Weng Kee Wong, 2017. "Optimal group testing designs for estimating prevalence with uncertain testing errors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1547-1563, November.
    7. H. Dette & K. Kettelhake & F. Bretz, 2015. "Designing dose-finding studies with an active control for exponential families," Biometrika, Biometrika Trust, vol. 102(4), pages 937-950.
    8. Kim, Soohyun & Kao, Ming-Hung, 2019. "Locally optimal designs for mixed binary and continuous responses," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 112-117.
    9. K Schorning & H Dette & K Kettelhake & W K Wong & F Bretz, 2017. "Optimal designs for active controlled dose-finding trials with efficacy-toxicity outcomes," Biometrika, Biometrika Trust, vol. 104(4), pages 1003-1010.
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    Cited by:

    1. Kang, Xiaoning & Kang, Lulu & Chen, Wei & Deng, Xinwei, 2022. "A generative approach to modeling data with quantitative and qualitative responses," Journal of Multivariate Analysis, Elsevier, vol. 190(C).

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