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Automatic generation of generalised regular factorial designs

Author

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  • Kobilinsky, André
  • Monod, Hervé
  • Bailey, R.A.

Abstract

The R package planor enables the user to search for, and construct, factorial designs satisfying given conditions. The user specifies the factors and their numbers of levels, the factorial terms which are assumed to be non-zero, and the subset of those which are to be estimated. Both block and treatment factors can be allowed for, and they may have either fixed or random effects, as well as hierarchy relationships. The designs are generalised regular designs, which means that each one is constructed by using a design key and that the underlying theory is that of finite abelian groups. The main theoretical results and algorithms on which planor is based are developed and illustrated, with the emphasis on mathematical rather than programming details. Sections 3–5 are dedicated to the elementary case, when the numbers of levels of all factors are powers of the same prime. The ineligible factorial terms associated with users’ specifications are defined and it is shown how they can be used to search for a design key by a backtrack algorithm. Then the results are extended to the case when different primes are involved, by making use of the Sylow decomposition of finite abelian groups. The proposed approach provides a unified framework for a wide range of factorial designs.

Suggested Citation

  • Kobilinsky, André & Monod, Hervé & Bailey, R.A., 2017. "Automatic generation of generalised regular factorial designs," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 311-329.
    • Handle: RePEc:eee:csdana:v:113:y:2017:i:c:p:311-329
    DOI: 10.1016/j.csda.2016.09.003
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    References listed on IDEAS

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    1. H. Monod & R. A. Bailey, 1992. "Pseudofactors: Normal Use to Improve Design and Facilitate Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 317-336, June.
    2. H. D. Patterson & R. A. Bailey, 1978. "Design Keys for Factorial Experiments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 27(3), pages 335-343, November.
    3. M. F. Franklin & R. A. Bailey, 1977. "Selection of Defining Contrasts and Confounded Effects in Two‐Level Experiments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(3), pages 321-326, November.
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    Cited by:

    1. Grömping, Ulrike & Fontana, Roberto, 2019. "An algorithm for generating good mixed level factorial designs," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 101-114.
    2. Rouger, Baptiste & Goldringer, Isabelle & Barbillon, Pierre & Miramon, Anne & Naino Jika, Abdel Kader & Thomas, Mathieu, 2023. "Sensitivity analysis of a crop metapopulation model," Ecological Modelling, Elsevier, vol. 475(C).
    3. Olivier David & Arnaud Le Rouzic & Christine Dillmann, 2022. "Optimization of sampling designs for pedigrees and association studies," Biometrics, The International Biometric Society, vol. 78(3), pages 1056-1066, September.

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