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Optimal splitk-plot designs

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  • Born, Mathias
  • Goos, Peter

Abstract

Completely randomized designs are often infeasible due to the hard-to-change nature of one or more experimental factors. In those cases, restrictions are imposed on the order of the experimental tests. The resulting experimental designs are often split-plot or split-split-plot designs in which the levels of certain hard-to-change factors are varied only a limited number of times. In agricultural machinery optimization, the number of hard-to-change factors is so large and the available time for experimentation is so short that split-plot or split-split-plot designs are infeasible as well. The only feasible kinds of designs are generalizations of split-split-plot designs, which are referred to as splitk-designs, where k is larger than 2. The coordinate-exchange algorithm is extended to construct optimal splitk-plot designs and the added value of the algorithm is demonstrated by applying it to an experiment involving a self propelled forage harvester. The optimal design generated using the extended algorithm is substantially more efficient than the design that was actually used. Update formulas for the determinant and the inverse of the information matrix speed up the coordinate-exchange algorithm, making it feasible for large designs.

Suggested Citation

  • Born, Mathias & Goos, Peter, 2025. "Optimal splitk-plot designs," Computational Statistics & Data Analysis, Elsevier, vol. 201(C).
    • Handle: RePEc:eee:csdana:v:201:y:2025:i:c:s0167947324001129
    DOI: 10.1016/j.csda.2024.108028
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    References listed on IDEAS

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    1. Eric Schoen, 1999. "Designing fractional two-level experiments with nested error structures," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(4), pages 495-508.
    2. D. R. Bingham & E. D. Schoen & R. R. Sitter, 2005. "Corrigendum: Designing fractional factorial split‐plot experiments with few whole‐plot factors," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(5), pages 955-958, November.
    3. Bradley Jones & Peter Goos, 2009. "D-optimal design of split-split-plot experiments," Biometrika, Biometrika Trust, vol. 96(1), pages 67-82.
    4. Arnouts, Heidi & Goos, Peter, 2010. "Update formulas for split-plot and block designs," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3381-3391, December.
    5. D. R. Bingham & E. D. Schoen & R. R. Sitter, 2004. "Designing fractional factorial split‐plot experiments with few whole‐plot factors," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(2), pages 325-339, April.
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