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Update formulas for split-plot and block designs

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  • ARNOUTS, Heidi
  • GOOS, Peter

Abstract

For the algorithmic construction of optimal experimental designs, it is important to be able to evaluate small modi_cations of given designs in terms of the optimality criteria at a low computational cost. In this article, we propose update formulas for evaluating the impact of changes to the levels of easy-to-change factors and hard-to-change factors in split-plot designs as well as the impact of a swap of points between blocks or whole plots in block designs or split-plot designs.

Suggested Citation

  • ARNOUTS, Heidi & GOOS, Peter, 2008. "Update formulas for split-plot and block designs," Working Papers 2008022, University of Antwerp, Faculty of Business and Economics.
    • Handle: RePEc:ant:wpaper:2008022
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    References listed on IDEAS

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    1. Nguyen, Nam-Ky & Liu, Min-Qian, 2008. "An algorithmic approach to constructing mixed-level orthogonal and near-orthogonal arrays," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5269-5276, August.
    2. Goos, Peter & Vandebroek, Martina, 2001. "-optimal response surface designs in the presence of random block effects," Computational Statistics & Data Analysis, Elsevier, vol. 37(4), pages 433-453, October.
    3. Nguyen, Nam-Ky & Miller, Alan J., 1992. "A review of some exchange algorithms for constructing discrete D-optimal designs," Computational Statistics & Data Analysis, Elsevier, vol. 14(4), pages 489-498, November.
    4. Kessels, Roselinde & Goos, Peter & Vandebroek, Martina, 2008. "Optimal designs for conjoint experiments," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2369-2387, January.
    5. J. A. John & D. Whitaker, 2000. "Recursive formulae for the average efficiency factor in block and row‐column designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(3), pages 575-583.
    6. Bradley Jones & Peter Goos, 2007. "A candidate‐set‐free algorithm for generating D‐optimal split‐plot designs," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(3), pages 347-364, May.
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    Cited by:

    1. Smucker, Byran J. & Castillo, Enrique del & Rosenberger, James L., 2012. "Model-robust designs for split-plot experiments," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4111-4121.
    2. CUERVO, Daniel Palhazi & GOOS, Peter & SÖRENSEN, Kenneth, 2013. "An iterated local search algorithm for the construction of large scale D-optimal experimental designs," Working Papers 2013006, University of Antwerp, Faculty of Business and Economics.
    3. JONES, Bradley & GOOS, Peter, 2012. "I-optimal versus D-optimal split-plot response surface designs," Working Papers 2012002, University of Antwerp, Faculty of Business and Economics.
    4. SYAFITRI, Utami & SARTONO, Bagus & GOOS, Peter, 2015. "D- and I-optimal design of mixture experiments in the presence of ingredient availability constraints," Working Papers 2015003, University of Antwerp, Faculty of Business and Economics.
    5. Born, Mathias & Goos, Peter, 2025. "Optimal splitk-plot designs," Computational Statistics & Data Analysis, Elsevier, vol. 201(C).

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    Keywords

    D-; A- and V-optimality; Point-exchange; Coordinate-exchange; Information matrix; Compound symmetry;
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