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I-optimal versus D-optimal split-plot response surface designs

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  • JONES, Bradley
  • GOOS, Peter

Abstract

Response surface experiments often involve only quantitative factors, and the response is fit using a full quadratic model in these factors. The term response surface implies that interest in these studies is more on prediction than parameter estimation since the points on the fitted surface are predicted responses. When computing optimal designs for response surface experiments, it therefore makes sense to focus attention on the predictive capability of the designs. However, the most popular criterion for creating optimal experimental designs is the D-optimality criterion, which aims to minimize the variance of the factor-effect estimates in an omnibus sense. Because I-optimal designs minimize the average variance of prediction over the region of experimentation, their focus is clearly on prediction. Therefore, the I-optimality criterion seems to be a more appropriate one than the D-optimality criterion for generating response surface designs. Here, we introduce I-optimal design of split-plot response surface experiments. We show through several examples that I-optimal split-plot designs provide substantial benefits in terms of prediction compared to D-optimal split-plot designs, while also performing very well in terms of the precision of the factor-effect estimates.

Suggested Citation

  • JONES, Bradley & GOOS, Peter, 2012. "I-optimal versus D-optimal split-plot response surface designs," Working Papers 2012002, University of Antwerp, Faculty of Applied Economics.
  • Handle: RePEc:ant:wpaper:2012002
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    File URL: https://repository.uantwerpen.be/docman/irua/06d157/da102bc1.pdf
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    References listed on IDEAS

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    1. MACHARIA, Harrison & GOOS, Peter, 2010. "D-optimal and D-efficient equivalent-estimation second-order split-plot designs," Working Papers 2010011, University of Antwerp, Faculty of Applied Economics.
    2. SCHOEN, Eric D. & JONES, Bradley & GOOS, Peter, 2010. "Split-plot experiments with factor-dependent whole-plot sizes," Working Papers 2010001, University of Antwerp, Faculty of Applied Economics.
    3. 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.
    4. 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.
    5. Peter Goos, 2006. "Optimal versus orthogonal and equivalent-estimation design of blocked and split-plot experiments," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 60(3), pages 361-378.
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    Citations

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    Cited by:

    1. GOOS, Peter & JONES, Bradley & SYAFITRI, Utami, 2013. "I-optimal mixture designs," Working Papers 2013033, University of Antwerp, Faculty of Applied Economics.
    2. ARNOUTS, Heidi & GOOS, Peter, 2013. "Staggered-level designs for response surface modeling," Working Papers 2013027, University of Antwerp, Faculty of Applied Economics.
    3. Marcin Dutka & Mario Ditaranto & Terese Løvås, 2015. "Application of a Central Composite Design for the Study of NO x Emission Performance of a Low NO x Burner," Energies, MDPI, Open Access Journal, vol. 8(5), pages 1-22, April.
    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 Applied Economics.

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