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D-optimal and D-efficient equivalent-estimation second-order split-plot designs

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  • MACHARIA, Harrison
  • GOOS, Peter

Abstract

Industrial experiments often involve factors which are hard to change or costly to manipulate and thus make it impossible to use a complete randomization. In such cases, the split-plot design structure is a cost-efficient alternative that reduces the number of independent settings of the hard-to-change factors. In general, model estimation for split-plot designs requires the use of generalized least squares (GLS). However, for some split-plot designs (including not only classical agricultural split-plot designs, but also some second-order split-plot response surface designs), ordinary least squares (OLS) estimates are equivalent to GLS estimates. These designs are called equivalent-estimation designs. As an alternative to these equivalent estimation designs, one can use D-optimal designs which guarantee efficient estimation of the fixed effects of the statistical model that is appropriate given the split-plot structure. We explore the relationship between equivalent-estimation and D-optimal split-plot designs for a second-order response surface model and propose an algorithm for generating D-efficient equivalent-estimation split-plot designs. This approach allows for a flexible choice of the number of hard-to-change factors, the number of easy-to-change factors, the number of whole plots and the total sample size.

Suggested Citation

  • 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.
  • Handle: RePEc:ant:wpaper:2010011
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    File URL: https://repository.uantwerpen.be/docman/irua/bb58db/83e4234b.pdf
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    References listed on IDEAS

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    1. Verhoef, Erik & Nijkamp, Peter & Rietveld, Piet, 1996. "Second-Best Congestion Pricing: The Case of an Untolled Alternative," Journal of Urban Economics, Elsevier, vol. 40(3), pages 279-302, November.
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    Cited by:

    1. Sambo, Francesco & Borrotti, Matteo & Mylona, Kalliopi, 2014. "A coordinate-exchange two-phase local search algorithm for the D- and I-optimal designs of split-plot experiments," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1193-1207.
    2. MYLONA, Kalliopi & MACHARIA, Harrison & GOOS, Peter, 2011. "Three-level equivalent-estimation split-plot designs based on subset and supplementary difference set designs," Working Papers 2011010, University of Antwerp, Faculty of Applied Economics.
    3. ARNOUTS, Heidi & GOOS, Peter, 2013. "Staggered-level designs for response surface modeling," Working Papers 2013027, University of Antwerp, Faculty of Applied Economics.
    4. 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.

    More about this item

    Keywords

    Coordinate-exchange algorithm; D-optimality; Equivalent estimation; Generalized least squares; Ordinary least squares; Split-plot design;

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