D-optimal and D-efficient equivalent-estimation second-order split-plot designs
AbstractIndustrial 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 equivalentestimation 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.
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Bibliographic InfoPaper provided by University of Antwerp, Faculty of Applied Economics in its series Working Papers with number 2010011.
Length: 21 pages
Date of creation: May 2010
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Web page: https://www.uantwerp.be/en/faculties/applied-economic-sciences/
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Coordinate-exchange algorithm; D-optimality; Equivalent estimation; Generalized least squares; Ordinary least squares; Split-plot design;
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- 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.
- 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.
- 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.
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