×

zbMATH — the first resource for mathematics

Update formulas for split-plot and block designs. (English) Zbl 1284.62485
Summary: For the algorithmic construction of optimal experimental designs, it is important to be able to evaluate small modifications of given designs in terms of the optimality criteria at a low computational cost. This can be achieved by using powerful update formulas for the optimality criteria during the design construction. The derivation of such 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 is described.

MSC:
62K10 Statistical block designs
62K05 Optimal statistical designs
PDF BibTeX Cite
Full Text: DOI
References:
[1] Atkinson, A.C.; Donev, A.N., The construction of exact D-optimum experimental designs with application to blocking response surface designs, Biometrika, 76, 515-526, (1989) · Zbl 0677.62066
[2] Eccleston, J.A., Recursive techniques for the construction of experimental designs, Journal of statistical planning and inference, 4, 291-297, (1980) · Zbl 0452.62065
[3] Goos, P.; Vandebroek, M., D-optimal response surface designs in the presence of random block effects, Computational statistics and data analysis, 37, 433-453, (2001) · Zbl 1079.62532
[4] Goos, P.; Vandebroek, M., Optimal split-plot designs, Journal of quality technology, 33, 436-450, (2001)
[5] Goos, P.; Vandebroek, M., D-optimal split-plot designs with given numbers and sizes of whole plots, Technometrics, 45, 235-245, (2003)
[6] Goos, P.; Vandebroek, M., Outperforming completely randomized designs, Journal of quality technology, 36, 12-26, (2004)
[7] Harville, D.A., Matrix algebra from a statistician’s perspective, (1997), Springer-Verlag Telos · Zbl 0881.15001
[8] John, J.A., Updating formula in an analysis of variance model, Biometrika, 88, 1175-1178, (2001) · Zbl 0986.62058
[9] John, J.A.; Whitaker, D., Recursive formulae for the average efficiency factor in block and row-column designs, Journal of the royal statistical society series B, 62, 575-583, (2000) · Zbl 0971.62041
[10] John, J.A.; Williams, E.R., Updating the average efficiency factor in -designs, Biometrika, 87, 695-699, (2000) · Zbl 0956.62060
[11] Johnson, M.E.; Nachtsheim, C.J., Some guidelines for constructing exact D-optimal designs on convex design spaces, Technometrics, 25, 271-277, (1983) · Zbl 0526.62070
[12] Jones, B.; Goos, P., A candidate-set-free algorithm for generating D-optimal split-plot designs, Applied statistics, 56, 347-364, (2007)
[13] Kessels, R.; Goos, P.; Vandebroek, M., Optimal designs for conjoint experiments, Computational statistics and data analysis, 52, 2369-2387, (2008) · Zbl 1452.62581
[14] Meyer, R.K.; Nachtsheim, C.J., The coordinate-exchange algorithm for constructing exact optimal experimental designs, Technometrics, 37, 60-69, (1995) · Zbl 0825.62652
[15] Nguyen, N.K., Construction of optimal block designs by computer, Technometrics, 36, 300-307, (1994) · Zbl 0798.62079
[16] Nguyen, N.K.; Liu, M.Q., An algorithmic approach to constructing mixed-level orthogonal and near-orthogonal arrays, Computational statistics and data analysis, 52, 2, 5269-5276, (2008) · Zbl 1452.62589
[17] Nguyen, N.K.; Miller, A.J., A review of some exchange algorithms for constructing discrete D-optimal designs, Computational statistics and data analysis, 14, 489-498, (1992) · Zbl 0937.62628
[18] Nguyen, N.K.; Williams, E.R., Experimental designs for 2-colour cdna microarray experiments, Applied stochastic models in business and industry, 22, 631-638, (2006) · Zbl 1164.62367
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.