×

A comparison of design and model selection methods for supersaturated experiments. (English) Zbl 1284.62477

Summary: Various design and model selection methods are available for supersaturated designs having more factors than runs but little research is available on their comparison and evaluation. Simulated experiments are used to evaluate the use of \(E(s^{2})\)-optimal and Bayesian \(D\)-optimal designs and to compare three analysis strategies representing regression, shrinkage and a novel model-averaging procedure. Suggestions are made for choosing the values of the tuning constants for each approach. Findings include that (i) the preferred analysis is via shrinkage; (ii) designs with similar numbers of runs and factors can be effective for a considerable number of active effects of only moderate size; and (iii) unbalanced designs can perform well. Some comments are made on the performance of the design and analysis methods when effect sparsity does not hold.

MSC:

62K05 Optimal statistical designs

Software:

lp_solve; R; lpSolve
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Abraham, B.; Chipman, H.; Vijayan, K., Some risks in the construction and analysis of supersaturated designs, Technometrics, 41, 135-141 (1999)
[2] Allen, T. T.; Bernshteyn, M., Supersaturated designs that maximize the probability of identifying active factors, Technometrics, 45, 90-97 (2003)
[3] Beattie, S. D.; Fong, D. K.H.; Lin, D. K.J., A two-stage Bayesian model selection strategy for supersaturated designs, Technometrics, 44, 55-63 (2002)
[5] Booth, K. H.V.; Cox, D. R., Some systematic supersaturated designs, Technometrics, 4, 489-495 (1962) · Zbl 0109.12201
[6] Box, G. E.P., Discussion of the papers of Satterthwaite and Budne, Technometrics, 1, 174-180 (1959)
[7] Box, G. E.P.; Meyer, R. D., An analysis for unreplicated fractional factorials, Technometrics, 28, 11-18 (1986) · Zbl 0586.62168
[8] Burnham, K. P.; Anderson, D. R., Model Selection and Multimodel Inference (2002), Springer · Zbl 1005.62007
[9] Candes, E.; Tao, T., The Dantzig selector: statistical estimation when \(p\) is much larger than \(n\), The Annals of Statistics, 35, 2313-2351 (2007) · Zbl 1139.62019
[10] DuMouchel, W.; Jones, B., A simple Bayesian modification of \(D\)-optimal designs to reduce dependence on an assumed model, Technometrics, 36, 37-47 (1994) · Zbl 0800.62472
[11] Gilmour, S. G., Supersaturated designs in factor screening, (Dean, A. M.; Lewis, S. M., Screening (2006), Springer: Springer New York), 169-190
[12] Holcomb, D. R.; Montgomery, D. C.; Carlyle, W. M., The use of supersaturated experiments in turbine engine development, Quality Engineering, 19, 17-27 (2007)
[13] Jones, B.; Lin, D. K.J.; Nachtsheim, C. J., Bayesian \(D\)-optimal supersaturated designs, Journal of Statistical Planning and Inference, 138, 86-92 (2008) · Zbl 1144.62058
[14] Lewis, S. M.; Dean, A. M., Detection of interactions in experiments on large numbers of factors (with discussion), Journal of the Royal Statistical Society B, 63, 633-672 (2001) · Zbl 0988.62050
[15] Li, R.; Lin, D. K.J., Data analysis in supersaturated designs, Statistics & Probability Letters, 59, 135-144 (2002) · Zbl 1092.62570
[16] Li, R.; Lin, D. K.J., Analysis methods for supersaturated design: some comparisons, Journal of Data Science, 1, 249-260 (2003)
[17] Lin, D. K.J., A new class of supersaturated designs, Technometrics, 35, 28-31 (1993)
[18] Lin, D. K.J., Generating systematic supersaturated designs, Technometrics, 37, 213-225 (1995) · Zbl 0822.62062
[19] Li, W. W.; Wu, C. F.J., Columnwise-pairwise algorithms with applications to the construction of supersaturated designs, Technometrics, 39, 171-179 (1997) · Zbl 0889.62066
[20] Madigan, D.; Raftery, A. E., Model selection and accounting for model uncertainty in graphical models using Occam’s window, Journal of the American Statistical Association, 89, 1535-1546 (1994) · Zbl 0814.62030
[21] Meyer, R. K.; Nachtsheim, C. J., The coordinate-exchange algorithm for constructing exact optimal experimental designs, Technometrics, 37, 60-69 (1995) · Zbl 0825.62652
[22] Miller, A., Subset Selection in Regression (2002), Chapman and Hall: Chapman and Hall Boca Raton · Zbl 1051.62060
[23] Nguyen, N. K., An algorithmic approach to constructing supersaturated designs, Technometrics, 38, 69-73 (1996) · Zbl 0900.62416
[24] Nguyen, N. K.; Cheng, C. S., New \(E(s^2)\)-optimal supersaturated designs constructed from incomplete block designs, Technometrics, 50, 26-31 (2008)
[25] O’Hagan, A.; Forster, J. J., Kendall’s Advanced Theory of Statistics Vol. 2B: Bayesian Inference (2004), Arnold: Arnold London · Zbl 1058.62002
[26] Phoa, F. K.H.; Pan, Y.-H.; Xu, H., Analysis of supersaturated designs via the Dantzig selector, Journal of Statistical Planning and Inference, 139, 2362-2372 (2009) · Zbl 1160.62071
[28] Ryan, K. J.; Bulutoglu, D. A., \(E(s^2)\)-optimal supersaturated designs with good minimax properties, Journal of Statistical Planning and Inference, 137, 2250-2262 (2007) · Zbl 1120.62059
[29] Satterthwaite, F., Random balance experimentation, Technometrics, 1, 111-137 (1959)
[30] Westfall, P. H.; Young, S. S.; Lin, D. K.J., Forward selection error control in the analysis of supersaturated designs, Statistica Sinica, 8, 101-117 (1998) · Zbl 0886.62077
[31] Wu, C. F.J., Construction of supersaturated designs through partially aliased interactions, Biometrika, 80, 661-669 (1993) · Zbl 0800.62483
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.