A mixed integer optimization approach for model selection in screening experiments

References

• Abraham, B., H. Chipman, and K. Vijayan. 1999. Some risks in the construction and analysis of supersaturated designs. Technometrics 41 (2):135–41. doi: 10.1080/00401706.1999.10485634.
   Web of Science ®Google Scholar
• Beale, E. M. L., and J. J. H. Forrest. 1976. Global optimization using special ordered sets. Mathematical Programming 10 (1):52–69. doi: 10.1007/BF01580653.
   Web of Science ®Google Scholar
• Bertsimas, D., and A. King. 2016. An algorithmic approach to linear regression. Operations Research 64 (1):2–16. doi: 10.1287/opre.2015.1436.
   Web of Science ®Google Scholar
• Bertsimas, D., A. King, and R. Mazumder. 2016. Best subset selection via a modern optimization lens. The Annals of Statistics 44 (2):813–52. doi: 10.1214/15-AOS1388.
   Web of Science ®Google Scholar
• Bertsimas, D., and R. Weismantel. 2005. Optimization over integers. Belmont: Dynamic Ideas Press.
   Google Scholar
• Bien, J., J. Taylor, and R. Tibshirani. 2013. A LASSO for hierarchical interactions. Annals of Statistics 41 (3):1111–41. doi: 10.1214/13-AOS1096.
   PubMed Web of Science ®Google Scholar
• Bixby, R. 2012. A brief history of linear and mixed-integer programming computation. Documenta Mathematica. Extra Volume: Optimization Stories:107–21.
   Google Scholar
• Box, G. E. P., and R. D. Meyer. 1986. An analysis for unreplicated fractional factorials. Technometrics 28 (1):11–8. doi: 10.1080/00401706.1986.10488093.
   Web of Science ®Google Scholar
• Candes, E., and T. Tao. 2007. The Dantzig selector: Statistical estimation when p is much larger than n. The Annals of Statistics 35 (6):2313–51. doi: 10.1214/009053606000001523.
   Web of Science ®Google Scholar
• Cheng, S.-W., and C. F. J. Wu. 2001. Factor screening and response surface exploration. Statistica Sinica (11):553–604. doi: 10.5705/ss.2012.210.
   Web of Science ®Google Scholar
• Chipman, H. 1996. Bayesian variable selection with related predictors. Canadian Journal of Statistics 24 (1):17–36. doi: 10.2307/3315687.
   Web of Science ®Google Scholar
• Chipman, H., M. Hamada, and C. F. J. Wu. 1997. A Bayesian variable selection approach for analyzing designed experiments with complex aliasing. Technometrics 39 (4):372–81. doi: 10.1080/00401706.1997.10485156.
   Web of Science ®Google Scholar
• Choi, N., W. Li, and J. Zhu. 2010. Variable selection with the strong heredity constraint and its oracle property. Journal of the American Statistical Association 105 (489):354–64. doi: 10.1198/jasa.2010.tm08281.
   Web of Science ®Google Scholar
• Draguljić, D.,. D. C. Woods, A. M. Dean, S. M. Lewis, and A.-J E. Vine. 2014. Screening strategies in the presence of interactions. Technometrics 56 (1):1–16. doi: 10.1080/00401706.2013.775900.
   Web of Science ®Google Scholar
• Errore, A., B. Jones, W. Li, and C. J. Nachtsheim. 2017. Using definitive screening designs to identify active first- and second-order factor effects. Journal of Quality Technology 49 (3):244–64. doi: 10.1080/00224065.2017.11917993.
   Web of Science ®Google Scholar
• Furnival, G., and R. Wilson. 1974. Regression by leaps and bounds. Technometrics 16 (4):499–511. doi: 10.1080/00401706.1974.10489231.
   Web of Science ®Google Scholar
• Gurobi Optimization Inc. 2019. Gurobi 8 performance benchmarks. Accessed 11 July 2019. http://www.gurobi.com/pdfs/benchmarks.pdf.
   Google Scholar
• Hamada, M., and C. F. J. Wu. 1992. Analysis of designed experiments with complex aliasing. Journal of Quality Technology 24 (3):130–7. doi: 10.1080/00224065.1992.11979383.
   Web of Science ®Google Scholar
• Hastie, T., R. Tibshirani, and J. H. Friedman. 2009. The elements of statistical learning: Data mining, inference, and prediction. 2nd ed. New York: Springer.
   Google Scholar
• Jones, B., and C. J. Nachtsheim. 2011. A class of three-level designs for definitive screening in the presence of second-order effects. Journal of Quality Technology 43 (1):1–15. doi: 10.1080/00224065.2011.11917841.
   Web of Science ®Google Scholar
• Lenth, R. 1989. Quick and easy analysis of unreplicated experiments. Technometrics 31 (4):469–73. doi: 10.1080/00401706.1989.10488595.
   Web of Science ®Google Scholar
• Li, X., N. Sudarsanam, and D. D. Frey. 2006. Regularities in data from factorial experiments. Complexity 11 (5):32–45. doi: 10.1002/cplx.20123.
   Web of Science ®Google Scholar
• Liu, H., J. Zhang, X. Jiang, and J. Liu. 2010. The group Dantzig selector. In Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, 461–8.
   Google Scholar
• Marley, C. J., and D. C. Woods. 2010. A comparison of design and model selection methods for supersaturated experiments. Computational Statistics & Data Analysis 54 (12):3158–67. doi: 10.1016/j.csda.2010.02.017.
   Web of Science ®Google Scholar
• Mee, R. W. 2013. Tips for analyzing nonregular fractional factorial experiments. Journal of Quality Technology 45 (4):330–49. doi: 10.1080/00224065.2013.11917942.
   Web of Science ®Google Scholar
• Mee, R. W., E. D. Schoen, and D. J. Edwards. 2017. Selecting an orthogonal or nonorthogonal two-level design for screening. Technometrics 59 (3):305–18. doi: 10.1080/00401706.2016.1186562.
   Web of Science ®Google Scholar
• Miller, A. 2002. Subset selection in regression. 2nd ed. Boca Raton, FL: Chapman & Hall/CRC.
   Google Scholar
• Miller, A., and R. R. Sitter. 2001. Using the folded-over 12-run Plackett-Burman design to consider interactions. Technometrics 43 (1):44–55. doi: 10.1198/00401700152404318.
   Web of Science ®Google Scholar
• Natarajan, B. 1995. Sparse approximate solutions to linear systems. SIAM Journal on Computing 24 (2):227–324. doi: 10.1137/S0097539792240406.
   Web of Science ®Google Scholar
• Ockuly, R., M. Weese, B. Smucker, D. J. Edwards, and L. Chang. 2017. Response surface experiments: A meta-analysis. Chemometrics and Intelligent Laboratory Systems 164:64–75. doi: 10.1016/j.chemolab.2017.03.009.
   Web of Science ®Google Scholar
• Phadke, M. S. 1986. Design optimization case studies. AT&T Technical Journal 65:51–68.
   Web of Science ®Google Scholar
• Phoa, F. K. H., Y. H. Pan, and H. Xu. 2009. Analysis of supersaturated designs via the Dantzig selector. Journal of Statistical Planning and Inference 139 (7):2362–72. doi: 10.1016/j.jspi.2008.10.023.
   Web of Science ®Google Scholar
• Schoen, E. D., and R. W. Mee. 2012. Two-level designs of strength 3 and up to 48 runs. Journal of the Royal Statistical Society: Series C (Applied Statistics) 61 (1):163–74. doi: 10.1111/j.1467-9876.2011.01013.x.
   Web of Science ®Google Scholar
• Schoen, E. D., N. Vo-Thanh, and P. Goos. 2017. Two-level orthogonal screening designs with 24, 28, 32, and 36 runs. Journal of the American Statistical Association 112 (519):1354–69. doi: 10.1080/01621459.2017.1279547.
   Web of Science ®Google Scholar
• Tibshirani, R. 1999. Regression shrinkage and selection via the LASSO. Journal of the Royal Statistical Society, Series B (52):267–88.
   Google Scholar
• Weese, M. L., B. J. Smucker, and D. J. Edwards. 2015. Searching for powerful supersaturated designs. Journal of Quality Technology 47 (1):66–84. doi: 10.1080/00224065.2015.11918107.
   Web of Science ®Google Scholar
• Westfall, P. H., S. S. Young, and D. K. J. Lin. 1998. Forward selection error control in the analysis of supersaturated designs. Statistica Sinica 8:101–17.
   Web of Science ®Google Scholar
• Williams, K. R. 1968. Designed experiments. Rubber Age (100):65–71.
   Google Scholar
• Wolters, M. A., and D. Bingham. 2011. Simulated annealing model search for subset selection in screening experiments. Technometrics 53 (3):225–37. doi: 10.1198/TECH.2011.08157.
   Web of Science ®Google Scholar
• Wu, C. F. J., and M. S. Hamada. 2009. Experiments: Planning, analysis, and optimization. 2nd ed. Hoboken, NJ: Wiley.
   Google Scholar
• Xu, H., S.-W. Cheng, and C. Wu. 2004. Optimal projective three-level designs for factor screening and interaction detection. Technometrics 46 (3):280–92. doi: 10.1198/004017004000000310.
   Web of Science ®Google Scholar
• Yamada, S., and D. K. J. Lin. 1999. Three-level supersaturated designs. Statistics & Probability Letters 45 (1):31–9. doi: 10.1016/S0167-7152(99)00038-3.
   Web of Science ®Google Scholar
• Yuan, M., and Y. Lin. 2006. Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 68 (1):49–67. doi: 10.1111/j.1467-9868.2005.00532.x.
   Web of Science ®Google Scholar