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Detection of interactions in experiments on large numbers of factors

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  • S. M. Lewis
  • A. M. Dean

Abstract

One of the main advantages of factorial experiments is the information that they can offer on interactions. When there are many factors to be studied, some or all of this information is often sacrificed to keep the size of an experiment economically feasible. Two strategies for group screening are presented for a large number of factors, over two stages of experimentation, with particular emphasis on the detection of interactions. One approach estimates only main effects at the first stage (classical group screening), whereas the other new method (interaction group screening) estimates both main effects and key two‐factor interactions at the first stage. Three criteria are used to guide the choice of screening technique, and also the size of the groups of factors for study in the first‐stage experiment. The criteria seek to minimize the expected total number of observations in the experiment, the probability that the size of the experiment exceeds a prespecified target and the proportion of active individual factorial effects which are not detected. To implement these criteria, results are derived on the relationship between the grouped and individual factorial effects, and the probability distributions of the numbers of grouped factors whose main effects or interactions are declared active at the first stage. Examples are used to illustrate the methodology, and some issues and open questions for the practical implementation of the results are discussed.

Suggested Citation

  • S. M. Lewis & A. M. Dean, 2001. "Detection of interactions in experiments on large numbers of factors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 633-672.
    • Handle: RePEc:bla:jorssb:v:63:y:2001:i:4:p:633-672
    DOI: 10.1111/1467-9868.00304
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    Cited by:

    1. Li, Peng & Zhao, Shengli & Zhang, Runchu, 2010. "A cluster analysis selection strategy for supersaturated designs," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1605-1612, June.
    2. Emanuele Borgonovo & Elmar Plischke & Giovanni Rabitti, 2022. "Interactions and computer experiments," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1274-1303, September.
    3. Michael Rosenblum & Ethan X. Fang & Han Liu, 2020. "Optimal, two‐stage, adaptive enrichment designs for randomized trials, using sparse linear programming," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 749-772, July.
    4. Wang, S. & Huang, G.H., 2014. "An integrated approach for water resources decision making under interactive and compound uncertainties," Omega, Elsevier, vol. 44(C), pages 32-40.
    5. Marley, Christopher J. & Woods, David C., 2010. "A comparison of design and model selection methods for supersaturated experiments," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3158-3167, December.
    6. Zhengping Liu & Wang Zhang & Hongxian Liu & Guohe Huang & Jiliang Zhen & Xin Qi, 2019. "Characterization of Renewable Energy Utilization Mode for Air-Environmental Quality Improvement through an Inexact Factorial Optimization Approach," Sustainability, MDPI, vol. 11(8), pages 1-19, April.
    7. Wang, S. & Huang, G.H., 2015. "A multi-level Taguchi-factorial two-stage stochastic programming approach for characterization of parameter uncertainties and their interactions: An application to water resources management," European Journal of Operational Research, Elsevier, vol. 240(2), pages 572-581.
    8. Dean, A. M. & Lewis, S. M., 2002. "Comparison of group screening strategies for factorial experiments," Computational Statistics & Data Analysis, Elsevier, vol. 39(3), pages 287-297, May.
    9. Last, Michael & Luta, Gheorghe & Orso, Alex & Porter, Adam & Young, Stan, 2008. "Pooled ANOVA," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5215-5228, August.
    10. Kleijnen, J.P.C., 2007. "Screening Experiments for Simulation : A Review," Discussion Paper 2007-21, Tilburg University, Center for Economic Research.
    11. Hong Wan & Bruce E. Ankenman & Barry L. Nelson, 2006. "Controlled Sequential Bifurcation: A New Factor-Screening Method for Discrete-Event Simulation," Operations Research, INFORMS, vol. 54(4), pages 743-755, August.

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