Construction of marginally coupled designs with mixed-level qualitative factors

Weiping Zhou; Wan He; Wei Wang; Shigui Huang; Weiping Zhou; Wan He; Wei Wang; Shigui Huang

doi:10.3934/math.20241610

AIMS Mathematics

2024, Volume 9, Issue 12: 33731-33755. doi: 10.3934/math.20241610

Previous Article Next Article

Research article Special Issues

Construction of marginally coupled designs with mixed-level qualitative factors

1.
School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China
2.
Center for Applied Mathematics of Guangxi (GUET), Guilin 541004, China
3.
Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation

Received: 25 May 2024 Revised: 24 October 2024 Accepted: 04 November 2024 Published: 29 November 2024
MSC : 62K05, 62K99

Marginally coupled designs (MCDs) with more economical run sizes than sliced Latin hypercube designs were widely used in computer experiments with both quantitative and qualitative factors. However, the construction of MCDs with mixed-level qualitative factors was still very challenging. We developed five algorithms to generate MCDs with mixed-level qualitative factors, which were very easy to implement. In some of the MCDs constructed in this paper, the quantitative factor designs have two- or higher-dimensional space-filling properties compared to the existing MCDs, where the qualitative factors were mixed-level. Moreover, the resulting MCDs had more flexible run sizes than the existing MCDs with mixed-level qualitative factors.
- resolvable orthogonal array,
- sliced Latin hypercube design,
- space-filling,
- stratification,
- difference scheme
Citation: Weiping Zhou, Wan He, Wei Wang, Shigui Huang. Construction of marginally coupled designs with mixed-level qualitative factors[J]. AIMS Mathematics, 2024, 9(12): 33731-33755. doi: 10.3934/math.20241610

Related Papers:

Abstract

Marginally coupled designs (MCDs) with more economical run sizes than sliced Latin hypercube designs were widely used in computer experiments with both quantitative and qualitative factors. However, the construction of MCDs with mixed-level qualitative factors was still very challenging. We developed five algorithms to generate MCDs with mixed-level qualitative factors, which were very easy to implement. In some of the MCDs constructed in this paper, the quantitative factor designs have two- or higher-dimensional space-filling properties compared to the existing MCDs, where the qualitative factors were mixed-level. Moreover, the resulting MCDs had more flexible run sizes than the existing MCDs with mixed-level qualitative factors.

References

[1]	K. T. Fang, R. Li, A. Sudjianto, Design and Modeling for Computer Experiments, CRC Press, 2006. https://doi.org/10.1201/9781420034899
[2]	T. J. Santner, B. J. Williams, W. I. Notz, The Design and Analysis of Computer Experiments, New York: Springer, 2013.
[3]	M. D. Morris, L. M. Moore, Design of computer experiments: Introduction and Background, Handbook of Design and Analysis of Experiments, 577 (2015), 591. https://doi.org/10.1201/b18619 doi: 10.1201/b18619
[4]	M. D. McKay, R. J. Beckman, W. J. Conover, A comparison of three methods for selecting values of input variables in the analysis of output from acomputer code, Technometrics, 21 (1979), 239–245. https://doi.org/10.1080/00401706.1979.10489755 doi: 10.1080/00401706.1979.10489755
[5]	J. J. Rawlinson, B. D. Furman, S. Li, T. M. Wright, D. L. Bartel, Retrieval, experimental, and computational assessment of the performance of total knee replacements, J. Orthop. Res., 24 (2006), 1384–1394. https://doi.org/10.1002/jor.20181 doi: 10.1002/jor.20181
[6]	P. Z. G. Qian, H. Wu, C. F. J. Wu, Gaussian process models for computer experiments with qualitative and quantitative factors, Technometrics, 50 (2008), 383–396. https://doi.org/10.1198/004017008000000262 doi: 10.1198/004017008000000262
[7]	G. Han, T. J. Santner, W. I. Notz, D. L. Bartel, Prediction for computer experiments having quantitative and qualitative input variables, Technometrics, 51 (2009), 278–288. https://doi.org/10.1198/tech.2009.07132 doi: 10.1198/tech.2009.07132
[8]	Q. Zhou, P. Z. G. Qian, S. Zhou, A simple approach to emulation for computer models with qualitative and quantitative factors, Technometrics, 53 (2011), 266–273. https://doi.org/10.1198/TECH.2011.10025 doi: 10.1198/TECH.2011.10025
[9]	X. Deng, C. D. Lin, K. W. Liu, R. K. Rowe, Additive Gaussian process for computer models with qualitative and quantitative factors, Technometrics, 59 (2017), 283–292. https://doi.org/10.1080/00401706.2016.1211554 doi: 10.1080/00401706.2016.1211554
[10]	P. Z. G. Qian, C. F. J. Wu, Sliced space- flling designs, Biometrika, 96 (2009), 945–956. https://doi.org/10.1093/biomet/asp044 doi: 10.1093/biomet/asp044
[11]	P. Z. G. Qian, Sliced Latin hypercube designs, J. Am. Stat. Assoc., 107 (2012), 393–399. https://doi.org/10.1080/01621459.2011.644132 doi: 10.1080/01621459.2011.644132
[12]	X. Deng, Y. Hung, C. D. Lin, Design for computer experiments with qualitative and quantitative factors, Stat. Sinica, 25 (2015), 1567–1581. http://dx.doi.org/10.5705/ss.2013.388 doi: 10.5705/ss.2013.388
[13]	Y. He, C. D. Lin, F. S. Sun, On construction of marginally coupled designs, Stat. Sinica, 27 (2017), 665–683. http://dx.doi.org/10.5705/ss.202015.0156 doi: 10.5705/ss.202015.0156
[14]	Y. He, C. D. Lin, F. S. Sun, B. J. Lv, Marginally coupled designs for two-level qualitative factors, J. Stat. Plan. Infer., 187 (2017), 103–108. https://doi.org/10.1016/j.jspi.2017.02.010 doi: 10.1016/j.jspi.2017.02.010
[15]	Y. He, C. D. Lin, F. S. Sun, Construction of marginally coupled designs by subspace theory, Bernoulli, 25 (2019), 2163–2182. https://doi.org/10.3150/18-BEJ1049 doi: 10.3150/18-BEJ1049
[16]	W. Zhou, J. Yang, M. Q. Liu, Construction of orthogonal marginally coupled designs, Stat. Pap., 62 (2021), 1795–1820. https://doi.org/10.1007/s00362-019-01156-1 doi: 10.1007/s00362-019-01156-1
[17]	F. Yang, C. D. Lin, Y. D. Zhou, Y. Z. He, Doubly coupled designs for computer experiments with both qualitative and quantitative factors, Stat. Sinica, 33 (2023), 1923–1942. https://doi.org/10.5705/ss.202020.0317 doi: 10.5705/ss.202020.0317
[18]	A. S. Hedayat, N. J. A. Sloane, J. Stufken, Orthogonal Arrays: Theory and Application, pringer, New York, 1999. https://doi.org/10.1007/978-1-4612-1478-6
[19]	M. E. Johnson, L. M. Moore, D. Ylvisaker, Minimax and maximin distance designs, J. Stat. Plan. Infer., 21 (1990), 131–148. https://doi.org/10.1016/0378-3758(90)90122-B doi: 10.1016/0378-3758(90)90122-B
[20]	F. J. Hickernell, A generalized discrepancy and quadrature error bound, Math. Comp., 67 (1998), 299–322. https://doi.org/10.1090/S0025-5718-98-00894-1 doi: 10.1090/S0025-5718-98-00894-1
[21]	F. J. Hickernell, Lattice rules: How well do they measure up? Random and Quasi-Random Point Sets, (1998), 106–166. New York, NY: Springer New York. https://doi.org/10.1007/978-1-4612-1702-2_3
[22]	M. D. Morris, T. J. Mitchell, Exploratory designs for computational experiments, J. Stat. Plan. Infer., 43 (1995), 381–402. https://doi.org/10.1016/0378-3758(94)00035-T doi: 10.1016/0378-3758(94)00035-T
[23]	S. Ba, W. R. Myers, W. A. Brenneman, Optimal sliced Latin hypercube designs, Technometrics, 57 (2015), 479–487. https://doi.org/10.1080/00401706.2014.957867 doi: 10.1080/00401706.2014.957867
[24]	F. Sun, B. Tang, A method of constructing space-filling orthogonal designs, J. Am. Stat. Assoc., 112 (2017), 683–689. https://doi.org/10.1080/01621459.2016.1159211 doi: 10.1080/01621459.2016.1159211

Reader Comments

Your name:*

Email:*
© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)