R-optimal designs for second-order Scheffé model with qualitative factors

Ling Ling; Guanghui Li; Xiaoyuan Zhu; Chongqi Zhang; Ling Ling; Guanghui Li; Xiaoyuan Zhu; Chongqi Zhang

doi:10.3934/math.2022253

AIMS Mathematics

2022, Volume 7, Issue 3: 4540-4551. doi: 10.3934/math.2022253

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R-optimal designs for second-order Scheffé model with qualitative factors

1.
School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China
2.
School of Science, Kaili University, Kaili 556011, China

Received: 29 September 2021 Revised: 15 December 2021 Accepted: 19 December 2021 Published: 23 December 2021
MSC : 62K05, 62K99

Considering a mixture model with qualitative factors, the $ R $-optimal design problem is investigated when the levels of the qualitative factor interact with the mixture factors. In this paper, the conditions for $ R $-optimality of designs with mixture and qualitative factors are presented. General analytical expressions are also derived for the decision function under the $ R $-optimal designs, in order to verify that the resulting designs satisfy the general equivalence theorem. In addition, the relative efficiency of the $ R $-optimal design is discussed.
- mixture experiments,
- qualitative factors,
- $ R $-optimality,
- equivalence theorem
Citation: Ling Ling, Guanghui Li, Xiaoyuan Zhu, Chongqi Zhang. R-optimal designs for second-order Scheffé model with qualitative factors[J]. AIMS Mathematics, 2022, 7(3): 4540-4551. doi: 10.3934/math.2022253

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Abstract

Considering a mixture model with qualitative factors, the $ R $-optimal design problem is investigated when the levels of the qualitative factor interact with the mixture factors. In this paper, the conditions for $ R $-optimality of designs with mixture and qualitative factors are presented. General analytical expressions are also derived for the decision function under the $ R $-optimal designs, in order to verify that the resulting designs satisfy the general equivalence theorem. In addition, the relative efficiency of the $ R $-optimal design is discussed.

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