R-optimal designs for second-order Scheffé model with qualitative factors
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 analyt...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022253?viewType=HTML |
| _version_ | 1798025234571329536 |
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| author | Ling LingChongqi Zhang Guanghui Li Xiaoyuan Zhu Chongqi Zhang |
| author_facet | Ling LingChongqi Zhang Guanghui Li Xiaoyuan Zhu Chongqi Zhang |
| author_sort | Ling LingChongqi Zhang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T18:15:29Z |
| format | Article |
| id | doaj.art-9d1914b372b14bfdad8ce2dfe334e8b4 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-11T18:15:29Z |
| publishDate | 2022-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-9d1914b372b14bfdad8ce2dfe334e8b42022-12-22T04:09:56ZengAIMS PressAIMS Mathematics2473-69882022-01-01734540455110.3934/math.2022253R-optimal designs for second-order Scheffé model with qualitative factorsLing LingChongqi Zhang0Guanghui Li1Xiaoyuan Zhu 2Chongqi Zhang31. School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China2. School of Science, Kaili University, Kaili 556011, China1. School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China1. School of Economics and Statistics, Guangzhou University, Guangzhou 510006, ChinaConsidering 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.https://www.aimspress.com/article/doi/10.3934/math.2022253?viewType=HTMLmixture experimentsqualitative factorsr-optimalityequivalence theorem |
| spellingShingle | Ling LingChongqi Zhang Guanghui Li Xiaoyuan Zhu Chongqi Zhang R-optimal designs for second-order Scheffé model with qualitative factors AIMS Mathematics mixture experiments qualitative factors r-optimality equivalence theorem |
| title | R-optimal designs for second-order Scheffé model with qualitative factors |
| title_full | R-optimal designs for second-order Scheffé model with qualitative factors |
| title_fullStr | R-optimal designs for second-order Scheffé model with qualitative factors |
| title_full_unstemmed | R-optimal designs for second-order Scheffé model with qualitative factors |
| title_short | R-optimal designs for second-order Scheffé model with qualitative factors |
| title_sort | r optimal designs for second order scheffe model with qualitative factors |
| topic | mixture experiments qualitative factors r-optimality equivalence theorem |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022253?viewType=HTML |
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