The performances of Custom A-, D-, and I-optimal designs on non-standard second-order models are examined using the alphabetic A-, D-, and G-optimality efficiencies, as well as the Average Variance of Prediction. Designs of varying sizes are constructed with the help of JMP Pro 14 software and are customized for specified non-standard models, optimality criteria, prespecified experimental runs, and a specified range of input variables. The results reveal that Custom-A optimal designs perform generally better in terms of G-efficiency. They show high superiority to A-efficiency as the worst G-efficiency value of the created Custom-A optimal designs exceeds the best A-efficiency value of the designs, and also does well in terms of D-efficiency. Custom-D optimal designs perform generally best in terms of G-efficiency, as the worst G-efficiency value exceeds all A- and D-efficiency values. Custom-I optimal designs perform generally best in terms of G-efficiency as the worst G-efficiency value is better than the best A-efficiency value and performs generally better than the corresponding D-efficiency values. For the Average Variance of Prediction, Custom A- and I-optimal designs perform competitively well, with relatively low Average Variances of Prediction. On the contrary, the Average Variance of Prediction is generally larger for Custom-D optimal designs. Hence when seeking designs that minimize the variance of the predicted response, it suffices to construct Custom A-, D-, or I-optimal designs, with a preference for Custom-D optimal designs.
| Published in | American Journal of Theoretical and Applied Statistics (Volume 13, Issue 5) |
| DOI | 10.11648/j.ajtas.20241305.11 |
| Page(s) | 92-114 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Custom A-, D-, and I-optimal Designs, Non-Standard Second-Order Model, Average Variance of Prediction, D-, G-, A-efficiency
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APA Style
Paschal, I. M., Fortune, I. C. (2024). Performance Evaluation of Custom A-, D-, and I-Optimal Designs for Non-Standard Second-Order Models. American Journal of Theoretical and Applied Statistics, 13(5), 92-114. https://doi.org/10.11648/j.ajtas.20241305.11
ACS Style
Paschal, I. M.; Fortune, I. C. Performance Evaluation of Custom A-, D-, and I-Optimal Designs for Non-Standard Second-Order Models. Am. J. Theor. Appl. Stat. 2024, 13(5), 92-114. doi: 10.11648/j.ajtas.20241305.11
AMA Style
Paschal IM, Fortune IC. Performance Evaluation of Custom A-, D-, and I-Optimal Designs for Non-Standard Second-Order Models. Am J Theor Appl Stat. 2024;13(5):92-114. doi: 10.11648/j.ajtas.20241305.11
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Download@article{10.11648/j.ajtas.20241305.11,
author = {Iwundu Mary Paschal and Israel Chinomso Fortune},
title = {Performance Evaluation of Custom A-, D-, and I-Optimal Designs for Non-Standard Second-Order Models
},
journal = {American Journal of Theoretical and Applied Statistics},
volume = {13},
number = {5},
pages = {92-114},
doi = {10.11648/j.ajtas.20241305.11},
url = {https://doi.org/10.11648/j.ajtas.20241305.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20241305.11},
abstract = {The performances of Custom A-, D-, and I-optimal designs on non-standard second-order models are examined using the alphabetic A-, D-, and G-optimality efficiencies, as well as the Average Variance of Prediction. Designs of varying sizes are constructed with the help of JMP Pro 14 software and are customized for specified non-standard models, optimality criteria, prespecified experimental runs, and a specified range of input variables. The results reveal that Custom-A optimal designs perform generally better in terms of G-efficiency. They show high superiority to A-efficiency as the worst G-efficiency value of the created Custom-A optimal designs exceeds the best A-efficiency value of the designs, and also does well in terms of D-efficiency. Custom-D optimal designs perform generally best in terms of G-efficiency, as the worst G-efficiency value exceeds all A- and D-efficiency values. Custom-I optimal designs perform generally best in terms of G-efficiency as the worst G-efficiency value is better than the best A-efficiency value and performs generally better than the corresponding D-efficiency values. For the Average Variance of Prediction, Custom A- and I-optimal designs perform competitively well, with relatively low Average Variances of Prediction. On the contrary, the Average Variance of Prediction is generally larger for Custom-D optimal designs. Hence when seeking designs that minimize the variance of the predicted response, it suffices to construct Custom A-, D-, or I-optimal designs, with a preference for Custom-D optimal designs.
},
year = {2024}
}
TY - JOUR T1 - Performance Evaluation of Custom A-, D-, and I-Optimal Designs for Non-Standard Second-Order Models AU - Iwundu Mary Paschal AU - Israel Chinomso Fortune Y1 - 2024/09/26 PY - 2024 N1 - https://doi.org/10.11648/j.ajtas.20241305.11 DO - 10.11648/j.ajtas.20241305.11 T2 - American Journal of Theoretical and Applied Statistics JF - American Journal of Theoretical and Applied Statistics JO - American Journal of Theoretical and Applied Statistics SP - 92 EP - 114 PB - Science Publishing Group SN - 2326-9006 UR - https://doi.org/10.11648/j.ajtas.20241305.11 AB - The performances of Custom A-, D-, and I-optimal designs on non-standard second-order models are examined using the alphabetic A-, D-, and G-optimality efficiencies, as well as the Average Variance of Prediction. Designs of varying sizes are constructed with the help of JMP Pro 14 software and are customized for specified non-standard models, optimality criteria, prespecified experimental runs, and a specified range of input variables. The results reveal that Custom-A optimal designs perform generally better in terms of G-efficiency. They show high superiority to A-efficiency as the worst G-efficiency value of the created Custom-A optimal designs exceeds the best A-efficiency value of the designs, and also does well in terms of D-efficiency. Custom-D optimal designs perform generally best in terms of G-efficiency, as the worst G-efficiency value exceeds all A- and D-efficiency values. Custom-I optimal designs perform generally best in terms of G-efficiency as the worst G-efficiency value is better than the best A-efficiency value and performs generally better than the corresponding D-efficiency values. For the Average Variance of Prediction, Custom A- and I-optimal designs perform competitively well, with relatively low Average Variances of Prediction. On the contrary, the Average Variance of Prediction is generally larger for Custom-D optimal designs. Hence when seeking designs that minimize the variance of the predicted response, it suffices to construct Custom A-, D-, or I-optimal designs, with a preference for Custom-D optimal designs. VL - 13 IS - 5 ER -
Department of Mathematics and Statistics, University of Port Harcourt, Port Harcourt, Nigeria
Department of Mathematics and Statistics, University of Port Harcourt, Port Harcourt, Nigeria
