Optimal Design of Blocked and Split-Plot Experiments for Fixed Effects and Variance Component Estimation
Abstract
In general, modeling data from blocked and split-plot response surface experiments requires the use of generalized least squares and the estimation of two variance components. The literature on the optimal design of blocked and split-plot response surface experiments, however, focuses entirely on the precise estimation of the fixed factor effects and completely ignores the necessity to estimate the variance components as well. To overcome this problem, we propose a new Bayesian optimal design criterion which focuses on both the variance components and the fixed effects. A novel feature of the criterion is that it incorporates prior information about the variance components through log-normal or beta prior distributions. The resulting designs allow for a more powerful statistical inference than traditional optimal designs. In our algorithm for generating optimal blocked and split-plot designs, we implement efficient quadrature approaches for the numerical approximation of the new optimal design criterion. Supplementary materials for this article are available online.
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The information matrix N in the existing composite criterion of Mylona et al. (2014) depends on the assumed response surface model through P and X, so using its determinant to quantify information on variance components is not model-robust.
“The main weakness of the composite D-optimality criterion of Mylona et al. (2014) is that the information matrix for the variance components, N, depends on the assumed response surface model through the matrices P and X.”
From Optimal Blocked and Split-Plot Designs Ensuring Precise Pure-Error Estimation of the Variance Components (2020) · cites this paper as Mylona et al. (2014)
The composite D-optimality criterion of Mylona et al. (2014) generally produces designs with insufficient replicates to allow for pure-error estimation of the variance components.
“Moreover, generally, the composite Doptimality criterion of Mylona et al. (2014) produces designs with insucient replicates to allow for pure-error estimation of the variance components.”
From Optimal Blocked and Split-Plot Designs Ensuring Precise Pure-Error Estimation of the Variance Components (2020) · cites this paper as Mylona et al. (2014)
Even the original composite criterion of Mylona et al. (2014) does not lead to inclusion of replicates in the 48-run blocked design.
“So, even the original composite criterion of Mylona et al. (2014), which takes into account the variance component estimation, does not lead to the inclusion of replicates in the design.”
From Optimal Blocked and Split-Plot Designs Ensuring Precise Pure-Error Estimation of the Variance Components (2020) · cites this paper as Mylona et al. (2014)
Cites
Searle, S. R., Casella, G., & McCulloch, C. E. (1992) · Wiley Series in Probability and Statistics · doi:10.1002/9780470316856 · Cited by 1,926 · see citing works
Analysis of Data from Non-Orthogonal Multistratum Designs in Industrial Experiments
Gilmour, S. G., & Goos, P. (2009) · Journal of the Royal Statistical Society Series C: Applied Statistics · doi:10.1111/j.1467-9876.2009.00662.x · Cited by 31 · see citing works
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Mylona, K., Gilmour, S. G., & Goos, P. (2020) · Technometrics · doi:10.1080/00401706.2019.1595153 · Cited by 13 · see citing works
Self-citation
- Authors
- Mylona, K., Goos, P., & Jones, B.
- Affiliations
- University of Southampton (GB)
- University of Antwerp (BE)
- SAS Institute (United States) (US)
- Venue
- Technometrics
- Publisher
- Informa UK Limited
- Published
- 2014-04-03
- Volume
- 56
- Issue
- 2
- Pages
- 132-144
- ISSN
- 0040-1706 (ISSN-L)
- 1537-2723
- OpenAlex
- W1991273308
- Cited by
- 31
- References
- 2
- Citations by year
- 2025: 3 · 2024: 4 · 2023: 1 · 2022: 5 · 2019: 4 · 2018: 3 · 2017: 4 · 2016: 3 · 2015: 4
- FWCI
- 3.19
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Technometrics (publishedVersion)
- ePrints Soton (University of Southampton) (acceptedVersion)
- Funders
- KU Leuven
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Optimal Experimental Design Methods
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Social Sciences › Decision Sciences › Management Science and Operations Research › Simulation Techniques and Applications
- Keywords
- optimal experimental design, split-plot design, response surface methodology, variance component estimation, fixed effects estimation, beta prior, generalized least squares, quadrature approximation
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