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Analysis of data from non‐orthogonal multistratum designs in industrial experiments

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  • Steven G. Gilmour
  • Peter Goos

Abstract

Summary. Split‐plot and other multistratum structures are widely used in factorial and response surface experiments. Residual maximum likelihood (REML) and generalized least squares (GLS) estimation is seen as the state of the art method of data analysis for non‐orthogonal designs. We analyse data from an experiment that was run to study the effects of five process factors on the drying rate for freeze‐dried coffee and find that the main plot variance component is estimated to be 0. We show that this is a typical property of REML–GLS estimation in non‐orthogonal split‐plot designs with few main plots which is highly undesirable and can give misleading conclusions. Instead, we recommend a Bayesian analysis, using an informative prior distribution for the main plot variance component and implement this by using Markov chain Monte Carlo sampling. Paradoxically, the Bayesian analysis is less dependent on prior assumptions than the REML–GLS analysis. Bayesian analyses of the coffee freeze‐drying data give more realistic conclusions than REML–GLS analysis, providing support for our recommendation.

Suggested Citation

  • Steven G. Gilmour & Peter Goos, 2009. "Analysis of data from non‐orthogonal multistratum designs in industrial experiments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(4), pages 467-484, September.
    • Handle: RePEc:bla:jorssc:v:58:y:2009:i:4:p:467-484
    DOI: 10.1111/j.1467-9876.2009.00662.x
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    References listed on IDEAS

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    1. Russell D. Wolfinger & Robert E. Kass, 2000. "Nonconjugate Bayesian Analysis of Variance Component Models," Biometrics, The International Biometric Society, vol. 56(3), pages 768-774, September.
    2. D. R. Bingham & E. D. Schoen & R. R. Sitter, 2004. "Designing fractional factorial split‐plot experiments with few whole‐plot factors," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(2), pages 325-339, April.
    3. Ching-Shui Cheng & Pi-Wen Tsai, 2009. "Optimal two-level regular fractional factorial block and split-plot designs," Biometrika, Biometrika Trust, vol. 96(1), pages 83-93.
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    Cited by:

    1. Aiste Ruseckaite & Dennis Fok & Peter Goos, 2016. "Flexible Mixture-Amount Models for Business and Industry using Gaussian Processes," Tinbergen Institute Discussion Papers 16-075/III, Tinbergen Institute.
    2. Vasiliki Koutra & Steven G. Gilmour & Ben M. Parker & Andrew Mead, 2023. "Design of Agricultural Field Experiments Accounting for both Complex Blocking Structures and Network Effects," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(3), pages 526-548, September.
    3. Palhazi Cuervo, Daniel & Goos, Peter & Sörensen, Kenneth, 2017. "An algorithmic framework for generating optimal two-stratum experimental designs," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 224-249.

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