Analysis of data from non-orthogonal multistratum designs in industrial experiments
Analysis of data from non-orthogonal multistratum designs in industrial experiments
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.
bayesian methods, coffee, effective degrees of freedom, freeze-drying, generalized least squares, hard-to-set factors, likelihood, markov chain monte carlo methods, response surface, residual maximum likelihood, split-plot experiment
467-484
Gilmour, Steven G.
984dbefa-893b-444d-9aa2-5953cd1c8b03
Goos, Peter
e85ac472-9312-4a77-ba77-b2f21b64f39e
September 2009
Gilmour, Steven G.
984dbefa-893b-444d-9aa2-5953cd1c8b03
Goos, Peter
e85ac472-9312-4a77-ba77-b2f21b64f39e
Gilmour, Steven G. and Goos, Peter
(2009)
Analysis of data from non-orthogonal multistratum designs in industrial experiments.
Journal of the Royal Statistical Society: Series C (Applied Statistics), 58 (4), .
(doi:10.1111/j.1467-9876.2009.00662.x).
Abstract
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.
This record has no associated files available for download.
More information
Published date: September 2009
Keywords:
bayesian methods, coffee, effective degrees of freedom, freeze-drying, generalized least squares, hard-to-set factors, likelihood, markov chain monte carlo methods, response surface, residual maximum likelihood, split-plot experiment
Organisations:
Statistics
Identifiers
Local EPrints ID: 174551
URI: http://eprints.soton.ac.uk/id/eprint/174551
ISSN: 0035-9254
PURE UUID: 6370de42-0ff3-4ec7-b838-434f49732599
Catalogue record
Date deposited: 14 Feb 2011 15:09
Last modified: 14 Mar 2024 02:34
Export record
Altmetrics
Contributors
Author:
Steven G. Gilmour
Author:
Peter Goos
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics