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

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), 467-484. (doi:10.1111/j.1467-9876.2009.00662.x).


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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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1111/j.1467-9876.2009.00662.x
ISSNs: 0035-9254 (print)
1467-9876 (electronic)
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
Subjects: H Social Sciences > HA Statistics
Divisions : University Structure - Pre August 2011 > School of Mathematics > Statistics
ePrint ID: 174551
Accepted Date and Publication Date:
September 2009Published
Date Deposited: 14 Feb 2011 15:09
Last Modified: 31 Mar 2016 13:32

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