Title
Analysis of data from nonorthogonal multi-stratum designs
Author
Faculty/Department
Faculty of Applied Economics
Publication type
article
Publication
London ,
Subject
Mathematics
Source (journal)
Journal of the Royal Statistical Society: series C: applied statistics. - London
Volume/pages
58(2009) :4 , p. 467-484
ISSN
0035-9254
ISI
000268714000003
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
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 REMLGLS 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 REMLGLS analysis. Bayesian analyses of the coffee freeze-drying data give more realistic conclusions than REMLGLS analysis, providing support for our recommendation
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