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Automatic generation of generalised regular factorial designs

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Bailey_2017_CSDA_AutomaticGeneration_CC.pdf (507.7Kb)
Date
09/2017
Author
Kobilinsky, André
Monod, Hervé
Bailey, R. A.
Keywords
Backtrack algorithm
Design key
Hierarchy constraint
Ineligible factorial term
Model specification
Multi-stratum design
QA Mathematics
QA75 Electronic computers. Computer science
3rd-DAS
BDC
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Abstract
The R package planor enables the user to search for, and construct, factorial designs satisfying given conditions. The user specifies the factors and their numbers of levels, the factorial terms which are assumed to be non-zero, and the subset of those which are to be estimated. Both block and treatment factors can be allowed for, and they may have either fixed or random effects, as well as hierarchy relationships. The designs are generalised regular designs, which means that each one is constructed by using a design key and that the underlying theory is that of finite abelian groups. The main theoretical results and algorithms on which planor is based are developed and illustrated, with the emphasis on mathematical rather than programming details. Sections 3–5 are dedicated to the elementary case, when the numbers of levels of all factors are powers of the same prime. The ineligible factorial terms associated with users’ specifications are defined and it is shown how they can be used to search for a design key by a backtrack algorithm. Then the results are extended to the case when different primes are involved, by making use of the Sylow decomposition of finite abelian groups. The proposed approach provides a unified framework for a wide range of factorial designs.
Citation
Kobilinsky , A , Monod , H & Bailey , R A 2017 , ' Automatic generation of generalised regular factorial designs ' , Computational Statistics and Data Analysis , vol. 113 , pp. 311-329 . https://doi.org/10.1016/j.csda.2016.09.003
Publication
Computational Statistics and Data Analysis
Status
Peer reviewed
DOI
https://doi.org/10.1016/j.csda.2016.09.003
ISSN
0167-9473
Type
Journal article
Rights
© 2016 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Description
Open Access for this article was paid for by the French Research Agency (ANR), project Escapade (ANR-12-AGRO-0003).
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/11025

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