Reparametrisation of interest in non-uniform factorial designs

Linear Algebra and Its Applications

Volumn 321, Issue 1-3, 2000, Pages 239-280

  Kobilinsky, A ^a  

^a CEMAGREF   (France)

Author keywords

Analysis of variance; ANOVA; Block structure; Hierarchy; Lattice; Nesting factor; Orthogonal designs; Partially ordered set; POSET; Projective limit

Indexed keywords

EID: 0034366846     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(99)00237-2     Document Type: Article

References (24)

1. M. Almena, Y. Noël, A. Kobilinsky, A. Cepeda, Texture of Arzúa-Ulloa cheese: I. Evaluation before ripening using a fractional design, J. Dairy Res., submitted.
2. Addelman S. Orthogonal main effects plans for asymmetrical factorial experiments. Technometrics. 4:1962;21-46.
3. Azaïs J.M. Analyse de variance non-orthogonale L'exemple de SAS/GLM. Rev. Statist. Appl. 42(2):1994;27-41.
4. Bailey R.A. Discussion of paper by T. Tjur. Int. Statist. Rev. 52:1984;65-77.
5. Bailey R.A. Orthogonal partitions in designed experiments. Designs, Codes and Cryptography. 8:1996;45-77.
6. Bailey R.A., Praeger C.E., Rowley C.A., Speed T.P. Generalized wreath products of permutation groups. Proc. London Math. Soc. 3(47):1983;69-82.
7. N. Bourbaki, Elements de mathématiques, Théorie des ensembles, chapter III: Ensemble ordonnés, cardinaux, nombres entiers, Hermann, Paris, 1977.
8. Cliquet S., Durier C., Kobilinsky A. Principle of a fractional factorial design for qualitative and quantitative factors: Application to the production of Bradyrhizobium japonicum in culture media. Agronomie. 14:1994;569-587.
9. M. Drton, Analyse de variance dans des situations hiérarchiques non-equirépétées, Mémoire de DEA mathématiques appliquées, Labo. Stat. Proba., Univ. Paul Sabatier, Toulouse, 1999.
10. Kobilinsky A. Confounding in relation to duality of finite Abelian groups. Linear Algebra Appl. 70:1985;321-347.
11. A. Kobilinsky, Les plans factorials, in: J.J. Droesbeke, J. Fine, I. Saporta (Eds.), Plans d'expériences: applications à l'entreprise, TECHNIP, Paris, 1997, Ch. 3, pp. 69-209.
12. Kobilinsky A., Monod H. Juxtaposition of regular factorial designs and the complex linear model. Scand. J. Statist. 22(2):1995;223-254.
13. MINITAB Inc., Reference manual, US ISBN 0 92 5636 22 3 (1994).
14. Nelder J.A. A reformulation of linear models (with discussion). J.R. Statist. Soc. A. 140(1):1977;48-77.
15. H. Scheffe, The Analysis of Variance, Wiley, New York, 1959, 477 pp.
16. SAS Institute, Inc., The four types of estimable functions, in: SAS/STAT User's Guide, Reference Version 6, fourth edition, SAS Institute Inc., Cary, NC, USA, 1990.
17. SAS Institute, Inc., Tests of hypotheses in fixed-effects linear models, Technical Report R-101, Cary, NC, USA, 1978.
18. S.R. Searle, Linear Models for Unbalanced Data, Wiley, New York, 1987, 536 pp.
19. Searle S.R. Analysis of variance computing package output for unbalanced data from fixed-effects models with nested factors. Amer. Statist. 48(2):1994;148-153.
20. Speed T.P., Bailey R.A. Factorial dispersion models. Internat. Statist. Rev. 55(3):1987;261-277.
21. T.P. Speed, R.A. Bailey, On a class of association schemes derived from lattices of equivalence relations, in: P. Schultz, C.E. Praeger, R.P. Sullivan (Eds.), Algebraic Structures and Applications, Marcel-Dekker, New York, 1982.
22. S-Plus4, Guide to Statistics, MathSoft, Inc., Seattle, Wahington, 1997.
23. SPSS Inc., SPSS Advanced Statistics 7.5, SPSS Inc, Chicago, 1997.
24. Tjur T. Analysis of variance models in orthogonal designs (with discussion). Internat. Statist. Rev. 52:1984;33-65.