Étude d'un modèle factoriel d'analyse de la variance comme modèle linéaire généralisé
Revue de Statistique Appliquée, Tome 41 (1993) no. 2, pp. 43-57. 
@article{RSA_1993__41_2_43_0,
     author = {Dorkenoo, K. M. M. and Mathieu, J.-R.},
     title = {\'Etude d'un mod\`ele factoriel d'analyse de la variance comme mod\`ele lin\'eaire g\'en\'eralis\'e},
     journal = {Revue de Statistique Appliqu\'ee},
     pages = {43--57},
     publisher = {Soci\'et\'e de Statistique de France},
     volume = {41},
     number = {2},
     year = {1993},
     mrnumber = {1253515},
     zbl = {0972.62534},
     language = {fr},
     url = {http://archive.numdam.org/item/RSA_1993__41_2_43_0/}
}
TY  - JOUR
AU  - Dorkenoo, K. M. M.
AU  - Mathieu, J.-R.
TI  - Étude d'un modèle factoriel d'analyse de la variance comme modèle linéaire généralisé
JO  - Revue de Statistique Appliquée
PY  - 1993
SP  - 43
EP  - 57
VL  - 41
IS  - 2
PB  - Société de Statistique de France
UR  - http://archive.numdam.org/item/RSA_1993__41_2_43_0/
LA  - fr
ID  - RSA_1993__41_2_43_0
ER  - 
%0 Journal Article
%A Dorkenoo, K. M. M.
%A Mathieu, J.-R.
%T Étude d'un modèle factoriel d'analyse de la variance comme modèle linéaire généralisé
%J Revue de Statistique Appliquée
%D 1993
%P 43-57
%V 41
%N 2
%I Société de Statistique de France
%U http://archive.numdam.org/item/RSA_1993__41_2_43_0/
%G fr
%F RSA_1993__41_2_43_0
Dorkenoo, K. M. M.; Mathieu, J.-R. Étude d'un modèle factoriel d'analyse de la variance comme modèle linéaire généralisé. Revue de Statistique Appliquée, Tome 41 (1993) no. 2, pp. 43-57. http://archive.numdam.org/item/RSA_1993__41_2_43_0/

[1] Aitchison J., Silvey S.D. (1958). Maximum likelihood estimation of parameters subject to restrictions. Annals of Math. Stat. 29, pp. 813 | MR | Zbl

[2] Allen D.M. (1971). Mean square error of prediction as criterion selecting variables. Technometrics 13, pp. 469 | Zbl

[3] Allen D.M. (1974). The relationship between variable selection and data augmentation and method of prediction. Technometrics 16, pp. 125 | MR | Zbl

[4] Boik R.J. (1986). Testing the rank of a matrix with applications to the analysis of interaction in ANOVA. J.A.S.A. 81, pp. 243 | MR | Zbl

[5] Boik R.J. (1989). Reduced-rank models for interaction in unequally replicated two-way classifications. Journal of Multivariate Analysis 28, pp. 69 | MR | Zbl

[6] Bradu D., Gabriel K.R. (1974). Simultaneous statistical inference on interactions in two-way analysis of variance. J.A.S.A. 68, pp. 428 | MR | Zbl

[7] Chadoeuf J., Denis J.B. (1991). Asymptotic variances for the multiplicative interaction model. Journal of Applied Statistics, Vol. 18, N° 3, pp. 331

[8] Corsten L.C.A., Van Eijsbergen A.C. (1972). Multiplicative effects in two-way analysis of variance. Statistica Neerlandica 26, pp. 61 | MR | Zbl

[9] Denis J.-B. (1991). Ajustements de modèles linéaires et bilinéaires sous contraintes linéaires avec données manquantes. R.S.A. Vol. 39 N° 2, pp. 5- 24 | Numdam

[10] Dorkenoo K.M.M. (1992). Etude de modèles avec interaction multiplicative en analyse de la variance. Thèse N.R. Toulouse-France

[11] Falguerolles A. De, Francis B.(1992). Algorithmic Approaches for Fitting Bilinear Models Computational Statistics, Physica-Verlag, pp. 77- 82

[121 Gabriel K.R. (1978). Least squares approximation of matrices by additive and multiplicative models. J.R.S.S. série B, 40, pp. 186 | MR | Zbl

[13] Gollob H.F. (1968) A statistical model wich combines features of factor analysis and anova techniques. Psychometrika 33, pp. 73 | MR | Zbl

[14] Goodman L.A., Haberman S. (1990). The analysis of non-additivity in two-way analysis of variance. J.A.S.A. 85, pp. 139 | MR | Zbl

[15] Hegemann V.J., Johnson D.E. (1976) On analyzing two-way analysis of variance data with interaction. Technometrics 18, pp. 273 | Zbl

[16] Johnson D.E., Graybill F.A. (1972). On analysis of a two-may model with interaction and no replication. J.A.S.A. 67, pp. 862 | MR | Zbl

[17] Johnson D.E. (1976). Some new multiple comparison procedures for two-way anova model with interaction. Biometrics 32, pp. 929 | MR | Zbl

[18] Krishnaiah P.R., Yochmowitz M.G. (1980). Inference of interaction in two-way classification model. Handbook of Statistics, Vol. 1, pp. 973 | Zbl

[19] Mallows C.L. (1973). Some comments on Cp. Technometrics 15, pp. 661 | Zbl

[20] Mandel J. (1969). The partitioning of interaction in analysis of variance. Journal of Research - National Bureau of Standard, B.73 | MR | Zbl

[21] Mandel J. (1970). Distribution of eigenvalues of covariance matrices of residuals in analysis of variance. Journal of Research - National Bureau of Standard, B.74, pp. 149 | MR | Zbl

[22] Mandel J. (1971). A new analysis of variance model for non-additive data. Technometrics 13, pp. 1 | Zbl

[23] Mathieu J.R. (1981). Tests of χ2 in the generalized linear model. Statistics Vol. 12, 4, pp. 509 | Zbl

[24] Nelder J.A., Wedderburn R.W.M. (1972). Generalized linear models. J.R.S.S. série A, 135, pp. 370

[25] Robert C. (1982). Propriétés optimales de certains estimateurs d'interaction en analyse de la variance. Thèse 3e cycle Grenoble, France

[26] Schuurmann F.J., Krischnaiah P.R., Chattopadhyay (1973). On the distributions of the ratios of the extreme roots to the trace of the Wishart matrix. Journal of Multivariate Analysis 3, pp. 445 | MR | Zbl

[27] Tukey J.W. (1949). One degree of freedom for non-additivity. Biometrics Vol. 5, pp. 232

[28] Williams E.J. (1952). The interpretation of interactions in factorials experiments. Biometrika 39, pp. 65 | MR | Zbl