Étude d'un modèle factoriel d'analyse de la variance comme modèle linéaire généralisé
Revue de Statistique Appliquée, Volume 41 (1993) no. 2, p. 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},
     publisher = {Soci\'et\'e de Statistique de France},
     volume = {41},
     number = {2},
     year = {1993},
     pages = {43-57},
     zbl = {0972.62534},
     mrnumber = {1253515},
     language = {fr},
     url = {http://www.numdam.org/item/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, Volume 41 (1993) no. 2, pp. 43-57. http://www.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 94873 | Zbl 0092.36704

[2] Allen D.M. (1971). Mean square error of prediction as criterion selecting variables. Technometrics 13, pp. 469 | Zbl 0219.62013

[3] Allen D.M. (1974). The relationship between variable selection and data augmentation and method of prediction. Technometrics 16, pp. 125 | MR 343481 | Zbl 0286.62044

[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 830588 | Zbl 0587.62108

[5] Boik R.J. (1989). Reduced-rank models for interaction in unequally replicated two-way classifications. Journal of Multivariate Analysis 28, pp. 69 | MR 996985 | Zbl 0665.62071

[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 359192 | Zbl 0291.62087

[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 320622 | Zbl 0245.62068

[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 517440 | Zbl 0393.62019

[13] Gollob H.F. (1968) A statistical model wich combines features of factor analysis and anova techniques. Psychometrika 33, pp. 73 | MR 221658 | Zbl 0167.48601

[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 1137360 | Zbl 0702.62064

[15] Hegemann V.J., Johnson D.E. (1976) On analyzing two-way analysis of variance data with interaction. Technometrics 18, pp. 273 | Zbl 0342.62045

[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 400566 | Zbl 0254.62042

[17] Johnson D.E. (1976). Some new multiple comparison procedures for two-way anova model with interaction. Biometrics 32, pp. 929 | MR 445732 | Zbl 0343.62064

[18] Krishnaiah P.R., Yochmowitz M.G. (1980). Inference of interaction in two-way classification model. Handbook of Statistics, Vol. 1, pp. 973 | Zbl 0462.62054

[19] Mallows C.L. (1973). Some comments on Cp. Technometrics 15, pp. 661 | Zbl 0269.62061

[20] Mandel J. (1969). The partitioning of interaction in analysis of variance. Journal of Research - National Bureau of Standard, B.73 | MR 251862 | Zbl 0195.17404

[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 273747 | Zbl 0213.44201

[22] Mandel J. (1971). A new analysis of variance model for non-additive data. Technometrics 13, pp. 1 | Zbl 0216.48104

[23] Mathieu J.R. (1981). Tests of χ2 in the generalized linear model. Statistics Vol. 12, 4, pp. 509 | Zbl 0514.62080

[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 331644 | Zbl 0286.62031

[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 50245 | Zbl 0046.36105