Abstract
Given an orthogonal model
an L model
is obtained, and the only restriction is the linear independency of the column vectors of matrix L. Special cases of the L models correspond to blockwise diagonal matrices L = D(L 1, . . . , L c ). In multiple regression designs this matrix will be of the form
with \({\check{{\bf X}}_j, j=1,\ldots,c}\) the model matrices of the individual regressions, while the original model will have fixed effects. In this way, we overcome the usual restriction of requiring all regressions to have the same model matrix.
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References
Fonseca M, Mexia JT, Zmyślony R (2007) Jordan algebras, generating pivot variables and ortogonal normal models. J Interdiscip Math 10(2): 305–326
Fonseca M, Mexia JT, Zmyślony R (2006) Binary operations on Jordan algebras and orthogonal normal models. Linear Algebra Appl 417: 75–86
Fonseca M, Mexia JT, Zmyślony R (2003) Estimators and tests for variance components in cross-nested orthogonal models. Discuss Math Probab Stat 23: 173–201
Lehmann EL, Casella G (1998) Theory of point estimation. Springer Texts in Statistics, New York
Lehmann EL (1997) Testing statistical hypotheses, Reprint of the 2nd edn. Wiley 1986, New York
Mexia JT (1990) Best linear unbiased estimates, duality of F tests and scheffé’s multiple comparison method in the presence of controlled heterocedasticity. Comp Stat Data Anal 10(3): 271–281
Mexia JT (1989) Simultaneous confidence intervals: generalization of the scheffé theorem. Trabalhos de Investigação N. 2, Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa
Mexia JT (1988) Estimable functions, duality of F tests and scheffé’s multiple comparison method. Trabalhos de investigação N. 1, Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa
Mexia JT (1987) Multi-treatment regression designs. Trabalhos de investigação N. 1, Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa
Montgomery DC (1997) Design and analysis of experiments, 5th edn. Willey, New York
Moreira EE, Mexia JT (2007) Multiple regression models with cross nested orthogonal base model. In: Proceedings of the 56th session of the ISI 2007—International Statistical Institute, Lisboa
Moreira EE, Ribeiro AB, Mateus EP, Mexia JT, Ottosen LM (2005) Regressional modeling of electrodialytic removal of Cu, Cr and As from CCA timber waste: application to sawdust. Wood Sci Technol 39(4): 291–309
Moreira EE, Ribeiro AB, Mateus EP, Mexia JT, Ottosen LM (2005) Regressional modeling of electrodialytic removal of Cu, Cr and As from CCA timber waste: application to wood chips. Biometri Lett 4(1): 11–25
Scheffé H (1959) The analysis of variance. Willey, New York
Seely J (1971) Quadratic subspaces and completeness. Ann Math Stat 42(2): 710–721
Silvey SD (1975) Statistical inference. Chapman and Hall, New York
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Moreira, E., Mexia, J.T., Fonseca, M. et al. L models and multiple regressions designs. Stat Papers 50, 869–885 (2009). https://doi.org/10.1007/s00362-009-0255-3
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DOI: https://doi.org/10.1007/s00362-009-0255-3