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A Generalization of the GMANOVA‐Model
Author(s) -
Hecker H.
Publication year - 1987
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710290702
Subject(s) - wishart distribution , mathematics , generalization , extension (predicate logic) , covariance , linear model , estimator , covariance matrix , statistical hypothesis testing , matrix (chemical analysis) , generalized linear model , general linear model , multivariate analysis of variance , statistics , multivariate statistics , computer science , mathematical analysis , materials science , composite material , programming language
It is shown that in some experimental designs the MANOVA‐ and the GMANOVA‐model are too restrictive either to yield all hypothesis tests of interest or to reflect all known features of the design. An extension of these models is derived by relating the response vectors with the unknown model parameters by linear equations which may be completely different for each of the p components of the response vector and for each of the n independent vectors. For situations, in which a Wishart‐distributed estimator for the underlying common covariance matrix is attainable, a test for any s ‐dimensional linear hypothesis on the model parameters is derived.