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A way of deriving ANOVA for mixed models and variance component models based on an historical representation of component sums of squares

Clarke, B.R. and Hogan, R. (2005) A way of deriving ANOVA for mixed models and variance component models based on an historical representation of component sums of squares. In: 55th Session of the International Statistical Institute, 6 - 12 April, Sydney, Australia.

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    Abstract

    A representation of sums of squares in two way layouts deriving from the history of the discussion of the introduction of the ANOVA method of R.A.Fisher by J.O.Irwin was introduced recently by the first listed author of this paper (see Clarke (2002)). Partitions of Helmert matrices and Kronecker products were used to easily derive the distribution theory of component sums of squares in fixed effect models to do with the two way layout. In this paper we show how the derivation of distribution theory to do with mixed models and variance component models can easily follow from the same representation.

    Publication Type: Conference Paper
    Murdoch Affiliation: School of Chemical and Mathematical Science
    Notes: Appears in Proceedings of the 55th International Statistical Institute Session, Sydney, 2005. The Hague, The Netherlands: ISI.
    URI: http://researchrepository.murdoch.edu.au/id/eprint/4843
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