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

摘要

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.